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A mathematical model for the optimization of adult education funding

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A mathematical model for the optimization of adult education funding
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Kimbrough, Ralph Bradley
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English
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x, 189 leaves : ; 29 cm.

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Adult education ( jstor )
Adult vocational education ( jstor )
County school districts ( jstor )
Funding ( jstor )
High school equivalency programs ( jstor )
High school students ( jstor )
Linear programming ( jstor )
Mathematical variables ( jstor )
School districts ( jstor )
Students ( jstor )
Dissertations, Academic -- Educational Leadership -- UF
Educational Leadership thesis, Ph. D
City of Tallahassee ( local )

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Thesis:
Thesis (Ph. D.)--University of Florida, 1994.
Bibliography:
Includes bibliographical references (leaves 182-188)
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Typescript.
General Note:
Vita.
Statement of Responsibility:
by Ralph Bradley Kimbrough, Jr.

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University of Florida
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Full Text
A MATHEMATICAL MODEL FOR THE OPTIMIZATION OF ADULT
EDUCATION FUNDING
By
RALPH BRADLEY KIMBROUGH, JR.
A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL
OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY
UNIVERSITY OF FLORIDA
1994


I dedicate this study to my wife Nancy N. Kimbrough; my daughter, Rachel L. Kimbrough; and son, Andrew R. Kimbrough. Because of their love and support this dissertation was made possible.


ACKNOWLEDGMENTS
I would like to thank the members of by doctoral committee for their advice and assistance. I would like to thank Dr. David Honeyman for contributing his expertise on educational finance for the school districts. Furthermore, Dr. Honeyman's detailed reading and editing of this dissertation was greatly appreciated. I would like to thank Dr. James Wattenbarger for his contribution of knowledge of the funding methods used by the community colleges. Dr. Wattenbarger's counseling and moral support made this dissertation possible. I would like to thank Dr. Eugene Todd for his assistance .in the areas such as school assessment and evaluation. Dr. Todd was also helpful in contributing literature concerning the problems experienced by the schools in educating disadvantaged students. Dr. Arthur Sandeen was continually helpful in giving advice during doctoral committee meetings. Dr. David Miller was essential in checking and evaluating the statistical results of the multiple regression analysis.
In addition to my committee members, I would like to thank Dr. William Hager, codirector of the Center for Applied Optimization for the Department of Mathematics at the University of Florida. His review of this dissertation and


the models was invaluable to the determination of my conclusion. Dr. William Hager's advice to continue researching the final model for the GED exam was inspiring and fostered my enthusiasm for future research.
I would also like to thank Ms. Patricia McGee and Ms. Barbara Smerage for reviewing this dissertation for editorial errors and making suggestions for its presentation. Their continued assistance was greatly appreciated.
Finally, I would like to thank my family members for their continued support of my completion of this dissertation. I would like to thank my father, Dr. Ralph Kimbrough, Sr., for his advice on dissertation topics and my mother, Gladys Kimbrough, for her support of this endeavor. My wife, Nancy, was very supportive, and her love was a major factor in helping me to complete this dissertation. Finally, my two children must take credit for easing my tension during the more difficult times with their love and affection.
iv


TABLE OF CONTENTS
Page
ACKNOWLEDGMENTS......................................... iii
ABSTRACT................................................ viii
CHAPTERS
1 BACKGROUND OF THE STUDY.......................... 1
Introduction..................................... 1
Definition of Optimization....................... 2
Background of the Problem........................ 2
The Current Status of Adult Education Funding
in Florida..................................... 7
The Florida Education Finance Program (FEFP)..... 8
Community College Program Fund (CCPF)............ 10
Other Funding Methods for Adult Education........ 14
The Purpose of the Study......................... 14
Need for the Study............................... 16
Definition of Terms.............................. 18
Limitations and Delimitations.................... 19
Organization of the Study by Chapters............ 20
2 REVIEW OF THE LITERATURE......................... 21
Introduction..................................... 21
The Need for Adult Education..................... 21
Adult Education: An International View........... 23
Adult Education in the United States............. 25
State Responsibilities Under the Adult
Education Act.................................. 27
Inequalities of Support in Adult Education....... 29
Benefits of Adult Education...................... 31
Research that Supports the Funding of Adult
Education...................................... 33
Critique of the Studies Performed in Adult
Education...................................... 41
Problems in Determining the Sociological
Benefits of Adult Education.................... 44
The Benefits of Consumer Education............... 45
Arguments Against Funding Adult Education........ 47
v


Research Findings Not in Favor of Funding
Adult Education................................ 50
Quantitative Methods Used for Evaluating
Educational Programs........................... 52
Chapter Summary.................................. 57
3 PROCEDURES....................................... 60
Introduction..................................... 60
Procedure of this Study.......................... 60
Population for the Study......................... 67
Research Design.................................. 68
Statement of Variables........................... 71
Collection of Data............................... 78
Analysis of Data................................. 79
Development of Vectors to Determine
Effects and Magnitude of Effects............... 86
4 PRESENTATION OF DATA............................. 88
Introduction..................................... 88
Analysis of Data................................. 88
Discussion of Administrative and Instructional
Variables...................................... 92
Qualitative Reasons for Variable Selection....... 93
Quantitative Reasons for Variable Selection...... 96
Evaluation of the Selection Procedures and
Their Results.................................. 104
Determination of Significance of Variables in
Model.......................................... 108
Tests of Partial Correlations of the Model's
Variables...................................... Ill
Problems of Determining Funding.................. 112
Test of Partial Correlations and Analysis
of Final Model................................. 116
Results of the Solution of Simultaneous
Equations...................................... 120
Summary.......................................... 122
5 CONCLUSIONS AND RECOMMENDATIONS.................. 123
Introduction..................................... 123
Problems and Limitations of the Study............ 124
Concluding Remarks Concerning the
Mathematical Model............................. 129
Discussion of the Variables of the
Cost Model..................................... 131
Conclusions and Remarks.......................... 133
Suggestions for Further Research................. 134
Final Conclusion................................. 136
vi


APPENDICES
ft
A PRESENTATION OF RAW DATA......................... 137
B LISTS OF LOCAL EDUCATION AGENCIES................ 168
C ANALYSIS OF COOK'S D PRINTOUT.................... 172
D LOCAL EDUCATION AGENCIES NOT INCLUDED ON
FEDERAL REPORT................................. 181
REFERENCES............................................... 182
BIOGRAPHICAL SKETCH...................................... 189
I t
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Abstract of Dissertation Presented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy
A MATHEMATICAL MODEL FOR THE OPTIMIZATION OF ADULT
EDUCATION FUNDING
By
Ralph Bradley Kimbrough, Jr.
December 1994
Chairman: James L. Wattenbarger
Cochair: David S. Honeyman
Major Department: Educational Leadership
The purpose of this study was to develop and analyze a
mathematical model to optimize the funding for adult
education programs in Florida through the simultaneous
solution of linear and nonlinear formulations. Multiple
regression techniques were used to determine the mathematical
model. Forward selection, backward elimination, and stepwise
techniques were used to determine the variables to be
included in the model. For purposes of this study, data
items used in these formulations were evaluated using
statistical techniques to determine their relevancy and
validity.
One of the major problems of education is the reality of declining resources. The same forces affecting public education in pre-kindergarten through public elementary and
I
Vlll


secondary programs also affect adult education programs. Since most states fund adult education programs with the funding allocated for pre-K through 12th grade, the growing needs for funds, combined with declining resources in kindergarten through 12th grade, will threaten adult education funding and may threaten the very existence of adult education programs. Thus, there is a need to allocate adult education funding in a more efficient and effective manner.
Twelve variables were used in the multiple regression analysis. Of these 12 variables, the variables that had the greatest effect on student success with the GED and the Adult High School Diploma were the state's expenditures on teacher salaries, the costs of other support services, and the costs of materials and supplies. Furthermore, three variables were found to be significant statistically to the increase in cost of adult education. These variables were the percentage of full-time teachers, the percentage of students involved in other educational programs, and percentage of students who resided in correctional facilities. Since the variables which affected success on the GED and the Adult High School Diploma did not coincide with the variables that affected total costs of adult education, a specific solution using simultaneous equations was not meaningful or possible. However, the study did conclude that the use of the formula developed from success on the GED and the Adult High School Diploma may be useful for determining the proper allocation


of funds. Future studies may be helpful in determining mathematical models could be used to determine cost allocations.
x


CHAPTER 1 BACKGROUND OF THE STUDY
Introduction
One of the major problems of education is the reality of declining resources. State legislatures across the country are under increasing pressure not to raise taxes. State revenues generated by either income taxes, sales taxes, property taxes, or other personal or intangible property taxes will not be enough to meet the increasing costs of state services, including public education. Thus, the movement toward obtaining more education for less money has now become an important issue in many states. In order to meet the growing needs of public education, state legislatures are forced into the thoughtful allocation of tax dollars for education in the most efficient and cost-effective manner.
The same forces affecting public education in pre-kindergarten through public elementary and secondary programs also affect adult education programs. Since most states fund adult education programs with the funding allocated for kindergarten through 12th grade, the growing needs for funds, combined with declining resources in kindergarten through 12th grade, threaten adult education funding and may threaten
1


2
the very existence of adult education programs. Thus, there is a need to allocate adult education funding in a more efficient and effective manner.
Definition of Optimization The definition of optimization used in this study is concentrated on making adult education funding as effective and efficient as possible. According to Webster's Third New International Dictionary, optimize means "to make as perfect, effective, or functional as possible" (p. 1585) Furthermore, the term optimization means "an act of optimizing or the fact of being optimized" (p. 1585) Thus, for this study, the term optimization will mean the act of optimizing adult education funding to make the funding both efficient and effective. In other words, if more monies need to be spent on certain areas, or groups of individuals to make adult education more effective, then the mathematical model will be used to address the needs for additional funding in these areas or groups. Therefore, the model developed herein emphasizes the need for effectiveness and functionality rather than complete efficiency.
Background of the Problem
Florida will be adversely affected by the reality of declining state revenues and a growing and increasingly diverse student population. According to Natale (1992, October),


3
By 2010, if the demographers are right, one-third of all the children in the United States will live in just four states--California, Florida, Texas, and New York. Those four statesaccording to A Demographic Look at Tomorrow, a report that extrapolates from U.S. Census information--will see significant increases in the number of children in the next 20 years, mostly because of increases in what is now considered minority population. ... In states with increases in the number of youths, the gains are largely attributable to gains in minority populations. And those increases point up another phenomenon of the future as well: Traditional minority populations--blacks, Hispanics, Asians--will become majority populations in some states. In California, Texas, and Florida, more than half of the youth population will be nonwhite well before the year 2010. (p. 24)
Although the growth in minority population in the public schools appears evident, the immediate need to train and teach the parents of these school children is even more critical. According to Edwards and Young (1992, September), "Recent hopes for successfully launching U.S. children into the 21st century have been pinned on reclaiming a part of our past--the involvement of parents as partners in the education of their children. The importance of parent involvement in children's schooling has been a persistent theme in the research and school reform efforts of the last three decades" (pp. 73-74) For example, Bronfenbrenner (1979) in The Ecology of Human Development: Experiments bv Nature and Design and Henderson (1987) in The Evidence Continues to
Grow: Parent Involvement Improves Student Achievement emphasized the importance of parental involvement in improving student performance. Thus the need to educate parents so they can help their children in school is evident.


4
Edwards and Young (1992, September) concluded, "Studies [Epstein, 1987; Heath & McLaughlin, April, 1987] point to higher student achievement when parents participate in school activities, monitor children's homework, and otherwise support the extension into the home of the work and values of the school" (p. 74).
The immediate need for English as a second language is evident in many counties in Florida. For example, one estimate lists 50 different languages spoken in Seminole County alone. Even more languages are spoken in Dade County. The realization that education of parents may have a direct influence on the success of their children further supports the thesis that more funding is needed for adult education in Florida.
Wood and Honeyman (1992) concurred with Natale (1992) that the changing diversity of Florida's school population will be a major factor in the growing needs for public education in Florida. Although Florida's growth rate recently has slowed, Florida's population continues to climb. According to Wood and Honeyman (1992), "The state [Florida] enjoys the uniqueness of being the fourth largest state in the nation as well as one of the fastest growing states. Florida is projected to be the third most populous state by the year 2000" (p. 170). The financial burden on such a fast-growing state is also being experienced by other states. Natale (1992) wrote, "For schools, the


5
implications of a student boom are severe. 'It's a terrible time for states to be in a state of terribly rapid growth,1 Hodgkinson [1988] says. 'With the deficit situation the way it is, there is no way for states to pay for [the growth]'" (p. 24).
Without new tax revenues Florida will be forced to reduce the extent of public education. Although funding for Florida's public schools has improved in recent years, the growth in population and language diversity of students may outstrip the availability of needed funds for education. According to Wood and Honeyman (1992), "During the period 1970 to 1973, several studies were conducted on Florida's finance system. Given the changes that were occurring, including growth and development in the southern half of the state, the legislature adopted recommendations to guarantee that students have access to an equal educational program" (p. 165).
This new program was titled the Florida Education Finance Program (FEFP). The standard for computing the state allocation was changed from a formula-based-upon-an-instructional-unit method to a weighted-average-per-pupil calculation based on cost calculations. Weights were determined for 26 student programs. Because adult education was funded in the same way as other public education programs, funding of adult education was governed by the assigned weights of the FEFP. Over the years, the Florida


6
legislature has changed the formula to reflect changes in population demographics. For example, in 1974 a cost-of-living differential was added. Although the state increased funding in real dollars during this period, funding declined during the 1970s. Wood and Honeyman (1992) wrote,
While approximately $93 million in new money was made available to school districts, rising inflation and rapidly increasing costs in the state resulted in a $78 per pupil increase in constant dollars. Per pupil revenue in constant dollars declined in 1975 as the legislature limited school boards to 8 mills total and included, but never funded, a sparsity adjustment factor. (Johns, 1975) (p. 166)
Further stresses on educational funding were experienced in the state during the 1980s. Because of political pressure to initiate programs to reduce taxes, the legislature lowered the required millage rate from 6.4 mills to 5.15 mills and also lowered the cap on total millage allowed to 6.75 (Wood and Honeyman, 1992, p. 167). Furthermore, the homestead exemption for property taxes was raised to $25,000 in 1980-1981. The legislature attempted to cover these revenue losses with an additional levy of 2 mills for capital outlay expenditures. Wood and Honeyman (1992) stated,
During the period 1981 to 1990, Florida experienced incredible growth and development. To promote educational reform and assist school districts with increasing pressure for special populations, several programs were enacted by the legislature. Program cost factors and weights continued as the heart of the FEFP. By 1989 the number of cost calculations had grown from the original 2 6 (in 1973) to 41. The growth in program classifications was the result of increased need to address special education, special need, and at risk student populations, (p. 167)


7
Other improvement programs were the Dropout Prevention Act of
1986 (which indirectly affects adult education), PRIME, First
Start, and other programs deemed necessary for preventing the
loss of at-risk kids (Wood and Honeyman, 1992, p. 167).
Unfortunately, these programs did not eliminate the need for
adult education.
Although the legislature addressed the need for more
programs in pre-K through 12, the area of adult education was
practically ignored. As a matter of fact, stringent
enrollment caps on funding adult education have been in place
since 1986. Without adequate increases in funding, adult
education programs will not be able to meet Florida's future
educational challenges.
The Current Status of Adult Education
Funding in Florida
The review of research about the funding of adult
education revealed that a comprehensive formula that
optimizes costs for state and local funding of adult
education has not been researched. Instead, states use a
variety of funding methods already used in pre-K through 12
funding and for the community colleges to determine how funds
are to be allocated for adult education. A majority of
states use the foundation method for funding pre-K through 12
(Thompson, Wood, & Honeyman, 1994). According to the staff
of the National Education Association Search (unpublished
evaluative report, 1987), the methods currently used for
pre-K through 12 education funding may be classified as flat


8
grants, minimum foundation, full state funding, and capacity equalization programs. Within capacity equalization programs are the percentage equalization (state aid ratio), guaranteed tax base, and guaranteed tax yield formulas. The effects of these funding formulas are varied and may or may not directly influence adult education funding. For instance, because much of the allocation of state funding for adult education may be finalized at the district level, the final funding for adult education may be decided at the local level and based on assessed needs, not on any particular formulas. There are several cases where the school district makes up shortfalls in funding for as much as 50% of the expenditures of the local district (Florida Department of Education, 1992-1993). These shortfalls may reflect a continual lack of adequate
funding of adult education.
The Florida Education Finance Program (FEFP) The current funding system for adult education in Florida's school districts is based upon predetermined weights for funding Adult Basic Education and Secondary Education and for educating the disabled (Florida Department of Education, 1993, May, p. 12). According to the 1993-1994 Florida Education Finance Program: Statistical Report, adult education funding was included in Group 3, which encompasses Adult Job Preparatory Vocational, Adult Supplemental Vocational, and Adult General programs. Because of fiscal priorities, an enrollment cap was established for adult


9
education. State funding is supplemented by student fees and tuition. According to the statistical report of the staff of the Florida Department of Education (1993, May), "Students who are enrolled in adult general and vocational adult programs who are reported for funding through the Florida Education Finance Programs must be charged tuition fees except those who are exempted by law" (p. 17). State statute (F.S. 239.117) provides a list of those students who are exempted from tuition or fees.
In addition to the current group status of adult education, certain weight factors are used to calculate "weighted FTE." According to the staff of the Florida Department of Education's Division of Public Schools (May 1993), "Multiplying the FTE students for a program by its cost factor produces 'weighted FTE'" (p. 12). Currently, the weight factors for adult education are .721 for Adult Basic Skills, .758 for Adult Secondary Education, and 1.140 for Adult Disabled. By multiplying the program cost factors by the FTE, the state determines the weighted FTE students. This figure of weighted FTE students is then multiplied by the base student allocation (currently $2,501.05 per student) and the district cost factor. The product of these multiplications is then added to legislative-approved adjustments. For instance, the district might obtain additional supplements, such as the declining enrollment


10
supplements, sparsity supplements, and the hold harmless adjustment.
The present system of funding does not allow for increments based upon the meeting of goals or performance targets. Alamprese and Koloski (1992, March) mentioned the need for adult education programs to be given incentives. Because of the scarcity of resources, recent legislative proposals have centered upon the use of performance-based funding (PBF), which has been defined as paying for production rather than process. In education, competency based programs, such as those in adult and vocational education, were easily adapted to PBF, resulting in payment for student outcomes rather than "seat time." Student outcomes were typically measured as a percentage of program completers and job placements. Enrollments were considered positive student outcomes when recruiting certain populations, such as minorities or the disadvantaged. Although the definition of performance-based funding has been defined rather loosely, the possibility of conforming to such a funding model has been a major topic of discussion in adult education circles.
Community College Program Fund (CCPF) Since 6% to 10% of the funding for adult education is provided by the community colleges, a review of the community college funding program is necessary. The Community College Program Fund (CCPF) is determined by following eight steps,


11
which become components of the funding formula used to fund the community colleges. These steps are as follows:
Base + Cost to Continue + Enrollment Workload + Operating Cost of New Facilities + Improved Programs + New Programs = Total CCPF Student Fee Revenues = State Funds CCPF.
In order to understand the funding process, one must review the meaning behind each step in the formula. The first step includes the base funding for the community colleges, and subsequent steps are added or subtracted from this base funding. First, the total state general revenue, lottery funds, and calculated student fees are included in the base funding for each college in the current fiscal year. Step two relates to the determination of the cost to continue current programs. The cost to continue current programs is added to the base. According to the The Fact Book 1991-92 (Florida Department of Education, 1992, Fall), "Using the amount of funds expended by each college in each of several expenditure categories, the price level guidelines are applied to these base amounts to determine the additional funds required to maintain the colleges1 existing programs at their present level" (p. 91). Funds are then allocated to cost categories, such as salaries, general expenditures, utility costs, and operating capital outlay expenditures. Each of these sums is multiplied by the price guideline amount, and any additional funding required by each college


is determined. Even though all colleges are subject to the same guidelines, the resulting increases may not be the same because the colleges spend money differently.
Step three relates to the identification of workload changes. According the The Fact Book 1991-92, "The statutes specify that the prior year enrollment shall be the basis of the assigned current enrollment" (p. 91). Last year's enrollment may be a determining factor in funding, even under conditions of high-growth rates. Step four was stated in The Fact Book 1991-92: "When a college adds a new building to its physical plant, additional operating costs are experienced. Based upon the specific college's average cost of operation per square foot, funding is appropriated for each new building's additional space to cover the cost of maintenance and operation" (p. 91). Thus any additional buildings that have been added to campuses will be reflected in increases in base funding.
Step five refers to funding for improving programs. According to The Fact Book 1991-92, "For programs for which the Legislature has previously provided funding, additional funds may be earmarked to improve or expand their delivery. Examples might be funding for the College Level Academic Skills Test, the Gordon Rule, and other such items which have been rolled into the program fund" (p. 91). Therefore, additional funds for program improvement are added to the base. Step six allows for additional funding to be added to


the base for new programs. According to The Fact Book 1991-92,
First time funding for systemwide programs specifically earmarked by the Legislature and which are to be rolled into the CCPF lump sum may be provided. Examples might include funding insurance rate increases or student advisement programs. Each college would receive a share of the total increased funds based on some distribution rationale. This might be FTE, headcount or other factors, (p. 92)
The seventh step is the process of adding the increases and decreases of steps 1 through 6 for each college and therefore determining the new funding base. Thus, each college will have a new total CCPF funding base. The Fact Book 1991-92 states, "Because factors other than FTE may be involved in distributing portions of the increased funding for all issues, it is to be expected that the increase per FTE and the overall percentage increase will probably not be the same for each college" (p. 92).
The final and eighth step is used to adjust the total CCPF funding base of each college for the calculation of student fees. Student fee collections are calculated by multiplying the assigned FTE enrollment by the standard fee rates. Once the student fees have been calculated, these fees are deducted from the total CCPF for each college to determine the state funding portion.
Thus, the state CCPF (Florida Department of Education, 1992, Fall) is clarified as the "lump sum appropriation for each college [that] is allocated to each local Board of Trustees to develop an operating budget for the college"


(p. 92) In conclusion, each board of each college may establish priorities for programs and expenditures to reflect the local needs or to satisfy the intent of the legislature expressed in the proviso language of the appropriations act.
Other Funding Methods for Adult Education
The rest of the funding for adult education originates from federal and state grants. Federal grants make up approximately 3% of the total funding for adult education in Florida. Even though this percentage is small, the need to examine the influence of federal funding is realized in the large number of small organizations funded by federal grants, including Hispanic Unity; Action, Inc.; and others. Because of the success of these organizations, it was necessary to include the funding for these organizations in this study.
The Purpose of the Study
The purpose of this study was to develop and analyze a mathematical model to optimize the funding for adult education programs in Florida. Since local districts may spend adult education funds in pre-K through 12 programs or may actually make up deficits in adult education funding, there is no formal method to determine the optimal funding needed in adult education. Therefore, an optimal funding model needs to be developed, subject to the variables affecting adult education and the budgetary constraints, and should be based on current funding (expenditures) for the 1992-1993 school year. An additional aspect of the study was


15
to determine relationships among the funding amounts estimated by the formula and student performance in the GED and ABE adult education programs in Florida. The research was designed to address the following subproblems:
1. A proposed, conceptually based formula was developed for the total optimal state funding of adult education programs for Florida.
2. The conceptually based formula was based on a production function that described the input-output relationship between selected variables.
3. The formula was used to determine the optimal combination of inputs to maximize output, subject to the budget and other constraints.
4. The formula was used to determine the optimal combination of inputs to maximize output, subject to certain constraints and given increments in the budget constraint.
Currently, the Florida Board of Education has experimented with several simulations of performance-based budgets. Because of the federally mandated requirements for adult education, these simulations include weights based upon the success of recruiting from target populations, status of students recruited, and activities provided by the adult education centers. The simulations do not attempt to look at the needs of the community that the center is attempting to serve. Furthermore, there has not been an attempt to optimize costs incurred in adult education. The methodology of this study included factors that were stated by the adult education administrators during personal interviews.
An alternative funding formula will have to optimize costs and include weights or factors relating to the success


16
of the center in accomplishing the goals of the adult
education program. For example, as discussed previously, the
problem of the current formula is that there is no measure
concerning how successful the adult education center is in
educating for the GED, ABE, or in educating a special student
in the student's special programs. Such factors as student
status, target populations, and center activities were
included in the different weighted factors.
Need for the Study
The factors associated with estimating costs for adult
learners are uniquely atypical (different) from funding
programs for children and youths in grades K-12. Therefore,
the attendance-based funding methods that are so common among
K-12 funding are not appropriate for adult education funding.
For example, Rose (1990) stated,
The attendance basis for distributing money has been problematical. It can contribute to the deterioration of standards of student performance. Students, particularly mandated students, know that they can sit around doing very little, take long unofficial breaks, and basically not be there except in body, if that is what they choose. As long as they are physically "attending," they will be carried on the books for funding purposes, (p. 127)
Furthermore, many single parents and minimally able students may benefit from attending a sheltered workshop environment without having to contribute to the adult daycare population. Finally, Rose concluded, "Another problem with attendance-based funding is that [it] can lead to discouraging the offering of desperately needed additional help to students,


17
if this help comes from outside agencies" (p. 127). Rickards (1983, September) would agree with Rose's discussion of adult education funding. According to the ERIC staff, which
paraphrased Rickards,
The need for the program was determined because it was felt that the existing formula for disbursing adult basic and high school completion funds in Utah and other states (based on class membership and attendance) was burdensome to rural school districts and inappropriate to the needs and preferences of the adult learner. Learning options available for adult students included traditional classes, home study, competency testing, on-the-job training, computer-assisted instruction, audio-tutorial plans, televised instruction, performance-based instruction, and one-to-one tutoring. The program was found to be successful in that some adults benefitted by each approach, and all the approaches were at least as effective as traditional' classroom instruction. The
program was also cost efficient and, although time-consuming to administer, possible to administer on the local level, (pp. 14-15)
As a result of his study, Rickards (1983, September) recommended that Utah change its methods of disbursing funds
for adult basic education and high school education.
Moreover, no study was found in the literature that
approached adult education from a comprehensive and totally
funded process. Finally, the need for the optimization of
school costs was best described by McAfee (1972) :
It is hardly to be questioned that studies confined to the practical applications of models should be energetically pursued to provide, eventually, a firmer basis than now exists for dealing with broad questions of educational policy. Mathematical models, such as was developed in this study, allow decision-makers to form expectations of future consequences, these expectations being based on known empirical relationships and the decision-makers' judgements, (p. 156)


Consequently, there is a need to develop a conceptually analyzed formula for the total funding of adult education programs.
Definition of Terms
The following definitions for Adult Basic Education and Adult Education were obtained from the staff, Florida's Program and Plan for Adult Education, Florida Department of Education (1989-93) .
Adult Basic Education (ABE) is defined as the
Provision of instruction for adults who are functioning at or below the eighth grade level. Such instructional services include reading, hand-writing, arithmetic, spelling, social studies, general (elementary) sciences, health, language arts, and consumer education for grade levels 1-8. Instruction in English-as-a-Second Language/English for Speakers of Other Languages
(ESL/ESOL), adult life stages, aging process and resources and in life coping skills may be included.
(p. 54)
Adult Education includes the
Services or instruction below the college level for adults: (a) who are not enrolled in secondary school; (b) who lack sufficient mastery of basic educational skills to enable them to function effectively in society or who do not have a certificate of graduation from a school providing secondary education and who have not achieved an equivalent level of education; (c) who are not currently required to be enrolled in school; and (d) whose lack of mastery of basic skills results in an inability to speak, read, or write the English language which constitutes a substantial impairment of their ability to get or retain employment commensurate with their ability, and thus are in need of programs to help eliminate such inability and raise the level of education of such individuals with a view to making them less likely to become dependent on others (Adult Education Act, 100-297, as amended), (p. 54)


19
Limitations and Delimitations This study was limited to the adult education programs administered through Florida's 58 county school districts, 11 community colleges, and other institutions, such as public libraries and correctional institutions. Adult education programs housed in other community colleges were also included.
Estimates of transportation and child care were not included as possible additions to the funding of adult education because reliable data were not available for estimating costs. Furthermore, every effort is made by adult education administrators in Florida to locate the adult classes as close as possible to the residential areas of the students.
Although some questions have been raised about the accuracy of information reported about the success variables used in the study, no documentation was found that would support these affirmations. Similar views were also expressed concerning the data reported about public education in areas other than adult education. Since the federal government has rather strict procedures for reporting the results of adult education, it was assumed that the data employed in the study were valid.
This study assumed that all variables are nonnegative. This requirement of nonnegativity refers only to variables. Parameter estimates that demonstrate the effect of the


20
independent variables on the dependent variable may be negative.
Finally, there are limitations concerning the use of linear and nonlinear programming to optimize the production model. These limitations are discussed later in Chapter 3.
Organization of the Study bv Chapters
This report of the study is organized into five chapters. Chapter 1 is an introduction to the problem consisting of a background of the problem, the current status of. adult education funding, brief reviews of educational funding in Florida, the purpose of and need for the study, definition of terms, and limitations. Chapter 2 is a review of the literature. The procedures used in the study are described in Chapter 3. Chapter 4 consists of a presentation and discussion of the data. The findings, conclusions, and recommendations are given in Chapter 5.


CHAPTER 2 REVIEW OF THE LITERATURE
Introduction
Relevant literature concerning the need for funding, and the benefits of, adult education in the United States is presented in this chapter. Also included is a review of literature in opposition to adult education programs. This review was conducted through an ERIC search and a review of the literature of the University of Florida libraries. Technological inquiries included computer searches of ProQuest-Dissertation Abstracts; University Microfilms, Inc.; Dissertation and Master's Thesis Reproductions; LUIS (Online Card Catalog for all State of Florida university libraries; ERIC Microfiche; Silver Platter 3.1 of Pcylic; and the General Periodicals Index. Also included was a search through Education Index. The results of correspondence and interviews with state and local officials in adult education were of assistance in the review. The search primarily spanned a 10-year period prior to 1993.
The Need for Adult Education The need for adult education is evident in a recently distributed report by the United States Department of Education. According to Kirsch, Jungeblut, Jenkins, and
21


Kolstad (1993, September), reporting on Adult Literacy in America: A First Look at the Results of the National Adult Literacy Survey, 21% to 23% or 40 to 44 million adults in the United States demonstrated skills in the lowest prose and quantitative abilities (Level 1: ABE), and 25% to 28% of the respondents, representing about 50 million adults nationwide, demonstrated skills at Level 2. The most shocking detail of the report was that the 90 million Americans who were performing only at Levels 1 and 2 did not realize they were "at risk." Only 21%, or 34 to 40 million adults, demonstrated literacy skills at the highest level of Levels 4 and 5. The need to educate adults not only in basic skills, but in the self-realization of their own abilities is evident in the report.
Beginning with the Smith-Hughes Act of 1917, Congress has demonstrated interest in vocational, adult, and community education programs (Costa, 1988). As a result of national concern, Congress passed the Adult Education Act (AEA) in 1966 (Costa, 1988). This act and subsequent amendments placed emphasis on basic fundamental skills for adults. The nation experienced increased educational needs for immigrants and refugees. The Comprehensive Employment and Training Act (CETA), passed in 1973, and Job Corps emphasized adult education for employment. Thus, the federal government has for many years been interested in the problem of providing for the educational needs of adults. As will be evident in


23
the following section, adult education is seen as essential
in the development of a global economy and its accompanying
social change.
Adult Education: An International View
The literature reveals that concern for the education of
adults is an international concern. Adult education is a
major issue in education in England, Canada, Sweden, and
France (Gordon, Ponticell, & Morgan, 1991). Stock (1992)
gave the following explanation:
In Europe, influenced by distinguished French thinkers and writers, we were beginning to grapple with concepts such as education oermanente and the awesome operational implications for implementation. In the U.K., stimulated by a strong social-anthropological intellectual movement, professional adult educators were encouraged to investigate the concept and reality of "community": the relation of individuals to groups, and of groups to networks; and the montage of networks which constitutes "community." All this resulted in radically different approaches to devising and organizing adult learning programs for constituent communities, as well as to fundamental reconsiderations about the purpose of the whole educational endeavour, (p. 28)
The French and English have recognized the need for
adult education and have also witnessed the social problems
that result when adult education is neglected. Stock (1992)
quoted a Final Report presented by the 1972 UNESCO
International Adult Education Conference in the following
(author's italic):
The widening gap between nations, groups and individuals constitutes the greatest moral challenge of our time. To close the gap is more than a question of social justice. In an era of ever-growing interdependence between countries and of increasing human wants, it is an economic imperative and precondition of world peace. This inequality is due


24
also to the unequal distribution of knowledge. But it cannot be solved simply bv enlarging existing educational facilities. Experience shows that the provision of more education in most communities tends to favour most the already well-educated; the educationally under-privileged have yet to claim their rights. Adult education is no exception to the rule, for those adults who most need education have been largely neglected--they are the forgotten people. (p. 29)
Educational leaders in Canada have also been interested
in adult education programs. The importance placed upon
adult education in Canada can be seen in the following
quotation from Kulich (1992):
Adult learning and adult education have been important to Canada as an immigrant society since the early days. With the increasing complexity of society and of social, economic, political and cultural issues facing the Canadian society and its members, adult learning and adult education become more and more important. Living in the global village of today and having to deal with the rapidly changing conditions, adult learning and education are crucial to the survival of society and individuals alike, (p. 45)
Although adult education has emerged as a great need in many countries around the world, adult educators are still faced with declining public interest and funding. Stock (1992) concluded with the following sobering prediction for the survival of humanity if adult education is ignored: "For unless we learn to change, adapt, negotiate and to re-learn, the ultimate challenge will be the very continuity of a species with any pretensions to humanity" (p. 33), Even though adult educators may have the best of intentions, most writers report little improvement in providing adult education. For example, Stock (1992) stated,


25
In the best local administrations the growing numbers of specialists in adult literacy, English as a second language, neighbourhood development, rehabilitation of offenders, or health education, were welcomed and incorporated into a holistic service of adult or community education. In the worst cases "private armies" were formed with little or no communication between one another. External analysis of national level policy and practice suggested that the apparently "new" money directed to the special target-group programs was almost exactly commensurate with the cuts in grants to national providing bodies of liberal adult education and the general grants to local education authorities, (pp. 29-30)
As discussed previously, the literature emphasizes an international concern for adult education based on evidence of rapidly changing economic and social conditions.
Adult Education in the United States
Adult education in the United States has not been
financed on a par with most educational programs. A study
done by Kutner, Furey, Webb, and Gadsden (1990, November), to
be reviewed subsequently, indicates that adult education
funding has been relegated to the lowest priority in most
states. However, as stated in the thesis of this study,
adult education may be the most important asset to society.
Yet, Cherem (1990) noted,
The poor stepchild remains in part due to adult education's professional associations, which have diverse interest, and typically, relatively small memberships. Without a coalescing of these associations' interest to common concerns, no sizable group exists to lobby policymakers. Unfavorable national policy and consequent funding formulas also stifle important movement in the field. (p. 23)
However, the United States cannot ignore the changes that are taking place. Cherem (1990) continued by stating the


26
following three major changes in society that will affect the field of adult education:
1. An exponential growth of information.
2. Changing demographics (i.e., the decrease in the base of taxpayers with children).
3. The emergence of a philosophy of adults 1 continuing development, (p. 24)
Social issues will become so great that the effects on adult
education will be prominent.
The status of adult education in the United States was
best presented in a U. S. Department of Education report
titled Adult Education Programs and Services: A View From
Nine Programs (1990, November). The authors of the report,
Kutner, Furey, Webb, and Gadsden (1990, November), detailed
four major aspects of adult education funding as follows
(authors' italic):
1. The Adult Education Act represented the manor Federal source of funds that supported adult literacy services in the sites studied. However, other major Federal programs such as JTPA [Job Training Partnership Act], FSA [Family Support Act], and SLIAG [State Legalization Impact Assistance Grants] were also important funding sources. The Family Support Act is expected to become a significant source of funding in future years.
2. Adult Education Act funds did not provide the majority of total funding for any site. For the eight sites that reported financial data--AEA funds represented 37 percent funding for one site, 11-12 percent at two other sites, and about 5 percent in two sites, and about 1 percent for the remaining two sites. One site did not receive AEA funding during the year of the site visit, but had received it in prior years.
3. Seven of the eight sites reported funding from at least one additional source of Federal funding than


27
Adult Education Act funds. Four sites had SLIAG funding--79 percent of all funds in one site, 54
in another, 20 percent at a third, and an undetermined amount at a fourth. Four sites had JTPA funding, with JTPA representing 11 percent, 8 percent, 6.5 percent, and 2 percent of funding in these sites.
4. States and localities also provided substantial support for adult basic education services. All sites received state funding. At five of the sites, state and local sources provided the majority of funding--ranging from 95 percent to 67 percent in those sites, (pp. ii-iii)
Kutner et al. (1990, November) observed
Nationally, states reported a total of $499.7 million spent on adult education programs in 1987, of which 19 percent ($96.3 million) was Adult Education Act funds and 81 percent ($403.5 million) was from state and local sources. However, two earlier studies have reported that some states may underreport adult education matching funds, providing only the minimum needed to qualify for Adult Education Act funding. (p. iii)
Thus, the funding of adult education by states and local school districts is a minimum requirement for participation in the federal program, which is itself at a low level of
financial support. Insofar as funding is concerned, adult education is indeed a stepchild of the total education
programs in the United States. The problem of inadequate funding is increasing because of federal decreases in financial support.
State Responsibilities Under the Adult Education Act
Kutner et al. (1990, November) wrote that the federal
government has placed a number of administrative duties, reporting requirements, and fiscal responsibilities on the states. Each state is required to (1) develop a state plan


28
and report it to the Department of Education describing
program needs, activities, and services; (2) allocate adult
education funds to local districts; and (3) evaluate the
effectiveness of all funded programs (p. 2). Kutner et al.
(1990, November) also stated,
The Adult Education Act places a number of fiscal restrictions on the states. States are required to contribute a percentage of the Federal share of expenditures under the program. The Federal share is 90 percent for fiscal year (FY) 1989, 85 percent for FY 1990, 80 percent for FY 1991, and 75 percent for FY 1992 and thereafter. No more than 20 percent of a state's allotment may be used for high school equivalency services. States must spend at least 10 percent for corrections education and education for other institutional adults. States also must spend a minimum of 10 percent for special demonstration projects and teacher training, (p. 2)
Federal funds are distributed to the states based on the proportion of individuals in the state at least 16 years of age who have not graduated from high school and are not enrolled in a secondary school. The decline in the percentage of federal funding, coupled with an aging population, will force many states to reassess their support of adult education. However, as stated above, the need for adult education will remain, regardless of the source of funding.
Many states have supplemented these declining federal funds by supporting adult education programs with funds from local education agencies, institutions of higher education, and other nonprofit agencies or private corporations.


29
Florida's responsibility toward the Adult Education Act of 1966 is formulated in Florida's Program and Plan for Adult Education (Florida Department of Education, 1989-1993) and The Florida Adult Literacy Plan (Florida Department of Education, 1988). Both reports, submitted and approved by the U.S. Department of Education, list target populations and mention proposals for recruiting and educating these target populations. Unfortunately, Florida's refusal to meet some of the federal requirements has resulted in the loss of some federal funds. Nevertheless, the success rate of GED passing in Florida has increased despite the shortcomings of the state's plan. For instance, the number of persons passing the GED in Florida was 35,546 in fiscal year 1991, 32,722 in fiscal year 1990, 25,280 in fiscal year 1989, and 21,826 in fiscal year 1988 (Florida Department of Education, 1993a). Based on these data, the cap on adult education funding has not affected the general goals of adult education in Florida. However, actual passing rates were not reported; only the total number passing the exam was reported. Thus, changes in the need for adult education have raised new concerns for the inequities of financial support of adult education.
Inequalities of Support in Adult Education
Concern over changes in demographics and student diversity has driven the movement to reassess the needs of adult education. There has been a large shift in the emphasis on adult education from teaching ABE and GED


30
programs to offering programs for English as a second
language. For instance, concern has been expressed regarding
the ability of current school districts to teach students of
multiple languages and cultures (Ward & Anthony, 1992) .
Thompson, Wood, and Honeyman (1994) expressed the
following concerns:
Of the 47.6 million children in school in 1992, more than 2 million faced severe language barriers, with some of the nation's larger school systems already approaching a majority of minorities. For example, Los Angeles's Limited English Proficient (LEP) students have increased from 15% of total school population in 1980 to nearly 50% in 1992. New York and Chicago also have huge language minorities speaking more than 100 languages, including Apache, Tagalog, Urdu, Cherokee, Greek, and Russian. Border states such as Texas have been especially affected, as in Brownsville where LEP enrollment in elementary grades reached 51% in 1989. LEP growth cannot be accurately estimated because the numbers are so large, but officials speculate that as many as 50% of school districts in some states may not be able to comply with bilingual mandates, (p. 16)
The lack of emphasis on the changing needs of adult
education could have major ramifications in Florida. The
Summary Report: Needs Assessment (Florida Department of
Education, 1993b), dealing with the needs of adult education,
did not emphasize the growing problem of immigration. The
FDOE staff revealed that, of the total targeted population,
Only 2.29% were so restricted in language capability
that they were identified as LEP [Limited English Proficiency] LEP students were represented in the greatest percentages in Home Economics programs at 3.37%, followed by Business at 2.61% and Industrial at 2.57%. Public Service at 0.04% and Agriculture at 0.3 6% served the smallest percentages of LEP students, (p. 11) Because many of Florida's migrant agriculture workers are
from Hispanic backgrounds, the low percentage in agriculture


would lead one to conclude that the state is not recruiting enough individuals with LEP status. These percentages reflect the limited success of the adult education programs in recruiting individuals with limited English proficiency.
Although largely ignored in the literature, some political leaders in Florida are demanding greater emphasis on performance-based funding for adult education programs. Interviews with selected leaders in adult education revealed much opposition to this idea. But, as previously indicated, performance budgeting is primarily absent in the literature.
Benefits of Adult Education
This review of the literature revealed that many writers
concluded that the benefits of adult education more than
outweigh the costs. For many years, writers have promoted
adult education as a potential solution to society's ills.
The ever-present problems of crime, unemployment, and
stagnant economy have been linked to the need for more adult
education. As early as the 1960s and 1970s, adult education
was considered a means to an end to America's growing social
problems. Holtmann (197 0, August 3) offered the following
comment on this point:
There may be a number of reasons for the increase in efficiency of fellow-workers attributable to a comrade's ability to read and write. Workers may have to spend less time in instructing the formerly illiterate in simple machine operations, in correcting his mistakes, etc. In addition, it may simply be impossible to use certain production techniques when some members of the work force are illiterate, (p. 5)


32
Holtmann continued by concluding that a cost-benefit analysis of adult education should be based primarily on the
assumption that the value of consumption in the society, given a certain distribution of income, is the goal of society. Other social goals of adult literacy education would be to redistribute income among certain racial groups,
certain age groups, or regions. Social goals could include
the stimulation of economic growth, the guarantee of a self-sufficient economy, and correction of the nation's balance-
of-payments problems. Another benefit of adult literacy may
have an indirect effect on the economy. For instance, the
future strength of a nation's economy may be dependent upon
the literacy of the future work force. Holtmann (1970,
August 3) stated, "Another benefit associated with literate parents is the ability they gain in educating their children
There seems little doubt that part of the return from a child's education can be attributed to early investments of
time and energy made in the home" (p. 4). Holtmann also
noted,
There are certain types of external benefits that are derived from large numbers of people being literate. For example, the cost of collecting taxes to support government services may be lower for a largely literate population. Along these same lines, some of the benefits associated with literacy may exhibit some of the attributes of public goods. In this case, it will be impossible to determine the individual's willingness to pay for the benefits since by the nature of the goods he cannot be excluded from the benefits if he can read, (p. 5)


33
Arthur (1989) mentioned that the nonmonetary benefits of adult education may outweigh the costs because many students make several sacrifices in order to complete an adult education program and receive a GED certificate. Arthur added,
The implication of this theory [expectancy theory] for adult education is that those adults who perceive formal education as a means of fulfilling certain needs and who believe that they are able to complete the activity will participate. Those adults who do not share this perception of the value of education, or who lack the will, desire, or confidence to complete the activity, will most likely not participate, (p. 26)
Again, successful participants in adult education must come to realize that the benefits of their participation in adult education more than outweigh the costs.
Research that Supports the Funding of Adult Education Holtmann's conclusions have been supported by several recent studies. According to a report (Utah State Office of Education, 1990, December) of Utah's adult education programs, "For every $1.00 invested [in adult education], our state receives $5.70 in saved, earned or returned income" (p. 1). The total savings were realized through new tax revenues of $4,417,442 and public assistance savings of $3,010,680. When these new revenues and cost savings were combined to make $7,428,122 and compared to a total federal and state expenditure on adult education of $5,179,667, the obvious benefits were realized. These findings were based on the following economic achievements:


34
1. Obtained a Job
3,091
2. Obtained a Better Job or Salary
1,320
3. Removed from Public Assistance
750
4. Unemployed Served
10,992
5. Public Assistance Recipients Served
3,307
The methods used to obtain the above information were not disclosed in the report.
A longitudinal study of adult education was conducted by the Department of Education for Iowa (State Board of Education, 1992, April). This study used telephone interviews and mailings to question GED graduates about their life status after graduation. Because of the importance of determining the benefits over different periods of time, the surveys were prepared for two, five, or more years after graduation. The findings support the benefits of adult education that were revealed in the Utah study. According to the Iowa study, the graduates' employment rate, job skills, and financial condition appeared to be improved. However, there was only correlated evidence of this improvement; evidence of the exact cause of these improvements did not exist. The study pointed out that "while nineteen percent of the respondents were unemployed and seeking work prior to passing the GED Tests, only nine percent were unemployed and seeking work in 1990" (p. xv). The success of the GED graduates was also reflected in the following statement by the staff: "Job skill level was measured by a five-point


35
scale on which 1 indicated low job skill level and 5 indicated high job skill level. The mean job skill level increased from 2.8 before passing the GED Tests to 3.5 in 1990" (p. xvi). One of the major benefits of the GED program was that it helped to make participants more independent of public assistance. The staff concluded, "Of the 192 respondents who received welfare prior to passing the GED Tests, 135 (seventy percent) had terminated welfare in 1990. Sixty-five (five percent) of those who did not receive welfare before passing the GED Tests did receive welfare in 1990" (p. xvii). Obviously, the results were mixed when reviewing whether possessing the GED really helped in taking individuals off of welfare. The overall change in those receiving public assistance was positive toward more independence. Furthermore, there were nonmonetary improvements such as improving general quality of life and becoming better parents. The passing of the GED test bolstered the participants' self-esteem and enabled them to help their children in their school work. The staff continued,
Of those in their thirties, the age group which was most likely to have school-age children, a majority of respondents (fifty-four percent) reported that passing the GED Tests helped them to assist their children in school "some" or "very much." In comparison, thirty-one percent of those in their late teens and twenties, who were likely to have pre-school children or no children, responded that earning a GED diploma helped them to assist their children in school "some" or "very much." (p. xxi)


36
This study reported several limitations. First, there was no control or relevant comparison of the group of adults who had earned traditional high school diplomas and those who had dropped out of high school and had not earned GED diplomas. Because of confidentiality, the researchers could not secure the names and addresses of those who had failed the GED test. Furthermore, the survey was subject to self-reported bias, even though the study's conclusions were based on the assumption that the respondents had answered truthfully. However, even with these qualifications the study has merit in that it further supports the contention that the GED is beneficial for both the recipient and society.
In another study in Wisconsin, the researcher came to the same conclusions that were found in Utah and Iowa. Hayes (1991, December), of the University of Wisconsin-Madison and the principal researcher in this study, noted,
A clear increase in the overall employment rate of the respondents is evident in Table 4. About 66% of respondents were employed full or part-time at the time of the survey in Spring 1991, as compared to 59% at the time of testing in Fall 1989. ... Of the 114 individuals who reported receiving public assistance before earning the GED credential, 34 (29.8%) indicated that they had stopped receiving assistance at the time of the survey, (pp. 18-19)
Other benefits of the GED were stated, such as the enhancement of job advancement, increased skills as parents, and increased self-esteem. As was true for earlier studies, these nonmonetary factors could have influenced indirectly


37
the respondents' ability to improve the monetary rewards.
Hayes placed the following disclaimer on her findings:
One final caution is relevant when interpreting these responses. The perceptions of these respondents cannot be considered representative of all individuals who participate in GED preparation programs. This sample represents successful GED candidates alone, and it is logical to assume that there is a relationship between positive educational experiences and success on the GED test. While this limitation does not negate the positive perceptions of this study's sample, it does suggest the need to assess perceptions of a wider range of program participants, including program dropouts and individuals who are not successful in passing the GED exam, to gain a more comprehensive student assessment of GED preparation programs in Wisconsin, (p. 33)
Even with these limitations, the author believed that the
surveys reflected the successes and benefits of adult
education programs.
More recently, a study performed at the University of
Akron found evidence of the benefits of adult education.
Daniels and Hess (1992, March 12-13) reported,
Clients scored higher on all parts of the Ekwall (Silent) following their participation in the PALS program. The higher the client's performance on the SIT the higher the individual's performance on the TABE and Ekwall posttests. PALS clients experienced positive and significant improvements in TABE Vocabulary, Comprehension and Total test scores. [F]acuity revealed that during the course of the PALS program, adult learners (1) began to exhibit greater complexity in ideation; (2) gained greater control over mechanical processes such as punctuation and spelling; (3) expanded their writing repertoire from strictly personal narratives to include letters and creative stories, (pp. 3-4)
In a review of California's adult education programs, Stern (1989, February 9) concluded that the reason for the growing demand for adult education was as follows: "Demand


38
for high school basic skills instruction is increasing because (1) today's adults place a high value on high school diplomas and (2) high school students are enrolling in adult education programs to meet increased graduation requirements" (p. 41). Although the demand for at least a high school education is important for the work force, the indirect benefits of adult education must be recognized as well. For instance, as has been found in other studies, the researchers in the California study found that adult education contributed to helping students become better parents. California is one of the few states that has developed an evaluation system for English as a Second Language (ESL), Adult Basic Education (ABE), and adult special education classes. The California Adult Student Assessment System (CASAS) program assesses both student and program outcomes. Florida has administered the CASAS to individuals in its literacy programs on a nonrecurring basis (Staff, The Florida Adult Literacy Plan, Florida Department of Education, 1988, p. 12). The core of the CASAS program involves administration of tests to ESL and ABE students to determine whether or not an individual can perform 247 different life skills. Because these life skills are expressed as competency statements, 2 03 are within the general life skills content areas of Consumer Economics, Community Resources, Health, Occupational Knowledge, Government and Law, and Domestic Skills. The balance of the life skills are in the


39
area of Occupational Skills. Scores on CASAS tests are then
used to evaluate student and program progress.
Mixed reactions have resulted from California's CASAS
evaluation program. According to Stern (1989),
ESL students have gained between 6.1 and 7.3 CASAS scale points per year, while ABE students have gained on the average between 5.7 and 7.0 points per year. ... In 1987-88 some 8,303 ESL and ABE students completed both the CASAS pre- and post-tests in life skills; overall, some 18,3 61 students in 1,312 classrooms completed CASAS pre- and post-tests, (p. 61)
The results of the California study must be qualified. For
instance, Stern wrote,
The accuracy and year to year comparability of this productivity measure [CASAS scores], however, may be suspect since the assumptions have not been tested. Also, the CASAS sample may not be representative of the entire ESL and ABE participant population because (1) half of the students leave the program before taking the post-test (leavers may have different learning rates than completers of both tests) and (2) sample size and sampling and test administration procedures are not uniform across programs (nor is sampling uniformity required by the State Department of Education). (p. 62)
It is possible that the CASAS measures could be made more meaningful by linking analytically the number of hours a student attended the ABE/ESL program with his or her CASAS test score. This would be a burden that any evaluation system would need to overcome.
A Texas study also maintained the need for adult
education. According to the report (Texas State Council on
Vocational Education, 1988, December),
The Texas Strategic Economic Policy Commission reports that when the current dropout dilemma is added to Texas' current near bottom rankings in literacy and SAT scores among the states, "the implications for our state's


40
economic vitality are clear--a less educated and trained work force, and a greater demand for public service, (pp. 1-2)
The Texas study continued by reviewing the possible benefits
of adult education.
Adult education could be instrumental in the
development of a nation's future economy. Fagerlind and Saha
(1989) expressed it this way:
The cumulative research evidence leaves little doubt that education can be a powerful agent of modernization. Education broadens perspectives and mental horizons, it instills new values and beliefs supportive of modernization programs and goals, and promotes national unity and identity. Furthermore, it provides individual opportunities for upward mobility, develops skills and knowledge important for technological and industrial change, and in general helps overcome immobile ways of thinking and immobile systems of social stratification and differentiation, (p. 110)
These benefits are based on the belief that a direct causal relationship of education on the modernization of individuals exists. These factors are particularly true when community college adult education programs are observed.
In conclusion, the benefits of adult education seem to rest on the needs of society. According to Dubay (1978), the educational needs of adults are often too complex to determine the obligation of the state for instructional programs. He indicated that "[a]s a general guide, however, we may observe that whenever the common welfare of the community requires that the adult population or a notable


41
section of it be given information of some kind, the
government is bound to provide it" (p. 184).
Critique of the Studies Performed in Adult Education
Most of the research in adult education is based on
surveys and opinion polls. Although the findings have merit,
too often the inadequacies of such studies severely limit the
ability of researchers to extend findings from the samples as
generalizations of the population. Rose (1990), paraphrasing
Smith-Burke (1987), evaluated adult education research in the
following manner: "A further reason for the small voice of
the community of adult education scholars on this topic is
the 'pragmatic orientation' cf the field. Of the 23 6
published articles on adult literacy between 1975 and 1980,
less than a dozen would qualify as research" (p. 24). Beder
(1991) quoted Fingeret (1984) in the following:
The literature in adult literacy education is voluminous, conveying the image of a substantive and useful knowledge base. However, a glance through an extensive bibliography, such as that generated through a thorough ERIC search, leaves the reader immersed in acronyms and discrete, site-specific reports that are difficult to relate to each other or to the planning of
future efforts. In addition, the literature is spread over a range of disciplinary perspectives, confounding
the difficulty of addressing such specific questions as "how do adults read?" (p. ix)
Much of the research in adult education has been based on surveys and expert opinions. Because of the diverse nature of adult education, attempts at evaluating the cost benefits have been lacking. For instance, in the Utah study (Utah State Office of Education, 1990, December) the findings


42
(i.e., obtained a job, obtained a better job, or removed from public assistance) were all based upon individuals who had attended and successfully completed the adult education programs and had passed the GED elsewhere. Unfortunately, the study does not indicate whether those who did not participate in adult education programs had achieved either less or more success than those who did. For example, the reader is not told of the percentage of individuals who passed the GED test but had not taken any adult education courses. Furthermore, if Utah had experienced a surge of economic growth, the same economic achievements experienced by the adult education participants might also have been experienced by those who had shunned adult education programs. Thus, who is to say whether adult education or passing the GED test contributed any real benefit to the Utah economy or state budget?
Other studies in adult education display similar weaknesses. For instance, the staff of the Iowa study (State Board of Education, 1992, April) admitted that there was no control or relevant comparison of the group of adults who had earned traditional high school diplomas and those who had dropped out of high school and had not earned GED certificates. Thus, the question of whether the GED or high school diploma really made any difference in the success of the individuals in question is not answered. Perhaps possessing a GED certificate was beneficial to the recipient.


43
However, it really is not known whether those without high school diplomas or GED certificates could have benefitted as well. Finally, the true value of the high school diploma is uncertain.
The Wisconsin study had the same weaknesses as the Iowa study. The researcher (Hayes, 1991, December) based all of her positive assumptions on the following: "[I]t is logical to assume that there is a relationship between positive educational experiences and success on the GED test" (p. 19) Unfortunately, there is little proof as to whether this relationship exists. Finally, Hayes admits that more studies are needed to assess the perceptions or successes of those individuals who dropped out of the program or were not successful in passing the GED test. Steam's (1989, February 9) study of adult education in California fairs no better than the others. However, at least Steam explains why he

did not pursue a study of those who had failed the GED test. California's privacy laws interfered with his ability to investigate the failures of adult education programs.
In summary, the benefits of adult education to those who participate in the courses and are successful are unquestioned. However, determination regarding the benefits to overall society remain unanswered. Because of the lightweight nature of research in adult education, the determination of whether adult education benefits society will be a question for future research. For now, one may


44
accept the findings with their limitations and assume the
general benefits of adult education.
Problems in Determining the Sociological Benefits of Adult Education
Burket (1992) proposed that several social indicators
would result from a lack of adult education. In his
dissertation, Burket outlined such factors as increased crime
rate, lack of voter registration, and other social ills as
measures of problems resulting from a lack of an educated
populace. According to Burket, "Minimally, it can be
concluded that those with low educational attainment levels
are more likely to be involved in crime, are less likely to
vote or be employed, and are more likely to have low incomes
and experience poverty" (p. 43). However, Drennan (1980) did
not agree that the data .support the social benefits of adult
education:
For example, although few ABE/ESOL staff members ever mention to the recipients-students that a program goal is to get them off welfare, and the program may offer training only in basic skills, a plethora of ABE/ESOL programs use numbers-off-welfare data to judge their success. This is not valid evaluation. Equally invalid are the number registered to vote and voting, the number employed and upgraded on jobs, the number attending PTA meetings, the number reading the newspaper, the number with new library borrowing privileges, and so forth. To judge an educational program mainly on covert criteria is absurd. This is not to say that ABE/ESOL never yields employment or increased citizenship activity or that these results should not be reported. They are important, but they are side effects, (p. 12 5)
The general literature in education has for many years
assumed that society benefits directly from an educated


45
citizenry. However, the fact remains that no one has
empirically evaluated the benefits of adult education.
The Benefits of Consumer Education
The benefits of consumer education have interested
business and industry. Knapp (1991) noted in his survey
report, "The Benefits of Consumer Education," that consumer
education helps business and industry because it creates more
educated consumers who are better able to make decisions
about the products they are buying. According to an abstract
of Knapp's (1991) survey report, "The responses provide
evidence that modern consumer education teaches more than
getting the best buy. Rather, it is a lifelong process
essential to the economic well-being of society" (ERIC
Document Number ED329772). Knapp further observed that
consumer education offers several benefits to individuals:
(1) encourages critical thinking; (2) imparts life skills that contribute to success in everyday living; (3) promotes self-confidence and independence; (4) fosters broadly accepted values; and (5) improves the quality of life. In addition, consumer education offers several benefits to society: it encourages citizen awareness and promotes a stable society. (ERIC Document Number ED329772)
Additionally, consumer awareness offers several benefits to
the business community.
In his research on the benefits of adult education in
Michigan, Kwon (1990) revealed in a qualitative study the
effect of a microcomputer application training program for
adults. The program contributed economic and noneconomic
benefits to its participants, business organizations, and


46
society. Finally, a follow-up study by Seppanen (1991, March) of the ABE and GED programs in Washington community colleges showed the following results: 77% of the respondents stated that they had a stronger self-image, 80% stated that they had met their individual goals of improving a basic skill, 50% believed that they had improved a skill that could be applied to their daily work, and 77% of the former students said that their lives had changed for the better since first starting the classes. Marson (1977, July) found, in a one-year cost benefit analysis study of nine full-time vocational technical programs and 3 6 adult education courses, that the benefits of these programs far outweighed the costs. According to Marson"s report (1977, July), the cost-benefit ratio was 2.7 to 1.00 for society and 2.17 to 1.00 for an individual student. Again, although these percentages appear to place adult education in a favorable light, the study is plagued by many of the same limitations of the other studies. Because the study is so dependent upon the honesty of respondents, the study may be biased by the halo effect. In other words, because the respondents were successful, these individuals may have exhibited a positive attitude toward adult education--however unwarranted.
Within recent years some leaders in the Florida legislature have demanded that adult educators justify their programs through outcomes. Marson (1977, July) supported


47
this concept, which appears to be consistent with the growth
of the accountability movement in the general field of
education. Some political leaders in Florida are demanding
that adult educators adopt performance-based budgeting.
Arguments Against Funding Adult Education
Over the course of history, the view that literacy could
endanger the social structure of society was widely held by
the aristocracy. Donald (1991) attributed to Davis Giddy,
the president of the Royal Society in England during the
1800s, the following statement:
However specious in theory the project might be of giving education to the labouring classes of the poor, it would, in effect, be found to be prejudicial to their morals and happiness; it would teach them to despise their lot in life, instead of making them good servants in agriculture, and other laborious employments to which their rank in society has destined them. [i]t would enable them to read seditious pamphlets, vicious books, and publications against Christianity; it would render them insolent to their superiors; and in a few years, the result would be, that the legislature would find it necessary to direct the strong arm of power against them. (pp. 214-215)
Not surprisingly, because the French Revolution had occurred not long before, the higher classes were dubious of educating the masses. Although this statement appears out of context in our modern world, some adult education administrators stated that some of today's employers exhibit the attitude that if their employees obtain more education, they will leave and go somewhere else. This attitude may seem surprising. Yet, some employers still think very much like Giddy. However, the birth of the public schools in the


United States foretold the movement toward educating the
masses. Costa (1988) stated, "By this time [1918], all
states have [instituted] compulsory school attendance laws;
three states will later repeal theirs (South Carolina in
1955, Mississippi in 1956, Virginia in 1959)" (p. 7). Costa
continued, "By this time [1927], most states have passed laws
encouraging adult education. For example, California
requires illiterates between the ages of 18 to 21 to attend
school and has a literacy test for voters; Connecticut
requires school districts with over 10,000 residents to
maintain evening schools for persons over 14" (p. 9).
Finally, during the 1960s and 1970s there were tremendous
pressures on the states to support adult education programs.
Many of these programs were supported by the Adult Education
Act of 1966. Even with these movements, many experts are
opposed to using public funds to support adult education.
The arguments against funding adult education have
focused upon the economic benefits to society and to business
firms. Because of increased automation and the decreasing
need for workers, there is some question as to the need for
adult education for the training or retraining of workers for
different jobs. Hough (1987) postulated,
[S]ince unemployment is here to stay and therefore labour surpluses will continue in the majority of occupations for the foreseeable future, the government should establish the scale of training activity on the basis of social objectives. [P]erhaps the main problem involved in so doing would be the heavy strain on public expenditure, quite apart from the economic


49
waste involved in providing training that might not subsequently be put to good use. (p. 114)
Drennan (1980) concurred with Hough:
In a society incapable of supplying enough jobs for everyone interested in working, these factors seem not to have been explored deeply by either adult educators or funders of adult education. In an economic sense the ABE/ESOL graduate who replaces the less-educated worker does not yield social profit; adult education programs often accomplish their goal of rendering graduates employable at the expense of already employed nongraduates. Thus the net gain to society at large is questionable, (p. 99)
Drennan further highlighted the difficulty of demonstrating a
causal relationship between adult instruction and benefits to
the individual in the following:
Even though many adults with limited basic skills who enroll in ABE programs probably are gambling on the purported causal relationship between education and income, economists state that the relationship between adult education and increased income has only the slimmest of documentation nationally. It is difficult to point to data which prove that a decade of remedial adult education programs has lessened the rate of either functional illiteracy among the undereducated adult public or their unemployment--in real numbers or percentages, (p. 99)
Since the beginning of history, the pursuit of adult
literacy has been a subject of constant debate. As
previously discussed, one argument holds that literacy might
have a negative impact on society. For instance, Kaestle
Damon-Moore, Stedman, and Trollinger (1991) wrote,
Although for purposes of public policy, increased literacy is assumed to benefit both individuals and the society as a whole, the association of literacy with progress has been challenged under certain circumstances. Paolo Freire has questioned whether literacy is a good thing for oppressed people if the content and conduct of literacy training are not under their control. From a variety of political viewpoints,


50
American and British culture critics of the 1950s questioned whether mass culture, including popular reading materials, was debilitating to its consumers, (p. 27)
Kaestle et al. quoted the Princeton historian Lawrence Stone: "[T]hat if you teach a man to read the Bible, he may also read pornography or seditious literature" (p. 27) Obviously, the teaching of literacy in adult education is dependent upon one's viewpoint, the illiterate individual in question, and whose benefit is under consideration.
As to proving the economic benefits of those who would
become employed as a result of adult education, additional
theoretical problems are identified. For instance, when
examining the theories of the human capital approach, the
true value of adult education becomes unclear. Fagerlind and
Saha (1989) further observed that radical critics of
education believe that adult education may create a "docile
and adaptive work force which serves the needs of the power
structure of the economy. For the radical critics, an
education system which does not alter the structure of an
inequitable capitalist society, does not contribute to the
change and development of that society" (p. 49).
Research Findings Not in Favor of Funding Adult Education
As has been stated earlier, most of the research in
adult education has been superficial. However, in one
dissertation study by Huffman (1992), the benefits of funding
vocational education appear mixed. Huffman analyzed the top


51
10 vocational education programs in Mississippi and compared the amount of funding the programs received with their individual rankings. Huffman reported the following important relationships.
1. The programs that spent less on teacher salaries had better rankings, which suggests that the programs were smaller and perhaps the students had more individualized assistance.
2. The less money spent on teacher travel--the better the ranking. More time with students may significantly increase enrollment, completion, and placement.
3. The less spent on contractual services--the better the ranking.
4. The less spent on supplies and materials--the better the ranking.
5. The intercorrelation did indicate that the less spent on facilities the better the performance.
6. Equipment costs did affect the program performance ranking, but the less spent on equipment--the better the ranking.
7. The enrollment was related to costs and indicated that as enrollments decreased, program costs/FTE increased. (pp. 95-97)
Although these controversies apply to vocational education, the same expenditures may come into question in adult education. Would this mean that if less money were spent on adult education programs, there would be a higher success realized from adult education students? This is a question that is unanswered and may need further study.
Finally, another researcher discovered that the dollar amount spent on adult education courses may not be the issue. The real issue may be how the monies are spent on adult


52
education. As indicated previously, Rose (1990) found that "students, particularly mandated students, know that they can sit around doing very little, take long unofficial breaks, and basically not be there except in body, if that is what they choose" (p. 127).
Three adult education administrators who were interviewed in preparation for this study had mentioned the above dilemma. According to them, about 50% of the adult education students will never pass ABE Level 2 or reach the grade of 8.9. Thus, for perhaps 50% of the adult education students, the state monies may be wasted. Even worse percentages were revealed when discussing the percentage of those passing the GED or receiving the adult high school diploma and the total population of adult education students. Thus, the jury may still be out on the true value of present adult education programs.
Quantitative Methods Used for Evaluating Educational Programs
Few quantitative studies have been performed on the cost benefits of adult education. Except for Burket1s (1992) and Huffman's (1992) related research in vocational education, few studies have attempted to relate the benefits of adult education with its costs. Such a study should add to the knowledge base in this area.
The use of systems like PPBS (planning-programing budgeting system) was emphasized during the surge of education acts passed by Congress in the 1960s. Because of


53
the need for efficiency and "getting things done," PPBS became a code word among educators during the 1960s and early 1970s. However, PPBS and related systems were not widely accepted in the field of education, and few of these systems survive today. In the field of vocational education, competency-based and performance-based evaluations have been used since the early 1970s. Many of these programs emphasized placement, so the final goal of employment was tied to the funding of the vocational program. Huffman (1992) wrote,
Several studies highlighted specific factors or outcome variables which should be analyzed in a technical-vocational performance evaluation, such as: enrollment data, job placement, community support, student performance, student aspirations, economic benefit, employer satisfaction, service to special populations, and overall cost-effectiveness, (p. 24)
However, limited literature exists concerning the use of
competency-based or performance-based evaluation or funding
in the field of adult education. One reason for such
omissions is the special nature of adult education. Unlike
vocational education, adult education does not have the goals
of instructing the students in specific skills for specific
jobs. Furthermore, employer expectations of vocational
education graduates range from their possessing the ability
to pass exams for licenses and certifications to their being
able to operate complex machinery. These expectations are
absent in adult education.


54
In order to review the literature most relevant to adult education, it is important to look at attempts at evaluating either K through 12 programs or programs in higher education, such as those at community colleges and universities. The literature centers upon the evaluation of costs incurred in a program. Most of the literature in adult education has utilized cost-benefit models for evaluation techniques.
For instance, Steele (1971, July) surveyed the possibility of applying cost-benefit techniques to adult education. She concluded that cost-benefit techniques were used in adult education programs that achieved economic outputs and were closely associated with industry. Steele concluded that, while cost-benefit models are useful in education, a more encompassing input-output analysis would be more useful because such a model could deal flexibly with human variables within an educational system. Marson (1977, July) also mentioned the possibility of using a cost-benefit method for evaluating adult education. In Marson's study, two cost-benefit models were tested on nine full-time vocational technical programs and 63 adult education courses, which reflected many different instructional areas in vocational technical education. His findings were that the benefits from vocational education programs and noncredit education courses did outweigh the cost of the courses. Even with these findings, the limitations on cost-benefit analysis


55
are such that other possible methods of evaluation have been suggested.
Determining the costs to assign to the benefits of adult
education may be difficult. First, if Net Present Value
(NPV) techniques are used, the researcher may have difficulty
in selecting appropriate discount rates. Furthermore, the
measurement and identification of indirect costs and
nonmonetary benefits in an educational organization are
difficult to apply to specific programs. Because many
educational benefits are intangible and are difficult to
quantify, the use of any costing formula would be held
suspect as a means for measuring educational outcomes
(Campen, 1986). Huffman (1992) observed,
Levine in 1981 noted that there were serious "data limitations and ambiguities" in cost-benefit analysis of human service programs. Shugoll and Helms (1982) and Levin (1983) indicated that cost-benefit analysis had significant limitations in measuring educational costs and benefits. Campen (1986) argued that cost-benefit analysis was "procedurally inappropriate" for establishing public policy since it attempted to subrogate the importance of "social ethics; rights, entitlements, and due process; the political process; and environmental values." (p. 46)
Rothenberg (1975) stated that "one of the truly serious
difficulties in conducting cost-benefit studies is the lack
of bases on which to value the flow of public services or the
benefits from public projects" (p. 78).
The concepts of cost-effectiveness and cost-feasibility
have been suggested as possible educational measures.
According to Levin (1983),


56
Under cost-effectiveness analysis, both the costs and effects of alternatives are taken into account in evaluating programs with similar goals. It is assumed that (1) only programs with similar or identical goals can be compared and (2) a common measure of effectiveness can be used to assess them. These effectiveness data can be combined with costs in order to provide a cost-effectiveness evaluation that will enable the selection of those approaches which provide the maximum effectiveness per level of cost or which require the least cost per level of effectiveness, (p. 18)
However, Levin (1983) reported the following strengths and
weaknesses of the cost-effectiveness model:
The cost-effectiveness approach has a number of strengths. Most important is that it merely requires combining costs data with the effectiveness data that are ordinarily available from an educational evaluation to create a cost-effectiveness comparison. Further, it lends itself well to an evaluation of alternatives that are being considered for accomplishing a particular educational goal. Its one major disadvantage is that one can compare the CE [cost-effectiveness] ratios among alternatives with only one goal. (p. 21)
The same problems that affect the cost-effectiveness
approach also plague the cost-utility approach. Levin (1983) continued,
The major disadvantage is the fact that the results cannot be reproduced on the basis of a standard methodology among different evaluators, since most of the assessments are highly subjective ones that take place in the head of the person doing the evaluation. Another evaluator with the same information and methodology may derive a drastically different result by using a different set of probabilities and utilities, (p. 29)
Finally, Levin (1983) concluded that cost-feasibility analysis "can determine only whether or not alternatives are within the boundaries of consideration" (p. 30). Because of these weaknesses, an evaluation of adult education would be


57
best suited to an input-output model, which optimizes the outputs of adult education based upon the budgetary-constraints existing at the time of the evaluation. Such a condition would imply that adult education programs can best be evaluated by using the input-output model. According to McAfee (1972),
The review of the literature appears to justify the following generalizations.
1. There is a need for decision-making based upon input-output relationships.
2. The challenge for input-output studies is to determine the proper mix of inputs that will maximize output.
3. In general, input-output studies have not interfaced with cost-effectiveness studies.
4. Serious reservations regarding methodology in input-output studies have been expressed.
5. A mathematical model is appropriate for systematically determining optimal allocation strategies, (p. 29)
Mathematical models have been used to determine funding for
education in K through 12 and other educational programs
(Johns, 1976, Fall). This mathematical model is discussed
more fully in Chapter 3.
Chapter Summary The release of a recently completed national study of adult education needs in the United States revealed that 90 million American citizens were seriously deficient in literacy skills, and many of these persons did not realize their predicament. Moreover, the literature indicated that


58
in other advanced nations (e.g., Canada, England, Sweden, France), there was an acute need for adult education programs. Some writers expressed concern for the survival of society without attention to adult education needs.
The emphasis for adult education programs was on program outcomes. Although the obvious social benefits of adult education were mentioned, the modern view of adult education was redirected toward cost effectiveness. More and more scrutiny was being placed on the success rate of adult education programs. According to an abstract of Mason's (1988) article, adult educators have not received the recognition for the contributions they have made to local economies; therefore, they should rethink their rationale, reject outmoded beliefs and patterns, and justify their work through program outcomes (ERIC Document number EF378460) Several programs have been reviewed and have been found to be beneficial to society. For instance, as indicated previously, Kwon (1990) remarked in a conference speech that a review of all qualitative data obtained from the Michigan study revealed that the program contributed economic and noneconomic benefits to the participants, the organizations, and society (ED326656).
The benefits of adult education are mostly accepted in the literature. Qualitative measures have been successful at determining the beneficial outcomes of adult education. However, the use of quantitative measures to evaluate adult


59
education programs has shown mixed results or has not been tried. There is little evidence that performance-based budgeting has been used in any educational programs. A review of the literature reveals no evidence of utilizing performance-based budgeting for funding adult education. Although their opinion was very much in opposition to traditional American thought about the value of an educated citizenry, some persons opposed the education of adults on the basis that helping persons become literate might make them unhappy with life and produce instability in society. But, some writers opposed adult education programs on the basis that they waste taxpayers' money in addition to creating additional problems for the government. Also noted was the opinion that further education of adults might destroy a stable source of unskilled labor and the economic system.


CHAPTER 3 PROCEDURES
Introduction
The purpose of this study was to develop and analyze a mathematical model to optimize the funding for adult education programs in Florida through the simultaneous solution of linear and nonlinear formulations. For purposes of this study, the evaluation of data items used in these formulations must be evaluated using statistical techniques to determine their relevancy and validity. Upon determination of their relevancy, further statistical analysis will help determine the variables that are key contributors of success in adult education.
Procedure of this Study
The procedure used for this study was to formulate production models and use stepwise linear and nonlinear programming techniques to optimize models to reveal the most efficient and cost-effective factors in adult education funding. By simultaneous solution of these models, the process would determine how adult education funding should be allocated to maximize the greatest outputs. Although this study utilized nonlinear models, a review of linear programming explains some of the complexities of nonlinear
60


61
programming. According to Sultan (1993), "In linear programming, one studies the best way to allocate limited resources" (p. 1). Dorfman, Samuelson, and Solow (1986) defined linear programming as "the analysis of problems in which a linear function of a number of variables is to be maximized (or minimized) when those variables are subject to a number of restraints in the form of linear inequalities" (p. 8). The present study utilized an input-output model to find the best way to allocate the resources of adult education.
Hillier and Lieberman (1974) pointed out that linear
programming is based on four main assumptions:
proportionality, additivity, divisibility, and that all
parameters of the model are deterministic. They gave the
following example of proportionality:
The assumption is that in this case (1) the measure of effectiveness Z [dependent variable] equals C^X^ [C is
the coefficient of the independent variable X and k is the subscript of the activity for n activities or observations], and (2) the usage of each resource i equals Ai^X^; that is, both quantities are directly
proportional to the level of each activity k conducted by itself (k = l,2,...,n). [A is coefficient of the independent variable X for each activity k for each independent variable X]. (p. 22)
The magnitude of each effect is proportional to the amount of
activity governing the effect in the model.
Hillier and Lieberman stated that "the additivity
assumption requires that, given any activity levels (Xi,
X2,...Xn), the total usage of each resource and the resulting


total measure of effectiveness equal the sum of the corresponding quantities generated by each activity conducted by itself" (p. 23). Of course, this assumption applies only to linear functions and would not always be possible for nonlinear formulations.
Hillier and Lieberman continued, "Therefore, the divisibility assumption is that activity units can be divided into any fractional levels, so that noninteger values for the decision variables are permissible" (p. 23). Finally, all parameters of the model must be deterministic. Although the parameters of nonlinear models sometimes are undeterminable, the necessity for known parameters limited the formulations used in this study. The solution of these parameters was estimated using multiple regression analysis, which is discussed later in this chapter.
Linear programming also entails certain properties that may or may not apply to some nonlinear models. Nonlinear models would be defined as mathematical models that involve nonlinear functions to describe the relationship between the dependent variable and the independent variables. First, this study assumed that all models were standard. According to Sultan (1993), "If we drop the requirement that all the variables be nonnegative in a linear program, then the program falls under the category of problems called nonstandard. Unless explicitly stated otherwise, however, all programs will be standard. That is, all


variables will be > 0" (p. 50). This study assumed that all variables are nonnegative, with the requirement of nonnegativity referring only to variables, estimates that demonstrate the effect of the independent variables on the dependent variable may be negative.
Another assumption concerning most linear models is that they will be canonical. Sultan also stated, "Then we say that the linear program is in canonical form if all of the main constraints are equations, and we can pick out from each main constraint one variable that occurs only in that equation, and which has coefficient 1" (p. 52). Since the
purpose of this study was to maximize outputs in response to restricted resources, a maximization program was adopted. Sultan continued by stating that a "standard maximum linear program is one in which (a) the objective function is to be
maximized, (b) all the main constraints are of the type 'less than or equal to constants,1 and (c) where all the variables are nonnegative" (pp. 149-150). Any maximization program can be made a minimization program by multiplying the models by
ive 1. Sultan defined the minimization program as follows: "A standard minimum program is one where (a) the objective is to be minimized, (b) all the main constraints
are of the form 'greater than or equal to constants,1 and (c) the variables are nonnegative" (p. 150). Hence, this study focused on the maximization of the production model in order to maximize output.


Because the adult education field possesses many goals, this study needed to adopt a model to allow for the simultaneous solution of multiple optimizations. Goal programming could be used in linear programming to attempt to optimize multiple goals. While a company may use linear programming to maximize profits or minimize costs, goal programming allows for several goals to be resolved simultaneously. Sultan (1993) explained, "One great advantage of this technique is that it allows us to treat several objectives at once even though these objectives may be measured in different units, and even though these objectives may be incompatible" (p. 473) The goals of
graduating from different ABE levels or obtaining the GED or
simply transferring to a new educational program may be
included in goal programming. Goal programming allows for
several objective functions or production models, so that all
goals are included in the optimization model. Although goal
programming may be utilized to find solutions to multiple
goals in linear programming, such formulations may fail
because of constraint problems. According to Sultan, "Of
course, there is the question of how we incorporate these
goals into a linear program, since solving linear programs
does not allow for the violation of the constraints" (p.
476). Sultan best describes the problems encountered with
linear programming in the following:
If in a goal we are indifferent as to whether we underachieve or overachieve a target, then the variables


65
u and v both occur in the objective function. If it is more desirable that we underachieve a target than overachieve a target, then only the overachievement variable associated with that goal occurs in the objective function. If it is more desirable that we overachieve a target than underachieve it, then only the underachievement variable associated with the goal occurs in the objective function. This also illustrates how drastically a solution can change by changing a goal. (pp. 479-480)
I
McAfee (1972) concurred with Sultan in the following:
"Consequently, it would be vain to hope to maximize the
outcomes of each student in several different areas. In the
utility function [optimization function or formula], only a
few of the outputs would be maximized, at the expense of
other outputs" (p. 51). Thus, any formulation that embraces
the optimization of outputs with the attainment of several
goals would require the complexity of nonlinear programming
models. A study could utilize only linear models; however,
linear programming is plagued with two major limitations that
would not only decrease the magnitude of a study, but could
jeopardize the purpose of the study, which is to determine
how scarce resources should be allocated. According to
Phelps (1992, March),
While Linear Programming appears to address most of the criteria, the remaining few are so critical that they easily become "fatal." Non-linear Optimization addresses these two last criteria: (1) changing returns or nonlinear relationship between the Outcomes and the Effects; and (2) finding an optimal solution without having intersection between competing Effects (some positive and some negative). (p. 32)


66
Most importantly, the nonlinear programming model allows for a "built-in" balancing effect, so that effects that result in a negative value do not negate potentially positive characteristics of those same effects included as factors in
the optimization model.
Phelps (1992, March) listed the following important
properties of nonlinear modeling:
Non-linear optimization measures the multiple outcomes and the relationship between the outcome and effect in terms of the non-linear and bounded values, (p. 33)
Non-linear optimization easily uses the non-linear function of "cumulative standard normal probability." In many ways, this is the most unique feature of the education production model being presented, (p. 34)
Non-linear optimization allows--indeed requirescost to be included as a constraint and provides the resulting interpretation of "what is the most efficient and effective combination of effects given the given costs
constraint?" (p. 34)
Non-linear optimization allows the relationship between and among effects to be defined as additional constraints, (p. 34)
The properties of the constraints or boundaries of
nonlinear models require further discussion. The constraints
used in nonlinear programming are known as functional
constraints, set constraints, and active constraints.
According to Luenberger (1989),
It is clear that, if it were known a priori which constraints were active at the solution to (1) [minimize f(x) subject to hi(x) = 0 etc.], the solution would be a local minimum point of the problem defined by ignoring the inactive constraints and treating all active constraints as equality constraints. Hence, with respect to local (or relative) solutions, the problem
could be regarded as having equality constraints only, (pp. 296-297)


67
Thus, for purposes of simplification, an assumption can be made where all constraints are equality constraints.
Nonlinear programming fits nicely with the needs of statewide budgets because of its magnitude. Luenberger
(1989) stated,
There are many examples of nonlinear programming in industrial operations and business decision making. Many of these are nonlinear versions of the kinds of examples that were discussed in the linear programing part of the book. Nonlinearities can arise in production functions, cost curves, and, in fact, in almost all facets of the problem formulation, (pp. 305-306)
Since nonlinear programming was necessary for this study, alternative techniques for determining the parameters of the production model were required. Furthermore, the very complexity of nonlinear models required the use of computer-based solutions. Nakamura (1993) wrote:
The primary reason why we solve nonlinear equations by using computer methods is that nonlinear equations have no closed-form solution except for very few problems. Analytical solution polynomial equations exist up to the fourth order..., but there are no closed-form solutions for higher orders. Therefore, roots of those nonlinear equations are found by computer methods based on iterative procedures." (p. 65)
The methods by which the production model parameters are estimated will be discussed later.
Population for the Study The population for this study consisted of all districts and adult education centers in Florida. Based on the information obtained from scholars of adult education, it was determined that accurate data on GED and ABE program


68
performance were indefinite for most of the states; however, all states must report annually to the federal government the results of their adult education programs. The data for this study were taken from Florida's reports to the federal government for the fiscal years of 1991-92 and 1992-93.
Research Design The research design was based upon a data set with 85 observations for fiscal year 1992-1993 and 5 unduplicated observations from fiscal year 1991-1992 on 12 variables for the dependent variable (i.e., number passing the GED or receiving the Adult High School Diploma); 1 cost variable for all 90 observations based on the 85 local education agencies for fiscal year 1992-1993 and 5 unduplicated local education agencies for fiscal year 1991-1992 that offered adult education courses--all representing more than 1,300 data items. Even though the observations are from two different years, the 5 observations from fiscal year 1991-1992 are not duplicated in the 1992-1993 year (i.e., the same students were not included in both years' data). These 5 observations were from organizations such as Action, Inc., the Dozier Schools, Dixie County School District, Glades County School District, and Washington County Council on Aging, Inc. Therefore, inclusion of these local education agencies in the data increased the total number of observations to 90. Stepwise regression was utilized to determine the major factors influencing the success factors. Because of the low


observations to variable ratio (8 to 1), an alpha level of .05 was used to increase the power of the test statistics while using the stepwise method.
The two outputs, the GED and the Adult High School Diploma, were accomplishments verified, using standardized tests. These tests were either statewide or nationally recognized as demonstrating student achievement above a minimum level of educational attainment. Therefore, this study had verifiable evidence of student accomplishment with standardized tests. Although the attainment of the Adult High School Diploma required the completion of different courses than the courses used for preparing for the GED, both the Adult High School Diploma and the GED were considered equivalent. Also, the expenditures for adult education could not be allocated to either the GED students or the students of the Adult High School. Thus, the success on the GED was combined with completion of the Adult High School Diploma to create one success variable. Furthermore, passing rates for the students on either the GED or Adult High School Diploma were not available. Therefore, the dependent variable or success variable encompassed the percentage of the total student population who completed the GED or the Adult High School Diploma. The mathematical model was developed from the use of stepwise regression techniques by using the sum of the GED and Adult High School Diploma as the dependent variable. A second model which was developed from the


70
stepwise method was then used to determine the coefficients for the budgetary model. The final expenditures of fiscal years 1992-1993 and 1991-1992 for the 90 local education agencies were used as the dependent variable for the second model. Other important constraints were developed and used as constraints on spending. Finally, the first model was maximized by using a solution of simultaneous equations with the second model or budgetary model. Constraints on the maximization of the simultaneous resolution were included in the process of simultaneous equations.
The local education agencies included public school districts, community colleges, correctional institutions, other institutions, local libraries, and other state agencies offering adult education courses. To obtain the most current picture of the relationship between adult education funding and the many variables tested, the latest Adult Education Reports sent to the federal government were used as the source for all data items. These reports encompassed data collected for fiscal years 1991-1992 and 1992-93. Since any regression formulation must be based upon sound research theory, the 12 variables were selected because previous research revealed the importance of these variables in the determination of success in education. Furthermore, the federal government has mandated that these data items be reported annually to the U. S. Department of Education.


71
Statement of Variables The independent variables associated with the participant inputs for the dependent variable of GED and Adult High School Diploma for adult education were listed by-category .
The variables associated with student factors were as follows:
Xl--Percentage of students (Adult Education students) who were enrolled in other educational programs. This percentage was calculated by dividing the number of students of each local education agency (LEA) who were enrolled in other educational programs by the total number of students at each LEA.
X2--Percentage of students who were female. This percentage was calculated by dividing the number of female students at each LEA by the total number of students at each LEA.
X3--Percentage of students who were handicapped. The percentage was calculated by dividing the number of handicapped students at each LEA by the total number of students at each LEA.
X4--Percentage of students who were eligible legalized aliens. The variable was calculated by dividing the total number of eligible legalized aliens in each LEA by the total number of students at each LEA.


X5Percentage of students who were in correctional institutions. This percentage was calculated by dividing the number of adults in correctional institutions at each LEA by the total number of adults at each LEA.
X6--Percentage of students who were employed. The percentage was calculated by dividing the number of students who were employed for each LEA by the total number of students at each LEA.
X7--Percentage of students who were receiving public assistance. The percentage was calculated by dividing the number of students who were on public assistance and/or homeless at each LEA by the total number of students at each LEA.
The variables associated with school factors were stated as follows:
X8--Percentage of teachers who were part-time. This percentage was calculated by dividing the total number of part-time teachers by the total number of staff members in adult education. The staff in adult education was defined as the part-time teachers, full-time teachers, volunteer teachers, part-time paraprofessionals, full-time paraprofessionals, part-time counselors, and full-time counselors.
X9--Percentage of teachers who were full-time. This percentage was calculated by dividing the total number of full-time teachers by the total number of staff members in


73
adult education. The staff in adult education was defined as the part-time teachers, full-time teachers, volunteer teachers, part-time paraprofessionals, full-time paraprofessionals, part-time counselors, and full-time counselors.
X10--The ratio of state instructional salary expenditures over total expenditures. This was calculated by dividing the total instructional salary expenditures for each LEA by the total expenditures by LEA. Total expenditures included the expenditures of both state and federal monies for instructional salaries, contracted services or other personnel services, other expenses, and equipment.
XI1--The ratio of state support personnel service or contracted services expenditures over total expenditures by LEA. This was calculated by dividing the total cost of other personnel services by the total expenditures by LEA. The total expenditures included the expenditures of both state and federal monies for instructional salaries, contracted services or other personnel services, other expenses, and equipment.
X12--The ratio of state expenses of material and supply expenditures over the total expenditures by LEA. This was calculated by dividing the total cost of other expenses by the number at each LEA by the total expenditures by LEA. The total expenditures by LEA included the total expenditures of


74
both state and federal monies for instructional salaries, contracted services or other personnel services, other expenses, and equipment.
The dependent variables used in the study were as follows:
Yl--Percentage of students who passed the GED or earned an Adult High School Diploma. This variable was calculated by dividing the total number of students who had passed the GED or earned an Adult High School Diploma for each LEA by the total number of students at each LEA.
Y2--The total adult education expenditures per student by LEA divided by 1,000. This was calculated by dividing the total costs (from both state and federal funding) incurred by each LEA and then dividing this number by the number of students of each LEA. The result of this calculation was divided by 1,000 for scaling purposes. Thus, actual coefficients have coefficeints that have moved the decimal three places.
Selection of variables was based upon logic and, in some cases, convenience. Because the focus of this study was on the controllable costs of adult education, only the variables which could be controlled by Florida and which are the generator of expenditures for Florida were chosen. Most of the 12 variables which were used for the model were the only variables which the state could control for cost purposes. Therefore, the 5 observations for fiscal year 1991-1992 and


75
the 85 observations for fiscal year 1992-1993, which total 90 observations, represented an 8-to-l ratio of observations to the variables. Multiple regression techniques were used to determine the major factors for the optimized model.
Although the number of legalized aliens and students enrolled in other educational programs were not reported on the 1992-1993 Federal Report, these variables had been reported in the 1991-1992 Federal Report. The number of legalized aliens and students enrolled in other educational programs had been reported for the three previous fiscal years of 1988-1989, 1989-1990, and 1990-1991. Therefore, these variables were included in the Adult Education Model.
Teaching in adult education in Florida is mostly done by part-time teachers from the pre-K through 12 program and volunteers. Some of the vital statistics for part-time teachers are listed in Tables 1 and 2. The totals for the volunteer counselors and paraprofessionals were excluded due to lack of data for these categories.
Since the state does not pay volunteers, teaching quality in the volunteer program is questioned. Furthermore, the state has no control over the number of volunteers recruited. Thus, since these volunteers are unpaid and the state cannot predetermine the number of volunteers recruited, the variables involving the number of volunteer counselors and paraprofessionals were ignored in this study.


Table 1
Vital Statistics on Part-Time Teachers for 1991-1992
Description Number Percentage
Part-time teachers 7,454 60
Full-time teachers 827 7
Part-time paraprofessionals 429 3
Full-time parapro f e s s i ona1s 148 1
Part-time counselors 275 2
Full-time counselors 174 2
Volunteer teachers 3,176 25
TOTAL 12,483 100
Table 2
Vital Stat ;istics on Part-Time Teachers f or 1992-1993

Description Number Percentage
Part-time teachers 7,671 60
Full-time teachers 886 7
Part-time paraprofessionals 491 4
Full-time paraprofessionals 190 1
Part-time counselors 285 2
Full-time counselors 190 2
Volunteer teachers 2.999 24
TOTAL 12,712 100


The use of so many part-time teachers and para-professionals made the analysis of whether part-time teachers and paraprofessionals were better or worse than full-time teachers impossible. Also, certification is not required for many paraprofessionals. Thus, the quality of assisted teaching of the paraprofessionals was a major question that could not be answered. However, the costs to the state for these paid individuals made their presence significant to the study. Therefore, variables for the costs of these full-time and part-time teachers were used in the study.
As stated previously, forward, backward, and stepwise procedures were used to determine the parameter estimates of the linear equation. After these estimates were determined, two separate linear equations were developed using stepwise regression with two separate dependent variables. The dependent variables that reflected the successes or outputs of the two equations were the total number of individuals who either passed the GED or received the Adult High School Diploma.
After the two production equations were solved simultaneously, a nonlinear formulation was attempted. By using the PROC NONLIN command with SAS, the program used the Newton method of elimination to develop the nonlinear formulation, which best describes the process of adult education funding. The PROC NONLIN does not guarantee that such a developed equation is truly representative. Furthermore, an


examination of the results of the PROC NONLIN procedure should not be used unless the estimated model demonstrates a strong significance with the dependent variable.
As was stated previously, since some of the nonlinear equation calculations demanded nonanalytical solutions, the parameter estimates required the numerical solutions of nonlinear equations. Furthermore, the need to increase the number of variables based on further hypothesized effects required the use of analytical procedures. However, as will be seen in Chapter 4, linear models developed with multiple regression appeared to be the best equations for the purposes of this study.
Collection of Data Data from the Florida Department of Education were used to construct and pre-analyze the proposed formula. Data about funding levels, GED and ABE performance, and related information were collected from directors of adult education programs in Florida, and the annual report, which is submitted to the federal government, was used for analysis of the developed formula. The annual report is not broken down by local education agencies. However, the reports that were produced by the individual local education agencies were summarized, so that specific data concerning each agency were obtained. Therefore, summary reports were used to develop the 90 observations that were discussed in the section titled "Research Design" (see p. 68). The numbers in these reports


79
were correlated using multiple regression techniques to determine the parameters of the mathematical models. Interviews from adult education administrators and expert faculty of adult education were also used to determine the funding effects and the estimate of the constants in the production function.
Although many of the experts interviewed in this study mentioned that transportation and child care would improve the success rates of adult education centers, these possible additions to adult education funding were not included. Because Florida political leaders have voiced strong opposition to transportation and child-care costs, these factors were not considered feasible as state expenditures. The emphasis was on feasibility of legislative approval of the factors included. Based on current information, it was decided that transportation and child care are not likely to be adopted now, or in the near future, by federal or state politicians. The emphasis in this study was on optimal outputs under existing legislation. Furthermore, because every effort is made to locate the adult classes as close to the residential areas of the pupils as possible, transportation was not considered a factor in the funding of adult education.
Analysis of Data First, the data were analyzed using PROC MEANS and PROC CORR procedures on the SAS system. Because of the low ratio


of observations to variables, the most prominent variables were selected for study. The 5-to-l ratio of observations to variables is a strongly recommended minimum ratio in research using multiple regression. According to Stevens (1992), "Many of the popular rules suggest that sample size be determined as a function of the number of variables being analyzed, ranging anywhere from two subjects per variable to 20 subjects per variable. And indeed, in the previous edition of this text, I suggested 5 subjects per variable as the minimum needed" (p. 384). In discussing stepwise discriminant analysis, Stevens wrote, "The F's to enter and the corresponding significance tests in stepwise discriminant analysis must be interpreted with caution, especially if the subject/variable ratio is small say < 5" (p. 284).
Two major assumptions must be met when using multiple regression analysis to determine a regression model. According to Chatterjee and Price (1991), "The assumptions are (1) the explanatory variables are nonstochastic, that is, the values of the x's are fixed or selected in advance, and (2) the x's are measured without error. These assumptions cannot be validated, so they do not play a major role in the analysis. However, they do influence interpretation of the regression results" (p. 67). Once these assumptions have been accepted, then the researcher can follow certain steps to determine variable selection.


81
The major procedures usually employed by researchers to develop a mathematical model for testing are the forward selection method, the backward elimination method, and the stepwise method. The forward selection technique was employed first. In the forward selection technique, the F statistics are calculated for each of the independent variables. The results of the forward selection procedure revealed the variables which would give the largest F statistic and R squared. Chatterjee and Price (1991) reported,
The forward selection procedure starts with an equation containing no explanatory variables, only a constant term. The first variable included in the equation is the one which has the highest simple correlation with the dependent variable y. If the regression coefficient of this variable is significantly different from zero it is retained in the equation, and a search for a second variable is made. The variable that enters the equation as the second variable is one which has the highest correlation with y, after y has been adjusted for the effect of the first variable, that is, the variable with the highest simple correlation coefficient with the residuals form step 1. The significance of the regression coefficient of the second variable is then tested. If the regression coefficient is significant, a search for a third variable is made in the same way. The procedure is terminated when the last variable entering the equation has an insignificant regression coefficient or all variables are included in the equation, (p. 23 6)
The backward elimination method is described by Agresti and Finlay (1986) as follows:
The backward elimination procedure works in the reverse direction from the forward selection method. In backward elimination, we begin by placing all of the independent variables under consideration in the model. If they all make significant partial contributions, then that model is the final one. Otherwise, the independent variable having the least absolute partial correlation


82
with Y, controlling for the other independent variables, is removed from the model. Next, for the model with that variable removed, the partial correlations with Y and each Xi (controlling for the other variables still in the model) are recomputed. If they are all significant, that model is the final model. The process continues until each remaining independent variable makes a significant partial contribution to explaining the variability in Y. (p. 379)
The stepwise procedure was performed in addition to
forward and backward elimination. According to Chatterjee
and Price (1991),
The stepwise method is essentially a forward selection procedure but with the added proviso that at each stage the possibility of deleting a variable, as in backward elimination, is considered. In this procedure a variable that entered in the earlier stages of selection may be eliminated at later stages. The calculations made for inclusion and deletion of variables are the same as FS and BE procedures. Often, different levels of significance are assumed for inclusion and exclusion of the variables from the equation, (p. 237)
In order to select the proper variables needed in the model, the researcher determined the theoretical significance to the model. In other words, common sense, past research, or sometimes just plain guessing was used to determine the variables that should be included in the model.
The summarized results of the backward elimination method listed the variables that were considered by the stepwise method. Although the original ratio of observations to variables was 8 to 1, the true ratio of observations to variables was much higher because the final summary of the backward elimination method included only the variables considered in either the forward selection method or the


83
stepwise method. Therefore, the final ratio of observations to variables became much higher than 10 to 1.
Even though there is a need to address theoretical considerations and to choose the best method of variables selection, the major purpose of this study was exploratory. Agresti and Finlay (1986) concluded, "In exploratory research, on the other hand, the goal is not to explain relationships among variables so much as it is to find a good set of predictors" (p. 380) Thus, the purpose of this study was to predict the optimized cost of adult education funding in Florida.
According to experts in adult education, the measures of success, for which data were considered most reliable, were graduation rates on the General Education Development (GED) test and completion rate for the Adult High School diploma, as defined by the Florida's Program and Plan for Adult Education (State of Florida, Department of Education, Division of Vocational, Adult, and Community Education, 1989-1993). These success variables were treated as dependent variables in order to determine if changes in adult education funding affected success variables.
The constraint on maximization of outcomes was the funding level of adult education based upon the total expenditures for adult education from all 90 local education agencies for fiscal years 1991-1992 and 1992-1993. The two regression equations were determined using the several


variables stated above. The B coefficients were estimated using multiple regression analysis, and the final optimized formula was determined using both linear and nonlinear programming techniques, as discussed below. The production model (first model) is stated as follows:
Yl = LI (B1)X1 + L2 (Bn)X2 + ... Ln (Bn)Xn.
The above production function was determined from the stepwise regression performed on the first dependent variable
Yl and the 12 independent variables stated previously. This
production function was solved subject to the expenditure
model (second model):
01 > LI (B1)X1 + L2 (B2)Xn + ...Ln (Bn)Xn.
The above constraint was determined by using the coefficients which were calculated using stepwise regression for the variable Y2 and the corresponding 12 independent variables. The variable 01 was the total expenditures for adult education for fiscal year 1992-1993 and the total expenditures for the 5 selected LEAs for fiscal year 1991-1992. This total was then adjusted for possible errors of truncation.
Equation symbols were defined as follows: Yl = The amount of the outcome based upon the performance of a local education agency (passing the GED, receiving the Adult High School Diploma).


01 = The total expenditures for adult education for Florida divided by 1,000. [The division by 1,000 is required to scale the total expenditures in order to prevent truncation errors ($1 = $1000).]
Ln = The unit measure of the effect in a nonlinear function.
Bn = The magnitude of the relationship or the coefficient obtained by using stepwise regression.
Budgetary constraints were based on the funding (expenditures) of each district in Florida. The equation of the funding of budgetary constraints was as follows:
Tn > Xn > Mn.
Tn = The minimum level of the respective effect.
Mn = The maximum level of the respective effect.
Xn = The variable representing the amount of the respective
effect.
Since the above equations were generic to the many outcomes of the simulation, a more specific listing of the several outcomes was revealed, and the result of the simultaneous equations was one final production equation. The final equation for the production model was as follows:
Yl: Completion of the GED and Adult High School Diploma. The equation would be as follows:
Yl = Zl Pi +... Zn Ln.


The symbols for the above-stated equations were as follows:
Pn = Vector of student or school factors to the nth local education agency.
Ln = Vector of school factors by the ith local education agency.
Zn = The nonlinear effect of each of the above vectors.
The mathematical model states the outputs of an individual
(nth) LEA equal the profile of the student Pn and the LEA's
contribution to education Ln.
Development of Vectors to Determine Effects and Magnitude of Effects
The variables used in the least-squares equations were
the many data items obtained from Florida's Adult Education
Annual Performance Report, Fiscal Year 1993. These variables
were grouped by their effects of community inputs, school
inputs, student ability inputs, and the endowment position of
the student. Since this study required that nonlinear
programming be used to optimize adult education funding, a
review of the techniques to determine the production model1s
parameters was necessary. The estimations of a model's
parameters were performed using either analytical or
numerical techniques. Much of the research, particularly in
engineering and science, has emphasized numerical techniques.
However, the social sciences have used more analytical
techniques, such as the stepwise regression method. McAfee


(1972) used such stepwise regression techniques in his study-on K through 12 funding. According to Darlington (1990),
The first method is stepwise regression. Standard computer programs for stepwise regression differ from each other more than do standard programs for ordinary regression, so we shall describe the method only in general terms. Both "forward" and "backward" versions exist. (p. 165)
In this study the stepwise regression model was used because of its simplicity. Furthermore, any additional predictions for production function parameters used the stepwise regression method.
The SAS computer program was utilized to determine the
parameters or fitting of the nonlinear relationships of the
production functions. Darlington (1990) stated,
There are some very general methods for fitting curves or curved surfaces to data, as represented, for instance, in SAS PROC NLIN or the STSTAT program NONLIN These are sometimes called nonlinear regression methods However, they are in fact not based on regression methods, so we might better call them general curve-fitting methods. (p. 279)
The estimates of the coefficients of the production function were estimated by using multiple regression analysis. After the production function was determined, the production function was solved with the budgetary constraint; by using mathematical programming. A software program using the SAS statistical package was used to solve simultaneous equations. The results of the simulations are presented in Chapter 4.


CHAPTER 4 PRESENTATION OF THE DATA
Introduction
As stated previously, the purpose of this study was to develop and analyze a mathematical model to optimize the funding for adult education programs in Florida. The simultaneous solution of linear and nonlinear formulations was attempted to develop the mathematical model. The final mathematical model created by the procedures in this study was formulated using raw data concerning adult education. Because the data used for development of the model were so crucial to its final appearance, an extensive analysis of the data was completed in order to ensure that all statistical assumptions governing the model had been satisfied.
Analysis of Data The SAS statistical program on the University of Florida's main frame was used to analyze the data. The data set was then examined by looking at the listings of these procedures.
The data set included a total of 5 observations for fiscal year 1991-1992. An additional total of 85 observations were noted in the second data set representing fiscal year 1992-1993. As was stated in Chapter 3, the 5
88


observations in fiscal year 1991-1992 were not duplicated in fiscal year 1992-1993. Therefore, these 5 observations were independent of the 85 observations in the fiscal year of 1992-1993. The total of 90 observations were then available to develop a model from regression analysis. The total list of LEAs used in this study is presented in Appendix B.
Since most researchers adhere to the rule of thumb that no more than 10% of the number of observations for each variable may be missing, the total number of missing data items allowable for this study would approximate nine for the combined observations of fiscal years 1991-1992 and 1992-1993. One of the contributing factors in selecting variables was the presence or absence of data items. However, if the variables were considered important, then, regardless of the "shape" of the data items, these variables were included in the model.
The data base was fairly complete for almost all of the variables. However, some of the local agencies either failed to turn in their report or were delinquent in doing so. As shown in Table 3, for fiscal year 1992-1993, Local Education Agency (LEA) A was missing all items of data for all of the variables except the costs expended for adult education. Because of this omission, the complete records for LEA A for fiscal year 1991-1992 were used in its place. Of the four observations in 1991-1992 (excluding LEA A), LEA D also was void of any data items except for costs data items. Again,


there is no explanation for the absence of data from either
LEA A or LEA D.
Table 3
Accumulated Missing Items
Total observations in analysis
90
Data Missing
Observations with missing data:
LEA A (1992-1993)
-1
All data items except costs.
LEA B (1992-1993)
LEA C (1991-1992)
-1
-1
Correctional facilities. Legalized aliens.
Full-time & part-time teachers, counselors, & full-time para-professionals Volunteer teachers
LEA D (1991-1992)
-1
All data items except costs.
LEA E (1991-1992)
-1
Receiving Public Assist. All teaching, counselor, Sc paraprof essionals.
LEA F (1991-1992)
-1
Full-time teachers counselors, para-professionals Volunteer teachers
Total missing items
-6
Other missing data items restricted the researcher's ability to maintain a data base that included all school districts in the study. For example, many of the


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81,9(56,7< 2) )/25,'$


A MATHEMATICAL MODEL FOR THE OPTIMIZATION OF ADULT
EDUCATION FUNDING
By
RALPH BRADLEY KIMBROUGH, JR.
A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL
OF THE UNIVERSITY OF FLORIDA
IN PARTIAL FULFILLMENT OF THE REQUIREMENTS
FOR THE DEGREE OF DOCTOR OF PHILOSOPHY
UNIVERSITY OF FLORIDA
1994

I dedicate this study to my wife Nancy N.
Kimbrough; my daughter, Rachel L. Kimbrough; and my
son, Andrew R. Kimbrough. Because of their love
and support this dissertation was made possible.

ACKNOWLEDGMENTS
I would like to thank the members of by doctoral
committee for their advice and assistance. I would like to
thank Dr. David Honeyman for contributing his expertise on
educational finance for the school districts. Furthermore,
Dr. Honeyman's detailed reading and editing of this
dissertation was greatly appreciated. I would like to thank
Dr. James Wattenbarger for his contribution of knowledge of
the funding methods used by the community colleges. Dr.
Wattenbarger's counseling and moral support made this
dissertation possible. I would like to thank Dr. Eugene Todd
for his assistance in the areas such as school assessment and
evaluation. Dr. Todd was also helpful in contributing
literature concerning the problems experienced by the schools
in educating disadvantaged students. Dr. Arthur Sandeen was
continually helpful in giving advice during doctoral
committee meetings. Dr. David Miller was essential in
checking and evaluating the statistical results of the
multiple regression analysis.
In addition to my committee members, I would like to
thank Dr. William Hager, codirector of the Center for Applied
Optimization for the Department of Mathematics at the
University of Florida. His review of this dissertation and
iii

the models was invaluable to the determination of my
conclusion. Dr. William Hager's advice to continue
researching the final model for the GED exam was inspiring
and fostered my enthusiasm for future research.
I would also like to thank Ms. Patricia McGee and Ms.
Barbara Smerage for reviewing this dissertation for editorial
errors and making suggestions for its presentation. Their
continued assistance was greatly appreciated.
Finally, I would like to thank my family members for
their continued support of my completion of this
dissertation. I would like to thank my father, Dr. Ralph
Kimbrough, Sr., for his advice on dissertation topics and
my mother, Gladys Kimbrough, for her support of this
endeavor. My wife, Nancy, was very supportive, and her love
was a major factor in helping me to complete this
dissertation. Finally, my two children must take credit for
easing my tension during the more difficult times with their
love and affection.
IV

TABLE OF CONTENTS
Page
ACKNOWLEDGMENTS iii
ABSTRACT viii
CHAPTERS
1 BACKGROUND OF THE STUDY 1
Introduction 1
Definition of Optimization 2
Background of the Problem 2
The Current Status of Adult Education Funding
in Florida 7
The Florida Education Finance Program (FEFP) 8
Community College Program Fund (CCPF) 10
Other Funding Methods for Adult Education 14
The Purpose of the Study 14
Need for the Study 16
Definition of Terms 18
Limitations and Delimitations 19
Organization of the Study by Chapters 20
2 REVIEW OF THE LITERATURE 21
Introduction 21
The Need for Adult Education 21
Adult Education: An International View 23
Adult Education in the United States 25
State Responsibilities Under the Adult
Education Act 27
Inequalities of Support in Adult Education 29
Benefits of Adult Education 31
Research that Supports the Funding of Adult
Education 33
Critique of the Studies Performed in Adult
Education 41
Problems in Determining the Sociological
Benefits of Adult Education 44
The Benefits of Consumer Education 45
Arguments Against Funding Adult Education 47
v

Research Findings Not in Favor of Funding
Adult Education 50
Quantitative Methods Used for Evaluating
Educational Programs 52
Chapter Summary 57
3 PROCEDURES 60
Introduction 60
Procedure of this Study 60
Population for the Study 67
Research Design 68
Statement of Variables 71
Collection of Data 78
Analysis of Data 79
Development of Vectors to Determine
Effects and Magnitude of Effects 86
4 PRESENTATION OF DATA 88
Introduction 88
Analysis of Data 88
Discussion of Administrative and Instructional
Variables 92
Qualitative Reasons for Variable Selection 93
Quantitative Reasons for Variable Selection 96
Evaluation of the Selection Procedures and
Their Results 104
Determination of Significance of Variables in
Model 108
Tests of Partial Correlations of the Model's
Variables Ill
Problems of Determining Funding 112
Test of Partial Correlations and Analysis
of Final Model 116
Results of the Solution of Simultaneous
Equations 120
Summary 122
5 CONCLUSIONS AND RECOMMENDATIONS 123
Introduction 123
Problems and Limitations of the Study 124
Concluding Remarks Concerning the
Mathematical Model 129
Discussion of the Variables of the
Cost Model 131
Conclusions and Remarks 133
Suggestions for Further Research 134
Final Conclusion 13 6
vi

APPENDICES
A PRESENTATION OF RAW DATA 137
B LISTS OF LOCAL EDUCATION AGENCIES 168
C ANALYSIS OF COOK'S D PRINTOUT 172
D LOCAL EDUCATION AGENCIES NOT INCLUDED ON
FEDERAL REPORT 181
REFERENCES 182
BIOGRAPHICAL SKETCH 189
vi 1

Abstract of Dissertation Presented to the Graduate School
of the University of Florida in Partial Fulfillment of the
Requirements for the Degree of Doctor of Philosophy
A MATHEMATICAL MODEL FOR THE OPTIMIZATION OF ADULT
EDUCATION FUNDING
By
Ralph Bradley Kimbrough, Jr.
December 1994
Chairman: James L. Wattenbarger
Cochair: David S. Honeyman
Major Department: Educational Leadership
The purpose of this study was to develop and analyze a
mathematical model to optimize the funding for adult
education programs in Florida through the simultaneous
solution of linear and nonlinear formulations. Multiple
regression techniques were used to determine the mathematical
model. Forward selection, backward elimination, and stepwise
techniques were used to determine the variables to be
included in the model. For purposes of this study, data
items used in these formulations were evaluated using
statistical techniques to determine their relevancy and
validity.
One of the major problems of education is the reality of
declining resources. The same forces affecting public
education in pre-kindergarten through public elementary and
viii

secondary programs also affect adult education programs.
Since most states fund adult education programs with the
funding allocated for pre-K through 12th grade, the growing
needs for funds, combined with declining resources in
kindergarten through 12th grade, will threaten adult education
funding and may threaten the very existence of adult education
programs. Thus, there is a need to allocate adult education
funding in a more efficient and effective manner.
Twelve variables were used in the multiple regression
analysis. Of these 12 variables, the variables that had the
greatest effect on student success with the GED and the Adult
High School Diploma were the state's expenditures on teacher
salaries, the costs of other support services, and the costs
of materials and supplies. Furthermore, three variables were
found to be significant statistically to the increase in cost
of adult education. These variables were the percentage of
full-time teachers, the percentage of students involved in
other educational programs, and percentage of students who
resided in correctional facilities. Since the variables
which affected success on the GED and the Adult High School
Diploma did not coincide with the variables that affected
total costs of adult education, a specific solution using
simultaneous equations was not meaningful or possible.
However, the study did conclude that the use of the formula
developed from success on the GED and the Adult High School
Diploma may be useful for determining the proper allocation
IX

of funds. Future studies may be helpful in determining if
mathematical models could be used to determine cost
allocations.
x

CHAPTER 1
BACKGROUND OF THE STUDY
Introduction
One of the major problems of education is the reality of
declining resources. State legislatures across the country
are under increasing pressure not to raise taxes. State
revenues generated by either income taxes, sales taxes,
property taxes, or other personal or intangible property
taxes will not be enough to meet the increasing costs of
state services, including public education. Thus, the
movement toward obtaining more education for less money has
now become an important issue in many states. In order to
meet the growing needs of public education, state
legislatures are forced into the thoughtful allocation of tax
dollars for education in the most efficient and cost-
effective manner.
The same forces affecting public education in pre¬
kindergarten through public elementary and secondary programs
also affect adult education programs. Since most states fund
adult education programs with the funding allocated for
kindergarten through 12th grade, the growing needs for funds,
combined with declining resources in kindergarten through
12th grade, threaten adult education funding and may threaten
1

2
the very existence of adult education programs. Thus, there
is a need to allocate adult education funding in a more
efficient and effective manner.
Definition of Optimization
The definition of optimization used in this study is
concentrated on making adult education funding as effective
and efficient as possible. According to Webster's Third New
International Dictionary, optimize means "to make as perfect,
effective, or functional as possible" (p. 1585) .
Furthermore, the term optimization means "an act of
optimizing or the fact of being optimized" (p. 1585) . Thus,
for this study, the term optimization will mean the act of
optimizing adult education funding to make the funding both
efficient and effective. In other words, if more monies need
to be spent on certain areas or groups of individuals to make
adult education more effective, then the mathematical model
will be used to address the needs for additional funding in
these areas or groups. Therefore, the model developed herein
emphasizes the need for effectiveness and functionality
rather than complete efficiency.
Background of the Problem
Florida will be adversely affected by the reality of
declining state revenues and a growing and increasingly
diverse student population. According to Natale (1992,
October),

3
By 2010, if the demographers are right, one-third of all
the children in the United States will live in just four
states--California, Florida, Texas, and New York. Those
four states--according to A Demographic Look at
Tomorrow. a report that extrapolates from U.S. Census
information--will see significant increases in the
number of children in the next 20 years, mostly because
of increases in what is now considered minority
population. ... In states with increases in the number
of youths, the gains are largely attributable to gains
in minority populations. And those increases point up
another phenomenon of the future as well: Traditional
minority populations--blacks, Hispanics, Asians--will
become majority populations in some states. In
California, Texas, and Florida, more than half of the
youth population will be nonwhite well before the year
2010. (p. 24)
Although the growth in minority population in the public
schools appears evident, the immediate need to train and
teach the parents of these school children is even more
critical. According to Edwards and Young (1992, September),
"Recent hopes for successfully launching U.S. children into
the 21st century have been pinned on reclaiming a part of our
past--the involvement of parents as partners in the education
of their children. The importance of parent involvement in
children's schooling has been a persistent theme in the
research and school reform efforts of the last three decades"
(pp. 73-74) . For example, Bronfenbrenner (1979) in The
Ecology of Human Development: Experiments bv Nature and
Pesian and Henderson (1987) in The Evidence Continues to
Grow: Parent Involvement Improves Student Achievement
emphasized the importance of parental involvement in
improving student performance. Thus the need to educate
parents so they can help their children in school is evident.

4
Edwards and Young (1992, September) concluded, "Studies
[Epstein, 1987; Heath & McLaughlin, April, 1987] point to
higher student achievement when parents participate in school
activities, monitor children's homework, and otherwise
support the extension into the home of the work and values of
the school" (p. 74).
The immediate need for English as a second language is
evident in many counties in Florida. For example, one
estimate lists 50 different languages spoken in Seminole
County alone. Even more languages are spoken in Dade County.
The realization that education of parents may have a direct
influence on the success of their children further supports
the thesis that more funding is needed for adult education in
Florida.
Wood and Honeyman (1992) concurred with Natale (1992)
that the changing diversity of Florida's school population
will be a major factor in the growing needs for public
education in Florida. Although Florida's growth rate
recently has slowed, Florida's population continues to
climb. According to Wood and Honeyman (1992), "The state
[Florida] enjoys the uniqueness of being the fourth largest
state in the nation as well as one of the fastest growing
states. . . . Florida is projected to be the third most
populous state by the year 2000" (p. 170). The financial
burden on such a fast-growing state is also being experienced
by other states. Natale (1992) wrote, "For schools, the

5
implications of a student boom are severe. 'It's a terrible
time for states to be in a state of terribly rapid growth,1
Hodgkinson [1988] says. 'With the deficit situation the way
it is, there is no way for states to pay for [the growth]'"
(p. 24).
Without new tax revenues Florida will be forced to
reduce the extent of public education. Although funding for
Florida's public schools has improved in recent years, the
growth in population and language diversity of students may
outstrip the availability of needed funds for education.
According to Wood and Honeyman (1992), "During the period
1970 to 1973, several studies were conducted on Florida's
finance system. Given the changes that were occurring,
including growth and development in the southern half of the
state, the legislature adopted recommendations to guarantee
that students have access to an equal educational program"
(p. 165).
This new program was titled the Florida Education
Finance Program (FEFP). The standard for computing the state
allocation was changed from a formula-based-upon-an-
instructional-unit method to a weighted-average-per-pupil
calculation based on cost calculations. Weights were
determined for 26 student programs. Because adult education
was funded in the same way as other public education
programs, funding of adult education was governed by the
assigned weights of the FEFP. Over the years, the Florida

6
legislature has changed the formula to reflect changes in
population demographics. For example, in 1974 a cost-of-
living differential was added. Although the state increased
funding in real dollars during this period, funding declined
during the 1970s. Wood and Honeyman (1992) wrote,
While approximately $93 million in new money was made
available to school districts, rising inflation and
rapidly increasing costs in the state resulted in a $78
per pupil increase in constant dollars. Per pupil
revenue in constant dollars declined in 1975 as the
legislature limited school boards to 8 mills total and
included, but never funded, a sparsity adjustment
factor. (Johns, 1975) (p. 166)
Further stresses on educational funding were experienced
in the state during the 1980s. Because of political pressure
to initiate programs to reduce taxes, the legislature lowered
the required millage rate from 6.4 mills to 5.15 mills and
also lowered the cap on total millage allowed to 6.75 (Wood
and Honeyman, 1992, p. 167). Furthermore, the homestead
exemption for property taxes was raised to $25,000 in 1980-
1981. The legislature attempted to cover these revenue
losses with an additional levy of 2 mills for capital outlay
expenditures. Wood and Honeyman (1992) stated,
During the period 1981 to 1990, Florida experienced
incredible growth and development. To promote
educational reform and assist school districts with
increasing pressure for special populations, several
programs were enacted by the legislature. Program cost
factors and weights continued as the heart of the FEFP.
By 1989 the number of cost calculations had grown from
the original 26 (in 1973) to 41. The growth in program
classifications was the result of increased need to
address special education, special need, and at risk
student populations, (p. 167)

7
Other improvement programs were the Dropout Prevention Act of
1986 (which indirectly affects adult education), PRIME, First
Start, and other programs deemed necessary for preventing the
loss of at-risk kids (Wood and Honeyman, 1992, p. 167).
Unfortunately, these programs did not eliminate the need for
adult education.
Although the legislature addressed the need for more
programs in pre-K through 12, the area of adult education was
practically ignored. As a matter of fact, stringent
enrollment caps on funding adult education have been in place
since 1986. Without adequate increases in funding, adult
education programs will not be able to meet Florida's future
educational challenges.
The Current Status of Adult Education
Funding in Florida
The review of research about the funding of adult
education revealed that a comprehensive formula that
optimizes costs for state and local funding of adult
education has not been researched. Instead, states use a
variety of funding methods already used in pre-K through 12
funding and for the community colleges to determine how funds
are to be allocated for adult education. A majority of
states use the foundation method for funding pre-K through 12
(Thompson, Wood, & Honeyman, 1994). According to the staff
of the National Education Association Search (unpublished
evaluative report, 1987), the methods currently used for
pre-K through 12 education funding may be classified as flat

8
grants, minimum foundation, full state funding, and capacity
equalization programs. Within capacity equalization programs
are the percentage equalization (state aid ratio), guaranteed
tax base, and guaranteed tax yield formulas. The effects of
these funding formulas are varied and may or may not directly
influence adult education funding. For instance, because
much of the allocation of state funding for adult education
may be finalized at the district level, the final funding for
adult education may be decided at the local level and based
on assessed needs, not on any particular formulas. There are
several cases where the school district makes up shortfalls
in funding for as much as 50% of the expenditures of the
local district (Florida Department of Education, 1992-1993).
These shortfalls may reflect a continual lack of adequate
funding of adult education.
The Florida Education Finance Program (FEFP)
The current funding system for adult education in
Florida’s school districts is based upon predetermined
weights for funding Adult Basic Education and Secondary
Education and for educating the disabled (Florida Department
of Education, 1993, May, p. 12). According to the 1993-1994
Florida Education Finance Program: Statistical Report, adult
education funding was included in Group 3, which encompasses
Adult Job Preparatory Vocational, Adult Supplemental
Vocational, and Adult General programs. Because of fiscal
priorities, an enrollment cap was established for adult

9
education. State funding is supplemented by student fees and
tuition. According to the statistical report of the staff
of the Florida Department of Education (1993, May), "Students
who are enrolled in adult general and vocational adult
programs who are reported for funding through the Florida
Education Finance Programs must be charged tuition fees
except those who are exempted by law" (p. 17). State statute
(F.S. 239.117) provides a list of those students who are
exempted from tuition or fees.
In addition to the current group status of adult
education, certain weight factors are used to calculate
"weighted FTE." According to the staff of the Florida
Department of Education's Division of Public Schools (May
1993), "Multiplying the FTE students for a program by its
cost factor produces 'weighted FTE'" (p. 12). Currently, the
weight factors for adult education are .721 for Adult Basic
Skills, .758 for Adult Secondary Education, and 1.140 for
Adult Disabled. By multiplying the program cost factors by
the FTE, the state determines the weighted FTE students.
This figure of weighted FTE students is then multiplied by
the base student allocation (currently $2,501.05 per student)
and the district cost factor. The product of these
multiplications is then added to legislative-approved
adjustments. For instance, the district might obtain
additional supplements, such as the declining enrollment

10
supplements, sparsity supplements, and the hold harmless
adjustment.
The present system of funding does not allow for
increments based upon the meeting of goals or performance
targets. Alamprese and Koloski (1992, March) mentioned the
need for adult education programs to be given incentives.
Because of the scarcity of resources, recent legislative
proposals have centered upon the use of performance-based
funding (PBF), which has been defined as paying for
production rather than process. In education, competency
based programs, such as those in adult and vocational
education, were easily adapted to PBF, resulting in payment
for student outcomes rather than "seat time." Student
outcomes were typically measured as a percentage of program
completers and job placements. Enrollments were considered
positive student outcomes when recruiting certain
populations, such as minorities or the disadvantaged.
Although the definition of performance-based funding has been
defined rather loosely, the possibility of conforming to such
a funding model has been a major topic of discussion in adult
education circles.
Community College Program Fund (CCPF)
Since 6% to 10% of the funding for adult education is
provided by the community colleges, a review of the community
college funding program is necessary. The Community College
Program Fund (CCPF) is determined by following eight steps,

11
which become components of the funding formula used to fund
the community colleges. These steps are as follows:
Base + Cost to Continue + Enrollment Workload +
Operating Cost of New Facilities + Improved Programs
+ New Programs = Total CCPF - Student Fee Revenues =
State Funds CCPF.
In order to understand the funding process, one must
review the meaning behind each step in the formula. The
first step includes the base funding for the community
colleges, and subsequent steps are added or subtracted from
this base funding. First, the total state general revenue,
lottery funds, and calculated student fees are included in
the base funding for each college in the current fiscal year.
Step two relates to the determination of the cost to continue
current programs. The cost to continue current programs is
added to the base. According to the The Fact Book 1991-92
(Florida Department of Education, 1992, Fall), "Using the
amount of funds expended by each college in each of several
expenditure categories, the price level guidelines are
applied to these base amounts to determine the additional
funds required to maintain the colleges' existing programs at
their present level" (p. 91). Funds are then allocated to
cost categories, such as salaries, general expenditures,
utility costs, and operating capital outlay expenditures.
Each of these sums is multiplied by the price guideline
amount, and any additional funding required by each college

12
is determined. Even though all colleges are subject to the
same guidelines, the resulting increases may not be the same
because the colleges’ spend money differently.
Step three relates to the identification of workload
changes. According the The Fact Book 1991-92. "The statutes
specify that the prior year enrollment shall be the basis of
the assigned current enrollment" (p. 91). Last year's
enrollment may be a determining factor in funding, even under
conditions of high-growth rates. Step four was stated in The
Fact Book 1991-92: "When a college adds a new building to
its physical plant, additional operating costs are
experienced. Based upon the specific college's average cost
of operation per square foot, funding is appropriated for
each new building's additional space to cover the cost of
maintenance and operation" (p. 91). Thus any additional
buildings that have been added to campuses will be reflected
in increases in base funding.
Step five refers to funding for improving programs.
According to The Fact Book 1991-92. "For programs for which
the Legislature has previously provided funding, additional
funds may be earmarked to improve or expand their delivery.
Examples might be funding for the College Level Academic
Skills Test, the Gordon Rule, and other such items which have
been rolled into the program fund" (p. 91). Therefore,
additional funds for program improvement are added to the
base. Step six allows for additional funding to be added to

13
the base for new programs. According to The Fact Book 1991-
92,
First time funding for systemwide programs specifically
earmarked by the Legislature and which are to be rolled
into the CCPF lump sum may be provided. Examples might
include funding insurance rate increases or student
advisement programs. Each college would receive a share
of the total increased funds based on some distribution
rationale. This might be FTE, headcount or other
factors, (p. 92)
The seventh step is the process of adding the increases
and decreases of steps 1 through 6 for each college and
therefore determining the new funding base. Thus, each
college will have a new total CCPF funding base. The Fact
Book 1991-92 states, "Because factors other than FTE may be
involved in distributing portions of the increased funding
for all issues, it is to be expected that the increase per
FTE and the overall percentage increase will probably not be
the same for each college" (p. 92).
The final and eighth step is used to adjust the total
CCPF funding base of each college for the calculation of
student fees. Student fee collections are calculated by
multiplying the assigned FTE enrollment by the standard fee
rates. Once the student fees have been calculated, these
fees are deducted from the total CCPF for each college to
determine the state funding portion.
Thus, the state CCPF (Florida Department of Education,
1992, Fall) is clarified as the "lump sum appropriation for
each college [that] is allocated to each local Board of
Trustees to develop an operating budget for the college"

14
(p. 92) . In conclusion, each board of each college may
establish priorities for programs and expenditures to reflect
the local needs or to satisfy the intent of the legislature
expressed in the proviso language of the appropriations act.
Other Funding Methods for Adult Education
The rest of the funding for adult education originates
from federal and state grants. Federal grants make up
approximately 3% of the total funding for adult education in
Florida. Even though this percentage is small, the need to
examine the influence of federal funding is realized in the
large number of small organizations funded by federal grants,
including Hispanic Unity; Action, Inc.; and others. Because
of the success of these organizations, it was necessary to
include the funding for these organizations in this study.
The Purpose of the Study
The purpose of this study was to develop and analyze a
mathematical model to optimize the funding for adult
education programs in Florida. Since local districts may
spend adult education funds in pre-K through 12 programs or
may actually make up deficits in adult education funding,
there is no formal method to determine the optimal funding
needed in adult education. Therefore, an optimal funding
model needs to be developed, subject to the variables
affecting adult education and the budgetary constraints, and
should be based on current funding (expenditures) for the
1992-1993 school year. An additional aspect of the study was

15
to determine relationships among the funding amounts
estimated by the formula and student performance in the GED
and ABE adult education programs in Florida. The research
was designed to address the following subproblems:
1. A proposed, conceptually based formula was developed
for the total optimal state funding of adult
education programs for Florida.
2. The conceptually based formula was based on a
production function that described the input-output
relationship between selected variables.
3. The formula was used to determine the optimal
combination of inputs to maximize output, subject to
the budget and other constraints.
4. The formula was used to determine the optimal
combination of inputs to maximize output, subject to
certain constraints and given increments in the
budget constraint.
Currently, the Florida Board of Education has
experimented with several simulations of performance-based
budgets. Because of the federally mandated requirements for
adult education, these simulations include weights based upon
the success of recruiting from target populations, status of
students recruited, and activities provided by the adult
education centers. The simulations do not attempt to look at
the needs of the community that the center is attempting to
serve. Furthermore, there has not been an attempt to
optimize costs incurred in adult education. The methodology
of this study included factors that were stated by the adult
education administrators during personal interviews.
An alternative funding formula will have to optimize
costs and include weights or factors relating to the success

16
of the center in accomplishing the goals of the adult
education program. For example, as discussed previously, the
problem of the current formula is that there is no measure
concerning how successful the adult education center is in
educating for the GED, ABE, or in educating a special student
in the student's special programs. Such factors as student
status, target populations, and center activities were
included in the different weighted factors.
Need for the Study
The factors associated with estimating costs for adult
learners are uniquely atypical (different) from funding
programs for children and youths in grades K-12. Therefore,
the attendance-based funding methods that are so common among
K-12 funding are not appropriate for adult education funding.
For example, Rose (1990) stated,
The attendance basis for distributing money has been
problematical. It can contribute to the deterioration
of standards of student performance. Students,
particularly mandated students, know that they can sit
around doing very little, take long unofficial breaks,
and basically not be there except in body, if that is
what they choose. As long as they are physically
"attending," they will be carried on the books for
funding purposes, (p. 127)
Furthermore, many single parents and minimally able students
may benefit from attending a sheltered workshop environment
without having to contribute to the adult daycare population.
Finally, Rose concluded, "Another problem with attendance-
based funding is that [it] can lead to discouraging the
offering of desperately needed additional help to students,

17
if this help comes from outside agencies" (p. 127). Rickards
(1983, September) would agree with Rose's discussion of adult
education funding. According to the ERIC staff, which
paraphrased Rickards,
The need for the program was determined because it was
felt that the existing formula for disbursing adult
basic and high school completion funds in Utah and other
states (based on class membership and attendance) was
burdensome to rural school districts and inappropriate
to the needs and preferences of the adult learner.
Learning options available for adult students included
traditional classes, home study, competency testing, on-
the-job training, computer-assisted instruction, audio¬
tutorial plans, televised instruction, performance-based
instruction, and one-to-one tutoring. The program was
found to be successful in that some adults benefitted by
each approach, and all the approaches were at least as
effective as traditional classroom instruction. The
program was also cost efficient and, although time-
consuming to administer, possible to administer on the
local level, (pp. 14-15)
As a result of his study, Rickards (1983, September)
recommended that Utah change its methods of disbursing funds
for adult basic education and high school education.
Moreover, no study was found in the literature that
approached adult education from a comprehensive and totally
funded process. Finally, the need for the optimization of
school costs was best described by McAfee (1972) :
It is hardly to be questioned that studies confined to
the practical applications of models should be
energetically pursued to provide, eventually, a firmer
basis than now exists for dealing with broad questions
of educational policy. Mathematical models, such as
was developed in this study, allow decision-makers to
form expectations of future consequences, these
expectations being based on known empirical
relationships and the decision-makers' judgements.
(p. 156)

18
Consequently, there is a need to develop a conceptually
analyzed formula for the total funding of adult education
programs.
Definition of Terms
The following definitions for Adult Basic Education and
Adult Education were obtained from the staff, Florida's
Program and Plan for Adult Education. Florida Department of
Education (1989-93).
Adult Basic Education (ABE) is defined as the
Provision of instruction for adults who are functioning
at or below the eighth grade level. Such instructional
services include reading, hand-writing, arithmetic,
spelling, social studies, general (elementary) sciences,
health, language arts, and consumer education for grade
levels 1-8. Instruction in English-as-a-Second
Language/English for Speakers of Other Languages
(ESL/ESOL), adult life stages, aging process and
resources and in life coping skills may be included.
(p. 54)
Adult Education includes the
Services or instruction below che college level for
adults: (a) who are not enrolled in secondary school;
(b) who lack sufficient mastery of basic educational
skills to enable them to function effectively in society
or who do not have a certificate of graduation from a
school providing secondary education and who have not
achieved an equivalent level of education; (c) who are
not currently required to be enrolled in school; and (d)
whose lack of mastery of basic skills results in an
inability to speak, read, or write the English
language which constitutes a substantial impairment of
their ability to get or retain employment commensurate
with their ability, and thus are in need of programs to
help eliminate such inability and raise the level of
education of such individuals with a view to making them
less likely to become dependent on others (Adult
Education Act, 100-297, as amended), (p. 54)

19
Limitations and Delimitations
This study was limited to the adult education programs
administered through Florida's 58 county school districts, 11
community colleges, and other institutions, such as public
libraries and correctional institutions. Adult education
programs housed in other community colleges were also
included.
Estimates of transportation and child care were not
included as possible additions to the funding of adult
education because reliable data were not available for
estimating costs. Furthermore, every effort is made by
adult education administrators in Florida to locate the adult
classes as close as possible to the residential areas of the
students.
Although some questions have been raised about the
accuracy of information reported about the success variables
used in the study, no documentation was found that would
support these affirmations. Similar views were also
expressed concerning the data reported about public education
in areas other than adult education. Since the federal
government has rather strict procedures for reporting the
results of adult education, it was assumed that the data
employed in the study were valid.
This study assumed that all variables are nonnegative.
This requirement of nonnegativity refers only to variables.
Parameter estimates that demonstrate the effect of the

20
independent variables on the dependent variable may be
negative.
Finally, there are limitations concerning the use of
linear and nonlinear programming to optimize the production
model. These limitations are discussed later in Chapter 3.
Organization of the Study bv Chapters
This report of the study is organized into five
chapters. Chapter 1 is an introduction to the problem
consisting of a background of the problem, the current status
of adult education funding, brief reviews of educational
funding in Florida, the purpose of and need for the study,
definition of terms, and limitations. Chapter 2 is a review
of the literature. The procedures used in the study are
described in Chapter 3. Chapter 4 consists of a presentation
and discussion of the data. The findings, conclusions, and
recommendations are given in Chapter 5.

CHAPTER 2
REVIEW OF THE LITERATURE
Introduction
Relevant literature concerning the need for funding, and
the benefits of, adult education in the United States is
presented in this chapter. Also included is a review of
literature in opposition to adult education programs. This
review was conducted through an ERIC search and a review of
the literature of the University of Florida libraries.
Technological inquiries included computer searches of
ProQuest-Dissertation Abstracts; University Microfilms, Inc.;
Dissertation and Master's Thesis Reproductions; LUIS (Online
Card Catalog for all State of Florida university libraries;
ERIC Microfiche; Silver Platter 3.1 of Pcylic; and the
General Periodicals Index. Also included was a search
through Education Index. The results of correspondence and
interviews with state and local officials in adult education
were of assistance in the review. The search primarily
spanned a 10-year period prior to 1993.
The Need for Adult Education
The need for adult education is evident in a recently
distributed report by the United States Department of
Education. According to Kirsch, Jungeblut, Jenkins, and
21

22
Kolstad (1993, September), reporting on Adult Literacy in
America: A First Look at the Results of the National Adult
Literacy Survey. 21% to 23% or 40 to 44 million adults in the
United States demonstrated skills in the lowest prose and
quantitative abilities (Level 1: ABE), and 25% to 28% of the
respondents, representing about 50 million adults nationwide,
demonstrated skills at Level 2. The most shocking detail of
the report was that the 90 million Americans who were
performing only at Levels 1 and 2 did not realize they were
"at risk." Only 21%, or 34 to 40 million adults,
demonstrated literacy skills at the highest level of Levels 4
and 5. The need to educate adults not only in basic skills,
but in the self-realization of their own abilities is evident
in the report.
Beginning with the Smith-Hughes Act of 1917, Congress
has demonstrated interest in vocational, adult, and community
education programs (Costa, 1988). As a result of national
concern, Congress passed the Adult Education Act (AEA) in
1966 (Costa, 1988). This act and subsequent amendments
placed emphasis on basic fundamental skills for adults. The
nation experienced increased educational needs for immigrants
and refugees. The Comprehensive Employment and Training Act
(CETA), passed in 1973, and Job Corps emphasized adult
education for employment. Thus, the federal government has
for many years been interested in the problem of providing
for the educational needs of adults. As will be evident in

23
the following section, adult education is seen as essential
in the development of a global economy and its accompanying
social change.
Adult Education: An International View
The literature reveals that concern for the education of
adults is an international concern. Adult education is a
major issue in education in England, Canada, Sweden, and
France (Gordon, Ponticell, & Morgan, 1991). Stock (1992)
gave the following explanation:
In Europe, influenced by distinguished French thinkers
and writers, we were beginning to grapple with concepts
such as education permanente and the awesome operational
implications for implementation. In the U.K.,
stimulated by a strong social-anthropological
intellectual movement, professional adult educators were
encouraged to investigate the concept and reality of
"community": the relation of individuals to groups, and
of groups to networks; and the montage of networks which
constitutes "community." All this resulted in radically
different approaches to devising and organizing adult
learning programs for constituent communities, as well
as to fundamental reconsiderations about the purpose of
the whole educational endeavour, (p. 28)
The French and English have recognized the need for
adult education and have also witnessed the social problems
that result when adult education is neglected. Stock (1992)
quoted a Final Report presented by the 1972 UNESCO
International Adult Education Conference in the following
(author's italic):
The widening gap between nations, groups and
individuals constitutes the greatest moral challenge of
our time. To close the gap is more than a question of
social justice. In an era of ever-growing
interdependence between countries and of increasing
human wants, it is an economic imperative and
precondition of world peace. This inequality is due

24
also to the unequal distribution of knowledge. But it
cannot be solved simply bv enlarging existing
educational facilities. Experience shows that the
provision of more education in most communities tends to
favour most the already well-educated; the educationally
under-privileaed have vet to claim their rights. Adult
education is no exception to the rule, for those adults
who most need education have been largely neglected--
they are the forgotten people. (p. 29)
Educational leaders in Canada have also been interested
in adult education programs. The importance placed upon
adult education in Canada can be seen in the following
quotation from Kulich (1992):
Adult learning and adult education have been important
to Canada as an immigrant society since the early days.
. . . With the increasing complexity of society and of
social, economic, political and cultural issues facing
the Canadian society and its members, adult learning and
adult education become more and more important. Living
in the global village of today and having to deal with
the rapidly changing conditions, adult learning and
education are crucial to the survival of society and
individuals alike, (p. 45)
Although adult education has emerged as a great need in
many countries around the world, adult educators are still
faced with declining public interest and funding. Stock
(1992) concluded with the following sobering prediction for
the survival of humanity if adult education is ignored: "For
unless we learn to change, adapt, negotiate and to re-learn,
the ultimate challenge will be the very continuity of a
species with any pretensions to humanity" (p. 33), Even
though adult educators may have the best of intentions, most
writers report little improvement in providing adult
education. For example, Stock (1992) stated,

25
In the best local administrations the growing numbers of
specialists in adult literacy, English as a second
language, neighbourhood development, rehabilitation of
offenders, or health education, were welcomed and
incorporated into a holistic service of adult or
community education. In the worst cases "private
armies" were formed with little or no communication
between one another. . . . External analysis of national
level policy and practice suggested that the apparently
"new" money directed to the special target-group
programs was almost exactly commensurate with the cuts
in grants to national providing bodies of liberal adult
education and the general grants to local education
authorities, (pp. 29-30)
As discussed previously, the literature emphasizes an
international concern for adult education based on evidence
of rapidly changing economic and social conditions.
Adult Education in the United States
Adult education in the United States has not been
financed on a par with most educational programs. A study
done by Kutner, Furey, Webb, and Gadsden (1990, November), to
be reviewed subsequently, indicates that adult education
funding has been relegated to the lowest priority in most
states. However, as stated in the thesis of this study,
adult education may be the most important asset to society.
Yet, Cherem (1990) noted,
The poor stepchild remains in part due to adult
education's professional associations, which have
diverse interest, and typically, relatively small
memberships. Without a coalescing of these
associations' interest to common concerns, no sizable
group exists to lobby policymakers. Unfavorable
national policy and consequent funding formulas also
stifle important movement in the field. (p. 23)
However, the United States cannot ignore the changes that are
taking place. Cherem (1990) continued by stating the

26
following three major changes in society that will affect the
field of adult education:
1. An exponential growth of information.
2. Changing demographics (i.e., the decrease in the base
of taxpayers with children).
3. The emergence of a philosophy of adults' continuing
development, (p. 24)
Social issues will become so great that the effects on adult
education will be prominent.
The status of adult education in the United States was
best presented in a U. S. Department of Education report
titled Adult Education Programs and Services: A View From
Nine Programs (1990, November). The authors of the report,
Kutner, Furey, Webb, and Gadsden (1990, November), detailed
four major aspects of adult education funding as follows
(authors' italic):
1. The Adult Education Act represented the major Federal
source of funds that supported adult literacy
services in the sites studied. However, other major
Federal programs such as JTPA [Job Training
Partnership Act], FSA [Family Support Act], and SLIAG
[State Legalization Impact Assistance Grants] were
also important funding sources. The Family Support
Act is expected to become a significant source of
funding in future years.
2. Adult Education Act funds did not provide the
majority of total funding for any site. For the
eight sites that reported financial data--AEA funds
represented 37 percent funding for one site, 11-12
percent at two other sites, and about 5 percent in
two sites, and about 1 percent for the remaining two
sites. One site did not receive AEA funding during
the year of the site visit, but had received it in
prior years.
3. Seven of the eight sites reported funding from at
least one additional source of Federal funding than

27
Adult Education Act funds. Four sites had SLIAG
funding--79 percent of all funds in one site, 54
percent in another, 20 percent at a third, and an
undetermined amount at a fourth. Four sites had JTPA
funding, with JTPA representing 11 percent, 8
percent, 6.5 percent, and 2 percent of funding in
these sites.
4. States and localities also provided substantial
support for adult basic education services. All
sites received state funding. At five of the sites,
state and local sources provided the majority of
funding--ranging from 95 percent to 67 percent in
those sites, (pp. ii-iii)
Kutner et al. (1990, November) observed,
Nationally, states reported a total of $499.7 million
spent on adult education programs in 1987, of which 19
percent ($96.3 million) was Adult Education Act funds
and 81 percent ($403.5 million) was from state and local
sources. However, two earlier studies have reported
that some states may underreport adult education
matching funds, providing only the minimum needed to
qualify for Adult Education Act funding. (p. iii)
Thus, the funding of adult education by states and local
school districts is a minimum requirement for participation
in the federal program, which is itself at a low level of
financial support. Insofar as funding is concerned, adult
education is indeed a stepchild of the total education
programs in the United States. The problem of inadequate
funding is increasing because of federal decreases in
financial support.
State Responsibilities Under the Adult Education Act
Kutner et al. (1990, November) wrote that the federal
government has placed a number of administrative duties,
reporting requirements, and fiscal responsibilities on the
states. Each state is required to (1) develop a state plan

28
and report it to the Department of Education describing
program needs, activities, and services; (2) allocate adult
education funds to local districts; and (3) evaluate the
effectiveness of all funded programs (p. 2). Kutner et al.
(1990, November) also stated,
The Adult Education Act places a number of fiscal
restrictions on the states. States are required to
contribute a percentage of the Federal share of
expenditures under the program. The Federal share is 90
percent for fiscal year (FY) 1989, 85 percent for FY
1990, 80 percent for FY 1991, and 75 percent for FY 1992
and thereafter. No more than 20 percent of a state's
allotment may be used for high school equivalency
services. States must spend at least 10 percent for
corrections education and education for other
institutional adults. States also must spend a minimum
of 10 percent for special demonstration projects and
teacher training, (p. 2)
Federal funds are distributed to the states based on the
proportion of individuals in the state at least 16 years of
age who have not graduated from high school and are not
enrolled in a secondary school. The decline in the
percentage of federal funding, coupled with an aging
population, will force many states to reassess their support
of adult education. However, as stated above, the need for
adult education will remain, regardless of the source of
funding.
Many states have supplemented these declining federal
funds by supporting adult education programs with funds from
local education agencies, institutions of higher education,
and other nonprofit agencies or private corporations.

29
Florida's responsibility toward the Adult Education Act
of 1966 is formulated in Florida's Program and Plan for
Adult Education (Florida Department of Education, 1989-1993)
and The Florida Adult Literacy Plan (Florida Department of
Education, 1988). Both reports, submitted and approved by
the U.S. Department of Education, list target populations and
mention proposals for recruiting and educating these target
populations. Unfortunately, Florida's refusal to meet some
of the federal requirements has resulted in the loss of some
federal funds. Nevertheless, the success rate of GED passing
in Florida has increased despite the shortcomings of the
state's plan. For instance, the number of persons passing
the GED in Florida was 35,546 in fiscal year 1991, 32,722 in
fiscal year 1990, 25,280 in fiscal year 1989, and 21,826 in
fiscal year 1988 (Florida Department of Education, 1993a).
Based on these data, the cap on adult education funding has
not affected the general goals of adult education in Florida.
However, actual passing rates were not reported; only the
total number passing the exam was reported. Thus, changes in
the need for adult education have raised new concerns for the
inequities of financial support of adult education.
Inequalities of Support in Adult Education
Concern over changes in demographics and student
diversity has driven the movement to reassess the needs of
adult education. There has been a large shift in the
emphasis on adult education from teaching ABE and GED

30
programs to offering programs for English as a second
language. For instance, concern has been expressed regarding
the ability of current school districts to teach students of
multiple languages and cultures (Ward & Anthony, 1992).
Thompson, Wood, and Honeyman (1994) expressed the
following concerns:
Of the 47.6 million children in school in 1992, more
than 2 million faced severe language barriers, with some
of the nation's larger school systems already
approaching a majority of minorities. For example, Los
Angeles's Limited English Proficient (LEP) students have
increased from 15% of total school population in 1980 to
nearly 50% in 1992. New York and Chicago also have huge
language minorities speaking more than 100 languages,
including Apache, Tagalog, Urdu, Cherokee, Greek, and
Russian. Border states such as Texas have been
especially affected, as in Brownsville where LEP
enrollment in elementary grades reached 51% in 1989.
LEP growth cannot be accurately estimated because the
numbers are so large, but officials speculate that as
many as 50% of school districts in some states may not
be able to comply with bilingual mandates, (p. 16)
The lack of emphasis on the changing needs of adult
education could have major ramifications in Florida. The
Summary Report: Needs Assessment (Florida Department of
Education, 1993b), dealing with the needs of adult education,
did not emphasize the growing problem of immigration. The
FDOE staff revealed that, of the total targeted population,
Only 2.29% were so restricted in language capability
that they were identified as LEP [Limited English
Proficiency] . . . LEP students were represented in the
greatest percentages in Home Economics programs at
3.37%, followed by Business at 2.61% and Industrial at
2.57%. Public Service at 0.04% and Agriculture at 0.36%
served the smallest percentages of LEP students, (p. 11)
Because many of Florida's migrant agriculture workers are
from Hispanic backgrounds, the low percentage in agriculture

31
would lead one to conclude that the state is not recruiting
enough individuals with LEP status. These percentages
reflect the limited success of the adult education programs
in recruiting individuals with limited English proficiency.
Although largely ignored in the literature, some
political leaders in Florida are demanding greater emphasis
on performance-based funding for adult education programs.
Interviews with selected leaders in adult education revealed
much opposition to this idea. But, as previously indicated,
performance budgeting is primarily absent in the literature.
Benefits of Adult Education
This review of the literature revealed that many writers
concluded that the benefits of adult education more than
outweigh the costs. For many years, writers have promoted
adult education as a potential solution to society's ills.
The ever-present problems of crime, unemployment, and
stagnant economy have been linked to the need for more adult
education. As early as the 1960s and 1970s, adult education
was considered a means to an end to America's growing social
problems. Holtmann (1970, August 3) offered the following
comment on this point:
There may be a number of reasons for the increase in
efficiency of fellow-workers attributable to a comrade's
ability to read and write. Workers may have to spend
less time in instructing the formerly illiterate in
simple machine operations, in correcting his mistakes,
etc. In addition, it may simply be impossible to use
certain production techniques when some members of the
work force are illiterate, (p. 5)

32
Holtmann continued by concluding that a cost-benefit analysis
of adult education should be based primarily on the
assumption that the value of consumption in the society,
given a certain distribution of income, is the goal of
society. Other social goals of adult literacy education
would be to redistribute income among certain racial groups,
certain age groups, or regions. Social goals could include
the stimulation of economic growth, the guarantee of a self-
sufficient economy, and correction of the nation's balance-
of-payments problems. Another benefit of adult literacy may
have an indirect effect on the economy. For instance, the
future strength of a nation's economy may be dependent upon
the literacy of the future work force. Holtmann (1970,
August 3) stated, "Another benefit associated with literate
parents is the ability they gain in educating their children.
There seems little doubt that part of the return from a
child's education can be attributed to early investments of
time and energy made in the home" (p. 4). Holtmann also
noted,
There are certain types of external benefits that are
derived from large numbers of people being literate.
For example, the cost of collecting taxes to support
government services may be lower for a largely literate
population. Along these same lines, some of the
benefits associated with literacy may exhibit some of
the attributes of public goods. In this case, it will
be impossible to determine the individual's willingness
to pay for the benefits since by the nature of the goods
he cannot be excluded from the benefits if he can read,
(p. 5)

33
Arthur (1989) mentioned that the nonmonetary benefits of
adult education may outweigh the costs because many students
make several sacrifices in order to complete an adult
education program and receive a GED certificate. Arthur
added,
The implication of this theory [expectancy theory]
for adult education is that those adults who perceive
formal education as a means of fulfilling certain
needs and who believe that they are able to complete
the activity will participate. Those adults who do
not share this perception of the value of education,
or who lack the will, desire, or confidence to
complete the activity, will most likely not participate,
(p. 26)
Again, successful participants in adult education must come
to realize that the benefits of their participation in adult
education more than outweigh the costs.
Research that Supports the Funding of Adult Education
Holtmann's conclusions have been supported by several
recent studies. According to a report (Utah State Office of
Education, 1990, December) of Utah's adult education
programs, "For every $1.00 invested [in adult education], our
state receives $5.70 in saved, earned or returned income" (p.
1). The total savings were realized through new tax revenues
of $4,417,442 and public assistance savings of $3,010,680.
When these new revenues and cost savings were combined to
make $7,428,122 and compared to a total federal and state
expenditure on adult education of $5,179,667, the obvious
benefits were realized. These findings were based on the
following economic achievements:

34
1. Obtained a Job 3,091
2. Obtained a Better Job or Salary 1,320
3. Removed from Public Assistance 750
4. Unemployed Served 10,992
5. Public Assistance Recipients Served 3,307
The methods used to obtain the above information were not
disclosed in the report.
A longitudinal study of adult education was conducted by
the Department of Education for Iowa (State Board of
Education, 1992, April). This study used telephone
interviews and mailings to question GED graduates about their
life status after graduation. Because of the importance of
determining the benefits over different periods of time, the
surveys were prepared for two, five, or more years after
graduation. The findings support the benefits of adult
education that were revealed in the Utah study. According to
the Iowa study, the graduates' employment rate, job skills,
and financial condition appeared to be improved. However,
there was only correlated evidence of this improvement;
evidence of the exact cause of these improvements did not
exist. The study pointed out that "while nineteen percent of
the respondents were unemployed and seeking work prior to
passing the GED Tests, only nine percent were unemployed and
seeking work in 1990" (p. xv). The success of the GED
graduates was also reflected in the following statement by
the staff: "Job skill level was measured by a five-point

35
scale on which 1 indicated low job skill level and 5
indicated high job skill level. The mean job skill level
increased from 2.8 before passing the GED Tests to 3.5 in
1990" (p. xvi). One of the major benefits of the GED
program was that it helped to make participants more
independent of public assistance. The staff concluded, "Of
the 192 respondents who received welfare prior to passing the
GED Tests, 135 (seventy percent) had terminated welfare in
1990. Sixty-five (five percent) of those who did not receive
welfare before passing the GED Tests did receive welfare in
1990" (p. xvii). Obviously, the results were mixed when
reviewing whether possessing the GED really helped in taking
individuals off of welfare. The overall change in those
receiving public assistance was positive toward more
independence. Furthermore, there were nonmonetary
improvements such as improving general quality of life and
becoming better parents. The passing of the GED test
bolstered the participants' self-esteem and enabled them to
help their children in their school work. The staff
continued,
Of those in their thirties, the age group which was most
likely to have school-age children, a majority of
respondents (fifty-four percent) reported that passing
the GED Tests helped them to assist their children in
school "some" or "very much." In comparison, thirty-one
percent of those in their late teens and twenties, who
were likely to have pre-school children or no children,
responded that earning a GED diploma helped them to
assist their children in school "some" or "very much."
(p. xxi)

36
This study reported several limitations. First, there
was no control or relevant comparison of the group of adults
who had earned traditional high school diplomas and those who
had dropped out of high school and had not earned GED
diplomas. Because of confidentiality, the researchers could
not secure the names and addresses of those who had failed
the GED test. Furthermore, the survey was subject to self-
reported bias, even though the study's conclusions were based
on the assumption that the respondents had answered
truthfully. However, even with these qualifications the
study has merit in that it further supports the contention
that the GED is beneficial for both the recipient and
society.
In another study in Wisconsin, the researcher came to
the same conclusions that were found in Utah and Iowa.
Hayes (1991, December), of the University of Wisconsin-
Madison and the principal researcher in this study, noted,
A clear increase in the overall employment rate of the
respondents is evident in Table 4. About 66% of
respondents were employed full or part-time at the time
of the survey in Spring 1991, as compared to 59% at the
time of testing in Fall 1989. ... Of the 114
individuals who reported receiving public assistance
before earning the GED credential, 34 (29.8%) indicated
that they had stopped receiving assistance at the time
of the survey, (pp. 18-19)
Other benefits of the GED were stated, such as the
enhancement of job advancement, increased skills as parents,
and increased self-esteem. As was true for earlier studies,
these nonmonetary factors could have influenced indirectly

37
the respondents' ability to improve the monetary rewards.
Hayes placed the following disclaimer on her findings:
One final caution is relevant when interpreting these
responses. The perceptions of these respondents cannot
be considered representative of all individuals who
participate in GED preparation programs. This sample
represents successful GED candidates alone, and it is
logical to assume that there is a relationship between
positive educational experiences and success on the GED
test. While this limitation does not negate the
positive perceptions of this study's sample, it does
suggest the need to assess perceptions of a wider range
of program participants, including program dropouts and
individuals who are not successful in passing the GED
exam, to gain a more comprehensive student assessment of
GED preparation programs in Wisconsin, (p. 33)
Even with these limitations, the author believed that the
surveys reflected the successes and benefits of adult
education programs.
More recently, a study performed at the University of
Akron found evidence of the benefits of adult education.
Daniels and Hess (1992, March 12-13) reported,
Clients scored higher on all parts of the Ekwall
(Silent) following their participation in the PALS
program. . . . The higher the client's performance on
the SIT the higher the individual's performance on the
TABE and Ekwall posttests. . . . PALS clients
experienced positive and significant improvements
in TABE Vocabulary, Comprehension and Total test scores.
. . . [F]acuity revealed that during the course of the
PALS program, adult learners (1) began to exhibit
greater complexity in ideation; (2) gained greater
control over mechanical processes such as punctuation
and spelling; (3) expanded their writing repertoire from
strictly personal narratives to include letters and
creative stories, (pp. 3-4)
In a review of California's adult education programs,
Stern (1989, February 9) concluded that the reason for the
growing demand for adult education was as follows: "Demand

38
for high school basic skills instruction is increasing
because (1) today's adults place a high value on high school
diplomas and (2) high school students are enrolling in adult
education programs to meet increased graduation requirements"
(p. 41). Although the demand for at least a high school
education is important for the work force, the indirect
benefits of adult education must be recognized as well. For
instance, as has been found in other studies, the researchers
in the California study found that adult education
contributed to helping students become better parents.
California is one of the few states that has developed an
evaluation system for English as a Second Language (ESL),
Adult Basic Education (ABE), and adult special education
classes. The California Adult Student Assessment System
(CASAS) program assesses both student and program outcomes.
Florida has administered the CASAS to individuals in its
literacy programs on a nonrecurring basis (Staff, The Florida
Adult Literacy Plan. Florida Department of Education, 1988,
p. 12). The core of the CASAS program involves
administration of tests to ESL and ABE students to determine
whether or not an individual can perform 247 different life
skills. Because these life skills are expressed as
competency statements, 203 are within the general life skills
content areas of Consumer Economics, Community Resources,
Health, Occupational Knowledge, Government and Law, and
Domestic Skills. The balance of the life skills are in the

39
area of Occupational Skills. Scores on CASAS tests are then
used to evaluate student and program progress.
Mixed reactions have resulted from California's CASAS
evaluation program. According to Stern (1989),
ESL students have gained between 6.1 and 7.3 CASAS scale
points per year, while ABE students have gained on the
average between 5.7 and 7.0 points per year. ... In
1987-88 some 8,303 ESL and ABE students completed both
the CASAS pre- and post-tests in life skills; overall,
some 18,361 students in 1,312 classrooms completed CASAS
pre- and post-tests, (p. 61)
The results of the California study must be qualified. For
instance, Stern wrote,
The accuracy and year to year comparability of this
productivity measure [CASAS scores], however, may be
suspect since the assumptions have not been tested.
Also, the CASAS sample may not be representative of the
entire ESL and ABE participant population because (1)
half of the students leave the program before taking the
post-test (leavers may have different learning rates
than completers of both tests) and (2) sample size and
sampling and test administration procedures are not
uniform across programs (nor is sampling uniformity
required by the State Department of Education). (p. 62)
It is possible that the CASAS measures could be made
more meaningful by linking analytically the number of hours a
student attended the ABE/ESL program with his or her CASAS
test score. This would be a burden that any evaluation
system would need to overcome.
A Texas study also maintained the need for adult
education. According to the report (Texas State Council on
Vocational Education, 1988, December),
The Texas Strategic Economic Policy Commission reports
that when the current dropout dilemma is added to Texas'
current near bottom rankings in literacy and SAT scores
among the states, "the implications for our state's

40
economic vitality are clear--a less educated and trained
work force, and a greater demand for public service.
(pp. 1-2)
The Texas study continued by reviewing the possible benefits
of adult education.
Adult education could be instrumental in the
development of a nation's future economy. Fagerlind and Saha
(1989) expressed it this way:
The cumulative research evidence leaves little doubt
that education can be a powerful agent of modernization.
Education broadens perspectives and mental horizons, it
instills new values and beliefs supportive of
modernization programs and goals, and promotes national
unity and identity. Furthermore, it provides individual
opportunities for upward mobility, develops skills and
knowledge important for technological and industrial
change, and in general helps overcome immobile ways of
thinking and immobile systems of social stratification
and differentiation, (p. 110)
These benefits are based on the belief that a direct
causal relationship of education on the modernization of
individuals exists. These factors are particularly true
when community college adult education programs are
observed.
In conclusion, the benefits of adult education seem to
rest on the needs of society. According to Dubay (1978), the
educational needs of adults are often too complex to
determine the obligation of the state for instructional
programs. He indicated that "[a]s a general guide, however,
we may observe that whenever the common welfare of the
community requires that the adult population or a notable

41
section of it be given information of some kind, the
government is bound to provide it" (p. 184).
Critique of the Studies Performed in Adult Education
Most of the research in adult education is based on
surveys and opinion polls. Although the findings have merit,
too often the inadequacies of such studies severely limit the
ability of researchers to extend findings from the samples as
generalizations of the population. Rose (1990), paraphrasing
Smith-Burke (1987), evaluated adult education research in the
following manner: "A further reason for the small voice of
the community of adult education scholars on this topic is
the 'pragmatic orientation' cf the field. Of the 236
published articles on adult literacy between 1975 and 1980,
less than a dozen would qualify as research" (p. 24). Beder
(1991) quoted Fingeret (1984) in the following:
The literature in adult literacy education is
voluminous, conveying the image of a substantive and
useful knowledge base. However, a glance through an
extensive bibliography, such as that generated through a
thorough ERIC search, leaves the reader immersed in
acronyms and discrete, site-specific reports that are
difficult to relate to each other or to the planning of
future efforts. In addition, the literature is spread
over a range of disciplinary perspectives, confounding
the difficulty of addressing such specific questions as
"how do adults read?" (p. ix)
Much of the research in adult education has been based
on surveys and expert opinions. Because of the diverse
nature of adult education, attempts at evaluating the cost
benefits have been lacking. For instance, in the Utah study
(Utah State Office of Education, 1990, December) the findings

42
(i.e., obtained a job, obtained a better job, or removed from
public assistance) were all based upon individuals who had
attended and successfully completed the adult education
programs and had passed the GED elsewhere. Unfortunately,
the study does not indicate whether those who did not
participate in adult education programs had achieved either
less or more success than those who did. For example, the
reader is not told of the percentage of individuals who
passed the GED test but had not taken any adult education
courses. Furthermore, if Utah had experienced a surge of
economic growth, the same economic achievements experienced
by the adult education participants might also have been
experienced by those who had shunned adult education
programs. Thus, who is to say whether adult education or
passing the GED test contributed any real benefit to the Utah
economy or state budget?
Other studies in adult education display similar
weaknesses. For instance, the staff of the Iowa study (State
Board of Education, 1992, April) admitted that there was no
control or relevant comparison of the group of adults who had
earned traditional high school diplomas and those who had
dropped out of high school and had not earned GED
certificates. Thus, the question of whether the GED or high
school diploma really made any difference in the success of
the individuals in question is not answered. Perhaps
possessing a GED certificate was beneficial to the recipient.

43
However, it really is not known whether those without high
school diplomas or GED certificates could have benefitted as
well. Finally, the true value of the high school diploma is
uncertain.
The Wisconsin study had the same weaknesses as the Iowa
study. The researcher (Hayes, 1991, December) based all of
her positive assumptions on the following: "[I]t is logical
to assume that there is a relationship between positive
educational experiences and success on the GED test" (p. 19) .
Unfortunately, there is little proof as to whether this
relationship exists. Finally, Hayes admits that more studies
are needed to assess the perceptions or successes of those
individuals who dropped out of the program or were not
successful in passing the GED test. Steam's (1989, February
9) study of adult education in California fairs no better
than the others. However, at least Stearn explains why he
did not pursue a study of those who had failed the GED test.
California's privacy laws interfered with his ability to
investigate the failures of adult education programs.
In summary, the benefits of adult education to those who
participate in the courses and are successful are
unquestioned. However, determination regarding the benefits
to overall society remain unanswered. Because of the light¬
weight nature of research in adult education, the
determination of whether adult education benefits society
will be a question for future research. For now, one may

44
accept the findings with their limitations and assume the
general benefits of adult education.
Problems in Determining the
Sociological Benefits of Adult Education
Burket (1992) proposed that several social indicators
would result from a lack of adult education. In his
dissertation, Burket outlined such factors as increased crime
rate, lack of voter registration, and other social ills as
measures of problems resulting from a lack of an educated
populace. According to Burket, "Minimally, it can be
concluded that those with low educational attainment levels
are more likely to be involved in crime, are less likely to
vote or be employed, and are more likely to have low incomes
and experience poverty" (p. 43). However, Drennan (1980) did
not agree that the data .support the social benefits of adult
education:
For example, although few ABE/ESOL staff members ever
mention to the recipients-students that a program goal
is to get them off welfare, and the program may offer
training only in basic skills, a plethora of ABE/ESOL
programs use numbers-off-welfare data to judge their
success. This is not valid evaluation. Equally invalid
are the number registered to vote and voting, the number
employed and upgraded on jobs, the number attending PTA
meetings, the number reading the newspaper, the number
with new library borrowing privileges, and so forth. To
judge an educational program mainly on covert criteria
is absurd. . . . This is not to say that ABE/ESOL never
yields employment or increased citizenship activity or
that these results should not be reported. They are
important, but they are side effects, (p. 125)
The general literature in education has for many years
assumed that society benefits directly from an educated

45
citizenry. However, the fact remains that no one has
empirically evaluated the benefits of adult education.
The Benefits of Consumer Education
The benefits of consumer education have interested
business and industry. Knapp (1991) noted in his survey
report, "The Benefits of Consumer Education," that consumer
education helps business and industry because it creates more
educated consumers who are better able to make decisions
about the products they are buying. According to an abstract
of Knapp's (1991) survey report, "The responses provide
evidence that modern consumer education teaches more than
getting the best buy. Rather, it is a lifelong process
essential to the economic well-being of society" (ERIC
Document Number ED329772). Knapp further observed that
consumer education offers several benefits to individuals:
(1) encourages critical thinking; (2) imparts life
skills that contribute to success in everyday living;
(3) promotes self-confidence and independence; (4)
fosters broadly accepted values; and (5) improves the
quality of life. In addition, consumer education offers
several benefits to society: it encourages citizen
awareness and promotes a stable society. (ERIC Document
Number ED329772)
Additionally, consumer awareness offers several benefits to
the business community.
In his research on the benefits of adult education in
Michigan, Kwon (1990) revealed in a qualitative study the
effect of a microcomputer application training program for
adults. The program contributed economic and noneconomic
benefits to its participants, business organizations, and

46
society. Finally, a follow-up study by Seppanen (1991,
March) of the ABE and GED programs in Washington community
colleges showed the following results: 77% of the
respondents stated that they had a stronger self-image, 80%
stated that they had met their individual goals of improving
a basic skill, 50% believed that they had improved a skill
that could be applied to their daily work, and 77% of the
former students said that their lives had changed for the
better since first starting the classes. Marson (1977, July)
found, in a one-year cost benefit analysis study of nine
full-time vocational technical programs and 36 adult
education courses, that the benefits of these programs far
outweighed the costs. According to Marson's report (1977,
July), the cost-benefit ratio was 2.7 to 1.00 for society and
2.17 to 1.00 for an individual student. Again, although
these percentages appear to place adult education in a
favorable light, the study is plagued by many of the same
limitations of the other studies. Because the study is so
dependent upon the honesty of respondents, the study may be
biased by the halo effect. In other words, because the
respondents were successful, these individuals may have
exhibited a positive attitude toward adult education--however
unwarranted.
Within recent years some leaders in the Florida
legislature have demanded that adult educators justify their
programs through outcomes. Marson (1977, July) supported

47
this concept, which appears to be consistent with the growth
of the accountability movement in the general field of
education. Some political leaders in Florida are demanding
that adult educators adopt performance-based budgeting.
Arguments Against Funding Adult Education
Over the course of history, the view that literacy could
endanger the social structure of society was widely held by
the aristocracy. Donald (1991) attributed to Davis Giddy,
the president of the Royal Society in England during the
1800s, the following statement:
However specious in theory the project might be of
giving education to the labouring classes of the poor,
it would, in effect, be found to be prejudicial to their
morals and happiness; it would teach them to despise
their lot in life, instead of making them good servants
in agriculture, and other laborious employments to which
their rank in society has destined them. . . . [i]t
would enable them to read seditious pamphlets, vicious
books, and publications against Christianity; it would
render them insolent to their superiors; and in a few
years, the result would be, chat the legislature would
find it necessary to direct the strong arm of power
against them. (pp. 214-215)
Not surprisingly, because the French Revolution had occurred
not long before, the higher classes were dubious of educating
the masses. Although this statement appears out of context
in our modern world, some adult education administrators
stated that some of today's employers exhibit the attitude
that if their employees obtain more education, they will
leave and go somewhere else. This attitude may seem
surprising. Yet, some employers still think very much like
Giddy. However, the birth of the public schools in the

48
United States foretold the movement toward educating the
masses. Costa (1988) stated, "By this time [1918], all
states have [instituted] compulsory school attendance laws;
three states will later repeal theirs (South Carolina in
1955, Mississippi in 1956, Virginia in 1959)" (p. 7). Costa
continued, "By this time [1927], most states have passed laws
encouraging adult education. For example, California
requires illiterates between the ages of 18 to 21 to attend
school and has a literacy test for voters; Connecticut
requires school districts with over 10,000 residents to
maintain evening schools for persons over 14" (p. 9).
Finally, during the 1960s and 1970s there were tremendous
pressures on the states to support adult education programs.
Many of these programs were supported by the Adult Education
Act of 1966. Even with these movements, many experts are
opposed to using public funds to support adult education.
The arguments against funding adult education have
focused upon the economic benefits to society and to business
firms. Because of increased automation and the decreasing
need for workers, there is some question as to the need for
adult education for the training or retraining of workers for
different jobs. Hough (1987) postulated,
[S]ince unemployment is here to stay and therefore
labour surpluses will continue in the majority of
occupations for the foreseeable future, the government
should establish the scale of training activity on the
basis of social objectives. . . . [P]erhaps the main
problem involved in so doing would be the heavy strain
on public expenditure, quite apart from the economic

49
waste involved in providing training that might not
subsequently be put to good use. (p. 114)
Drennan (1980) concurred with Hough:
In a society incapable of supplying enough jobs for
everyone interested in working, these factors seem not
to have been explored deeply by either adult educators
or funders of adult education. In an economic sense the
ABE/ESOL graduate who replaces the less-educated worker
does not yield social profit; adult education programs
often accomplish their goal of rendering graduates
employable at the expense of already employed
nongraduates. Thus the net gain to society at large is
questionable, (p. 99)
Drennan further highlighted the difficulty of demonstrating a
causal relationship between adult instruction and benefits to
the individual in the following:
Even though many adults with limited basic skills who
enroll in ABE programs probably are gambling on the
purported causal relationship between education and
income, economists state that the relationship between
adult education and increased income has only the
slimmest of documentation nationally. It is difficult
to point to data which prove that a decade of remedial
adult education programs has lessened the rate of either
functional illiteracy among the undereducated adult
public or their unemployment--in real numbers or
percentages, (p. 99)
Since the beginning of history, the pursuit of adult
literacy has been a subject of constant debate. As
previously discussed, one argument holds that literacy might
have a negative impact on society. For instance, Kaestle
Damon-Moore, Stedman, and Trollinger (1991) wrote,
Although for purposes of public policy, increased
literacy is assumed to benefit both individuals and the
society as a whole, the association of literacy with
progress has been challenged under certain
circumstances. Paolo Freire has questioned whether
literacy is a good thing for oppressed people if the
content and conduct of literacy training are not under
their control. From a variety of political viewpoints,

50
American and British culture critics of the 1950s
questioned whether mass culture, including popular
reading materials, was debilitating to its consumers.
(p. 27)
Kaestle et al. quoted the Princeton historian Lawrence
Stone: "[T]hat if you teach a man to read the Bible, he may
also read pornography or seditious literature" (p. 27).
Obviously, the teaching of literacy in adult education is
dependent upon one's viewpoint, the illiterate individual in
question, and whose benefit is under consideration.
As to proving the economic benefits of those who would
become employed as a result of adult education, additional
theoretical problems are identified. For instance, when
examining the theories of the human capital approach, the
true value of adult education becomes unclear. Fagerlind and
Saha (1989) further observed that radical critics of
education believe that adult education may create a "docile
and adaptive work force which serves the needs of the power
structure of the economy. For the radical critics, an
education system which does not alter the structure of an
inequitable capitalist society, does not contribute to the
change and development of that society" (p. 49).
Research Findings Not in
Favor of Funding Adult Education
As has been stated earlier, most of the research in
adult education has been superficial. However, in one
dissertation study by Huffman (1992), the benefits of funding
vocational education appear mixed. Huffman analyzed the top

51
10 vocational education programs in Mississippi and compared
the amount of funding the programs received with their
individual rankings. Huffman reported the following
important relationships.
1. The programs that spent less on teacher salaries had
better rankings, which suggests that the programs
were smaller and perhaps the students had more
individualized assistance.
2. The less money spent on teacher travel--the better
the ranking. More time with students may
significantly increase enrollment, completion, and
placement.
3. The less spent on contractual services--the better
the ranking.
4. The less spent on supplies and materials--the better
the ranking.
5. The intercorrelation did indicate that the less spent
on facilities--the better the performance.
6. Equipment costs did affect the program performance
ranking, but the less spent on equipment—the better
the ranking.
7. The enrollment was related to costs and indicated
that as enrollments decreased, program costs/FTE
increased. (pp. 95-97)
Although these controversies apply to vocational
education, the same expenditures may come into question in
adult education. Would this mean that if less money were
spent on adult education programs, there would be a higher
success realized from adult education students? This is a
question that is unanswered and may need further study.
Finally, another researcher discovered that the dollar
amount spent on adult education courses may not be the issue.
The real issue may be how the monies are spent on adult

52
education. As indicated previously, Rose (1990) found that
"students, particularly mandated students, know that they can
sit around doing very little, take long unofficial breaks,
and basically not be there except in body, if that is what
they choose" (p. 127).
Three adult education administrators who were
interviewed in preparation for this study had mentioned the
above dilemma. According to them, about 50% of the adult
education students will never pass ABE Level 2 or reach the
grade of 8.9. Thus, for perhaps 50% of the adult education
students, the state monies may be wasted. Even worse
percentages were revealed when discussing the percentage of
those passing the GED or receiving the adult high school
diploma and the total population of adult education students.
Thus, the jury may still be out on the true value of present
adult education programs.
Quantitative Methods Used for
Evaluating Educational Programs
Few quantitative studies have been performed on the cost
benefits of adult education. Except for Burket's (1992) and
Huffman's (1992) related research in vocational education,
few studies have attempted to relate the benefits of adult
education with its costs. Such a study should add to the
knowledge base in this area.
The use of systems like PPBS (planning-programing
budgeting system) was emphasized during the surge of
education acts passed by Congress in the 1960s. Because of

53
the need for efficiency and "getting things done," PPBS
became a code word among educators during the 1960s and early
1970s. However, PPBS and related systems were not widely
accepted in the field of education, and few of these systems
survive today. In the field of vocational education,
competency-based and performance-based evaluations have been
used since the early 1970s. Many of these programs
emphasized placement, so the final goal of employment was
tied to the funding of the vocational program. Huffman
(1992) wrote,
Several studies highlighted specific factors or outcome
variables which should be analyzed in a technical-
vocational performance evaluation, such as: enrollment
data, job placement, community support, student
performance, student aspirations, economic benefit,
employer satisfaction, service to special populations,
and overall cost-effectiveness, (p. 24)
However, limited literature exists concerning the use of
competency-based or performance-based evaluation or funding
in the field of adult education. One reason for such
omissions is the special nature of adult education. Unlike
vocational education, adult education does not have the goals
of instructing the students in specific skills for specific
jobs. Furthermore, employer expectations of vocational
education graduates range from their possessing the ability
to pass exams for licenses and certifications to their being
able to operate complex machinery. These expectations are
absent in adult education.

54
In order to review the literature most relevant to adult
education, it is important to look at attempts at evaluating
either K through 12 programs or programs in higher education,
such as those at community colleges and universities. The
literature centers upon the evaluation of costs incurred in a
program. Most of the literature in adult education has
utilized cost-benefit models for evaluation techniques.
For instance, Steele (1971, July) surveyed the
possibility of applying cost-benefit techniques to adult
education. She concluded that cost-benefit techniques were
used in adult education programs that achieved economic
outputs and were closely associated with industry. Steele
concluded that, while cost-benefit models are useful in
education, a more encompassing input-output analysis would be
more useful because such a model could deal flexibly with
human variables within an educational system. Marson (1977,
July) also mentioned the possibility of using a cost-benefit
method for evaluating adult education. In Marson's study,
two cost-benefit models were tested on nine full-time
vocational technical programs and 63 adult education courses,
which reflected many different instructional areas in
vocational technical education. His findings were that the
benefits from vocational education programs and noncredit
education courses did outweigh the cost of the courses. Even
with these findings, the limitations on cost-benefit analysis

55
are such that other possible methods of evaluation have been
suggested.
Determining the costs to assign to the benefits of adult
education may be difficult. First, if Net Present Value
(NPV) techniques are used, the researcher may have difficulty
in selecting appropriate discount rates. Furthermore, the
measurement and identification of indirect costs and
nonmonetary benefits in an educational organization are
difficult to apply to specific programs. Because many
educational benefits are intangible and are difficult to
quantify, the use of any costing formula would be held
suspect as a means for measuring educational outcomes
(Campen, 1986). Huffman (1992) observed,
Levine in 1981 noted that there were serious "data
limitations and ambiguities" in cost-benefit analysis of
human service programs. Shugoll and Helms (1982) and
Levin (1983) indicated that cost-benefit analysis had
significant limitations in measuring educational costs
and benefits. Campen (1986) argued that cost-benefit
analysis was "procedurally inappropriate" for
establishing public policy since it attempted to
subrogate the importance of "social ethics; rights,
entitlements, and due process; the political process;
and environmental values." (p. 46)
Rothenberg (1975) stated that "one of the truly serious
difficulties in conducting cost-benefit studies is the lack
of bases on which to value the flow of public services or the
benefits from public projects" (p. 78).
The concepts of cost-effectiveness and cost-feasibility
have been suggested as possible educational measures.
According to Levin (1983),

56
Under cost-effectiveness analysis, both the costs and
effects of alternatives are taken into account in
evaluating programs with similar goals. It is assumed
that (1) only programs with similar or identical goals
can be compared and (2) a common measure of
effectiveness can be used to assess them. These
effectiveness data can be combined with costs in order
to provide a cost-effectiveness evaluation that will
enable the selection of those approaches which provide
the maximum effectiveness per level of cost or which
require the least cost per level of effectiveness, (p.
18)
However, Levin (1983) reported the following strengths and
weaknesses of the cost-effectiveness model:
The cost-effectiveness approach has a number of
strengths. Most important is that it merely requires
combining costs data with the effectiveness data that
are ordinarily available from an educational evaluation
to create a cost-effectiveness comparison. Further, it
lends itself well to an evaluation of alternatives that
are being considered for accomplishing a particular
educational goal. Its one major disadvantage is that
one can compare the CE [cost-effectiveness] ratios among
alternatives with only one goal. (p. 21)
The same problems that affect the cost-effectiveness
approach also plague the cost-utility approach. Levin (1983)
continued,
The major disadvantage is the fact that the results
cannot be reproduced on the basis of a standard
methodology among different evaluators, since most of
the assessments are highly subjective ones that take
place in the head of the person doing the evaluation.
Another evaluator with the same information and
methodology may derive a drastically different result by
using a different set of probabilities and utilities.
(p. 29)
Finally, Levin (1983) concluded that cost-feasibility
analysis "can determine only whether or not alternatives are
within the boundaries of consideration" (p. 30). Because of
these weaknesses, an evaluation of adult education would be

57
best suited to an input-output model, which optimizes the
outputs of adult education based upon the budgetary
constraints existing at the time of the evaluation. Such a
condition would imply that adult education programs can best
be evaluated by using the input-output model. According to
McAfee (1972),
The review of the literature appears to justify the
following generalizations.
1. There is a need for decision-making based upon input-
output relationships.
2. The challenge for input-output studies is to
determine the proper mix of inputs that will maximize
output.
3. In general, input-output studies have not interfaced
with cost-effectiveness studies.
4. Serious reservations regarding methodology in input-
output studies have been expressed.
5. A mathematical model is appropriate for
systematically determining optimal allocation
strategies, (p. 29)
Mathematical models have been used to determine funding for
education in K through 12 and other educational programs
(Johns, 1976, Fall). This mathematical model is discussed
more fully in Chapter 3.
Chapter Summary
The release of a recently completed national study of
adult education needs in the United States revealed that 90
million American citizens were seriously deficient in
literacy skills, and many of these persons did not realize
their predicament. Moreover, the literature indicated that

58
in other advanced nations (e.g., Canada, England, Sweden,
France), there was an acute need for adult education
programs. Some writers expressed concern for the survival of
society without attention to adult education needs.
The emphasis for adult education programs was on program
outcomes. Although the obvious social benefits of adult
education were mentioned, the modern view of adult education
was redirected toward cost effectiveness. More and more
scrutiny was being placed on the success rate of adult
education programs. According to an abstract of Mason's
(1988) article, adult educators have not received the
recognition for the contributions they have made to local
economies; therefore, they should rethink their rationale,
reject outmoded beliefs and patterns, and justify their work
through program outcomes (ERIC Document number EF378460) .
Several programs have been reviewed and have been found to be
beneficial to society. For instance, as indicated
previously, Kwon (1990) remarked in a conference speech that
a review of all qualitative data obtained from the Michigan
study revealed that the program contributed economic and
noneconomic benefits to the participants, the organizations,
and society (ED326656).
The benefits of adult education are mostly accepted in
the literature. Qualitative measures have been successful at
determining the beneficial outcomes of adult education.
However, the use of quantitative measures to evaluate adult

59
education programs has shown mixed results or has not been
tried. There is little evidence that performance-based
budgeting has been used in any educational programs. A
review of the literature reveals no evidence of utilizing
performance-based budgeting for funding adult education.
Although their opinion was very much in opposition to
traditional American thought about the value of an educated
citizenry, some persons opposed the education of adults on
the basis that helping persons become literate might make
them unhappy with life and produce instability in society.
But, some writers opposed adult education programs on the
basis that they waste taxpayers' money in addition to
creating additional problems for the government. Also noted
was the opinion that further education of adults might
destroy a stable source of unskilled labor and the economic
system.

CHAPTER 3
PROCEDURES
Introduction
The purpose of this study was to develop and analyze a
mathematical model to optimize the funding for adult
education programs in Florida through the simultaneous
solution of linear and nonlinear formulations. For purposes
of this study, the evaluation of data items used in these
formulations must be evaluated using statistical techniques
to determine their relevancy and validity. Upon
determination of their relevancy, further statistical
analysis will help determine the variables that are key
contributors of success in adult education.
Procedure of this Study
The procedure used for this study was to formulate
production models and use stepwise linear and nonlinear
programming techniques to optimize models to reveal the most
efficient and cost-effective factors in adult education
funding. By simultaneous solution of these models, the
process would determine how adult education funding should be
allocated to maximize the greatest outputs. Although this
study utilized nonlinear models, a review of linear
programming explains some of the complexities of nonlinear
60

61
programming. According to Sultan (1993), "In linear
programming, one studies the best way to allocate limited
resources" (p. 1). Dorfman, Samuelson, and Solow (1986)
defined linear programming as "the analysis of problems in
which a linear function of a number of variables is to be
maximized (or minimized) when those variables are subject to
a number of restraints in the form of linear inequalities"
(p. 8). The present study utilized an input-output model to
find the best way to allocate the resources of adult
education.
Hillier and Lieberman (1974) pointed out that linear
programming is based on four main assumptions:
proportionality, additivity, divisibility, and that all
parameters of the model are deterministic. They gave the
following example of proportionality:
The assumption is that in this case (1) the measure of
effectiveness Z [dependent variable] equals [C is
the coefficient of the independent variable X and k is
the subscript of the activity for n activities or
observations], and (2) the usage of each resource i
equals A^X*; that is, both quantities are directly
proportional to the level of each activity k conducted
by itself (k = l,2,...,n). [A is coefficient of the
independent variable X for each activity k for each
independent variable X]. (p. 22)
The magnitude of each effect is proportional to the amount of
activity governing the effect in the model.
Hillier and Lieberman stated that "the additivity
assumption requires that, given any activity levels (Xi,
X2,...Xn) , the total usage of each resource and the resulting

62
total measure of effectiveness equal the sum of the
corresponding quantities generated by each activity conducted
by itself" (p. 23). Of course, this assumption applies only
to linear functions and would not always be possible for
nonlinear formulations.
Hillier and Lieberman continued, "Therefore, the
divisibility assumption is that activity units can be divided
into any fractional levels, so that noninteger values for the
decision variables are permissible" (p. 23). Finally, all
parameters of the model must be deterministic. Although
the parameters of nonlinear models sometimes are
undeterminable, the necessity for known parameters limited
the formulations used in this study. The solution of these
parameters was estimated using multiple regression analysis,
which is discussed later in this chapter.
Linear programming also entails certain properties that
may or may not apply to some nonlinear models. Nonlinear
models would be defined as mathematical models that involve
nonlinear functions to describe the relationship between the
dependent variable and the independent variables. First,
this study assumed that all models were standard. According
to Sultan (1993), "If we drop the requirement that all the
variables be nonnegative in a linear program, then the
program falls under the category of problems called
nonstandard. . . . Unless explicitly stated otherwise,
however, all programs will be standard. That is, all

63
variables will be > O" (p. 50). This study assumed that all
variables are nonnegative, with the requirement of
nonnegativity referring only to variables. Parameter
estimates that demonstrate the effect of the independent
variables on the dependent variable may be negative.
Another assumption concerning most linear models is that
they will be canonical. Sultan also stated, "Then we say
that the linear program is in canonical form if all of the
main constraints are equations, and we can pick out from each
main constraint one variable that occurs only in that
equation, and which has coefficient 1" (p. 52). Since the
purpose of this study was to maximize outputs in response to
restricted resources, a maximization program was adopted.
Sultan continued by stating that a "standard maximum linear
program is one in which (a) the objective function is to be
maximized, (b) all the main constraints are of the type 'less
than or equal to constants,' and (c) where all the variables
are nonnegative" (pp. 149-150). Any maximization program can
be made a minimization program by multiplying the models by
negative 1. Sultan defined the minimization program as
follows: "A standard minimum program is one where (a) the
objective is to be minimized, (b) all the main constraints
are of the form 'greater than or equal to constants,' and (c)
the variables are nonnegative" (p. 150). Hence, this study
focused on the maximization of the production model in order
to maximize output.

64
Because the adult education field possesses many goals,
this study needed to adopt a model to allow for the
simultaneous solution of multiple optimizations. Goal
programming could be used in linear programming to attempt to
optimize multiple goals. While a company may use linear
programming to maximize profits or minimize costs, goal
programming allows for several goals to be resolved
simultaneously. Sultan (1993) explained, "One great
advantage of this technique is that it allows us to treat
several objectives at once even though these objectives may
be measured in different units, and even though these
objectives may be incompatible" (p. 473). The goals of
graduating from different ABE levels or obtaining the GED or
simply transferring to a new educational program may be
included in goal programming. Goal programming allows for
several objective functions or production models, so that all
goals are included in the optimization model. Although goal
programming may be utilized to find solutions to multiple
goals in linear programming, such formulations may fail
because of constraint problems. According to Sultan, "Of
course, there is the question of how we incorporate these
goals into a linear program, since solving linear programs
does not allow for the violation of the constraints" (p.
476). Sultan best describes the problems encountered with
linear programming in the following:
If in a goal we are indifferent as to whether we
underachieve or overachieve a target, then the variables

65
u and v both occur in the objective function. If it is
more desirable that we underachieve a target than
overachieve a target, then only the overachievement
variable associated with that goal occurs in the
objective function. If it is more desirable that we
overachieve a target than underachieve it, then only the
underachievement variable associated with the goal
occurs in the objective function. . . . This also
illustrates how drastically a solution can change by
changing a goal. (pp. 479-480)
McAfee (1972) concurred with Sultan in the following:
"Consequently, it would be vain to hope to maximize the
outcomes of each student in several different areas. In the
utility function [optimization function or formula], only a
few of the outputs would be maximized, at the expense of
other outputs" (p. 51). Thus, any formulation that embraces
the optimization of outputs with the attainment of several
goals would require the complexity of nonlinear programming
models. A study could utilize only linear models; however,
linear programming is plagued with two major limitations that
would not only decrease the magnitude of a study, but could
jeopardize the purpose of the study, which is to determine
how scarce resources should be allocated. According to
Phelps (1992, March),
While Linear Programming appears to address most of the
criteria, the remaining few are so critical that they
easily become "fatal." . . . Non-linear Optimization
addresses these two last criteria: (1) changing returns
or nonlinear relationship between the Outcomes and the
Effects; and (2) finding an optimal solution without
having intersection between competing Effects (some
positive and some negative). (p. 32)

66
Most importantly, the nonlinear programming model allows for
a "built-in" balancing effect, so that effects that result in
a negative value do not negate potentially positive
characteristics of those same effects included as factors in
the optimization model.
Phelps (1992, March) listed the following important
properties of nonlinear modeling:
Non-linear optimization measures the multiple outcomes
and the relationship between the outcome and effect in
terms of the non-linear and bounded values, (p. 33)
Non-linear optimization easily uses the non-linear
function of "cumulative standard normal probability."
In many ways, this is the most unique feature of the
education production model being presented, (p. 34)
Non-linear optimization allows--indeed requires--cost to
be included as a constraint and provides the resulting
interpretation of "what is the most efficient and
effective combination of effects given the given costs
constraint?" (p. 34)
Non-linear optimization allows the relationship between
and among effects to be defined as additional
constraints, (p. 34)
The properties of the constraints or boundaries of
nonlinear models require further discussion. The constraints
used in nonlinear programming are known as functional
constraints, set constraints, and active constraints.
According to Luenberger (1989),
It is clear that, if it were known a priori which
constraints were active at the solution to (1) [minimize
f(x) subject to hl(x) = 0 etc.], the solution would be a
local minimum point of the problem defined by ignoring
the inactive constraints and treating all active
constraints as equality constraints. Hence, with
respect to local (or relative) solutions, the problem
could be regarded as having equality constraints only,
(pp. 296-297)

67
Thus, for purposes of simplification, an assumption can be
made where all constraints are equality constraints.
Nonlinear programming fits nicely with the needs of
statewide budgets because of its magnitude. Luenberger
(1989) stated,
There are many examples of nonlinear programming in
industrial operations and business decision making.
Many of these are nonlinear versions of the kinds of
examples that were discussed in the linear programing
part of the book. Nonlinearities can arise in
production functions, cost curves, and, in fact, in
almost all facets of the problem formulation, (pp.
305-306)
Since nonlinear programming was necessary for this
study, alternative techniques for determining the parameters
of the production model were required. Furthermore, the very
complexity of nonlinear models required the use of computer-
based solutions. Nakamura (1993) wrote:
The primary reason why we solve nonlinear equations by
using computer methods is that nonlinear equations have
no closed-form solution except for very few problems.
Analytical solution polynomial equations exist up to the
fourth order..., but there are no closed-form solutions
for higher orders. Therefore, roots of those nonlinear
equations are found by computer methods based on
iterative procedures." (p. 65)
The methods by which the production model parameters are
estimated will be discussed later.
Population for the Study
The population for this study consisted of all districts
and adult education centers in Florida. Based on the
information obtained from scholars of adult education, it was
determined that accurate data on GED and ABE program

68
performance were indefinite for most of the states; however,
all states must report annually to the federal government the
results of their adult education programs. The data for this
study were taken from Florida's reports to the federal
government for the fiscal years of 1991-92 and 1992-93.
Research Design
The research design was based upon a data set with 85
observations for fiscal year 1992-1993 and 5 unduplicated
observations from fiscal year 1991-1992 on 12 variables for
the dependent variable (i.e., number passing the GED or
receiving the Adult High School Diploma); 1 cost variable for
all 90 observations based on the 85 local education agencies
for fiscal year 1992-1993 and 5 unduplicated local education
agencies for fiscal year 1991-1992 that offered adult
education courses--all representing more than 1,300 data
items. Even though the observations are from two different
years, the 5 observations from fiscal year 1991-1992 are not
duplicated in the 1992-1993 year (i.e., the same students
were not included in both years' data). These 5 observations
were from organizations such as Action, Inc., the Dozier
Schools, Dixie County School District, Glades County School
District, and Washington County Council on Aging, Inc.
Therefore, inclusion of these local education agencies in the
data increased the total number of observations to 90.
Stepwise regression was utilized to determine the major
factors influencing the success factors. Because of the low

69
observations to variable ratio (8 to 1), an alpha level of
.05 was used to increase the power of the test statistics
while using the stepwise method.
The two outputs, the GED and the Adult High School
Diploma, were accomplishments verified, using standardized
tests. These tests were either statewide or nationally
recognized as demonstrating student achievement above a
minimum level of educational attainment. Therefore, this
study had verifiable evidence of student accomplishment with
standardized tests. Although the attainment of the Adult
High School Diploma required the completion of different
courses than the courses used for preparing for the GED, both
the Adult High School Diploma and the GED were considered
equivalent. Also, the expenditures for adult education could
not be allocated to either the GED students or the students
of the Adult High School. Thus, the success on the GED was
combined with completion of the Adult High School Diploma to
create one success variable. Furthermore, passing rates for
the students on either the GED or Adult High School Diploma
were not available. Therefore, the dependent variable or
success variable encompassed the percentage of the total
student population who completed the GED or the Adult High
School Diploma. The mathematical model was developed from
the use of stepwise regression techniques by using the sum of
the GED and Adult High School Diploma as the dependent
variable. A second model which was developed from the

70
stepwise method was then used to determine the coefficients
for the budgetary model. The final expenditures of fiscal
years 1992-1993 and 1991-1992 for the 90 local education
agencies were used as the dependent variable for the second
model. Other important constraints were developed and used
as constraints on spending. Finally, the first model was
maximized by using a solution of simultaneous equations with
the second model or budgetary model. Constraints on the
maximization of the simultaneous resolution were included in
the process of simultaneous equations.
The local education agencies included public school
districts, community colleges, correctional institutions,
other institutions, local libraries, and other state agencies
offering adult education courses. To obtain the most current
picture of the relationship between adult education funding
and the many variables tested, the latest Adult Education
Reports sent to the federal government were used as the
source for all data items. These reports encompassed data
collected for fiscal years 1991-1992 and 1992-93. Since any
regression formulation must be based upon sound research
theory, the 12 variables were selected because previous
research revealed the importance of these variables in the
determination of success in education. Furthermore, the
federal government has mandated that these data items be
reported annually to the U. S. Department of Education.

71
Statement of Variables
The independent variables associated with the
participant inputs for the dependent variable of GED and
Adult High School Diploma for adult education were listed by-
category.
The variables associated with student factors were as
follows:
Xl--Percentage of students (Adult Education students)
who were enrolled in other educational programs. This
percentage was calculated by dividing the number of
students of each local education agency (LEA) who were
enrolled in other educational programs by the total number of
students at each LEA.
X2--Percentage of students who were female. This
percentage was calculated by dividing the number of female
students at each LEA by the total number of students at each
LEA.
X3--Percentage of students who were handicapped. The
percentage was calculated by dividing the number of
handicapped students at each LEA by the total number of
students at each LEA.
X4--Percentage of students who were eligible legalized
aliens. The variable was calculated by dividing the total
number of eligible legalized aliens in each LEA by the total
number of students at each LEA.

72
X5--Percentage of students who were in correctional
institutions. This percentage was calculated by dividing the
number of adults in correctional institutions at each LEA by
the total number of adults at each LEA.
X6—Percentage of students who were employed. The
percentage was calculated by dividing the number of
students who were employed for each LEA by the total number
of students at each LEA.
X7--Percentage of students who were receiving public
assistance. The percentage was calculated by dividing the
number of students who were on public assistance and/or
homeless at each LEA by the total number of students at each
LEA.
The variables associated with school factors were stated
as follows:
X8--Percentage of teachers who were part-time. This
percentage was calculated by dividing the total number of
part-time teachers by the total number of staff members in
adult education. The staff in adult education was defined as
the part-time teachers, full-time teachers, volunteer
teachers, part-time paraprofessionals, full-time
paraprofessionals, part-time counselors, and full-time
counselors.
X9--Percentage of teachers who were full-time. This
percentage was calculated by dividing the total number of
full-time teachers by the total number of staff members in

73
adult education. The staff in adult education was defined as
the part-time teachers, full-time teachers, volunteer
teachers, part-time paraprofessionals, full-time
paraprofessionals, part-time counselors, and full-time
counselors.
X10--The ratio of state instructional salary
expenditures over total expenditures. This was calculated
by dividing the total instructional salary expenditures for
each LEA by the total expenditures by LEA. Total
expenditures included the expenditures of both state and
federal monies for instructional salaries, contracted
services or other personnel services, other expenses, and
equipment.
Xll—The ratio of state support personnel service or
contracted services expenditures over total expenditures by
LEA. This was calculated by dividing the total cost of other
personnel services by the total expenditures by LEA. The
total expenditures included the expenditures of both state
and federal monies for instructional salaries, contracted
services or other personnel services, other expenses, and
equipment.
X12—The ratio of state expenses of material and supply
expenditures over the total expenditures by LEA. This was
calculated by dividing the total cost of other expenses by
the number at each LEA by the total expenditures by LEA. The
total expenditures by LEA included the total expenditures of

74
both state and federal monies for instructional salaries,
contracted services or other personnel services, other
expenses, and equipment.
The dependent variables used in the study were as
follows:
Yl--Percentage of students who passed the GED or earned
an Adult High School Diploma. This variable was calculated
by dividing the total number of students who had passed the
GED or earned an Adult High School Diploma for each LEA by
the total number of students at each LEA.
Y2--The total adult education expenditures per student
by LEA divided by 1,000. This was calculated by dividing the
total costs (from both state and federal funding) incurred by
each LEA and then dividing this number by the number of
students of each LEA. The result of this calculation was
divided by 1,000 for scaling purposes. Thus, actual
coefficients have coefficeints that have moved the decimal
three places.
Selection of variables was based upon logic and, in some
cases, convenience. Because the focus of this study was on
the controllable costs of adult education, only the variables
which could be controlled by Florida and which are the
generator of expenditures for Florida were chosen. Most of
the 12 variables which were used for the model were the only
variables which the state could control for cost purposes.
Therefore, the 5 observations for fiscal year 1991-1992 and

75
the 85 observations for fiscal year 1992-1993, which total 90
observations, represented an 8-to-l ratio of observations to
the variables. Multiple regression techniques were used to
determine the major factors for the optimized model.
Although the number of legalized aliens and students
enrolled in other educational programs were not reported on
the 1992-1993 Federal Report, these variables had been
reported in the 1991-1992 Federal Report. The number of
legalized aliens and students enrolled in other educational
programs had been reported for the three previous fiscal
years of 1988-1989, 1989-1990, and 1990-1991. Therefore,
these variables were included in the Adult Education Model.
Teaching in adult education in Florida is mostly done by
part-time teachers from the pre-K through 12 program and
volunteers. Some of the vital statistics for part-time
teachers are listed in Tables 1 and 2. The totals for the
volunteer counselors and paraprofessionals were excluded due
to lack of data for these categories.
Since the state does not pay volunteers, teaching
quality in the volunteer program is questioned. Furthermore,
the state has no control over the number of volunteers
recruited. Thus, since these volunteers are unpaid and the
state cannot predetermine the number of volunteers recruited,
the variables involving the number of volunteer counselors
and paraprofessionals were ignored in this study.

76
Table 1
Vital Statistics on Part-Time Teachers for 1991-1992
Description
Number
Percentage
Part-time teachers
7,454
60
Full-time teachers
827
7
Part-time paraprofessionals
429
3
Full-time paraprofessionals
148
1
Part-time counselors
275
2
Full-time counselors
174
2
Volunteer teachers
3 . 176
25
TOTAL
12,483
100
Table 2
Vital Statistics on Part-Time
Teachers
for 1992-1993
Description
Number
Percentage
Part-time
teachers
7,671
60
Full-time
teachers
886
7
Part-time
paraprofessionals
491
4
Full-time
paraprofessionals
190
1
Part-time
counselors
285
2
Full-time
counselors
190
2
Volunteer
teachers
2.999
24
TOTAL
12,712
100

77
The use of so many part-time teachers and para-
professionals made the analysis of whether part-time teachers
and paraprofessionals were better or worse than full-time
teachers impossible. Also, certification is not required for
many paraprofessionals. Thus, the quality of assisted
teaching of the paraprofessionals was a major question that
could not be answered. However, the costs to the state for
these paid individuals made their presence significant to the
study. Therefore, variables for the costs of these full¬
time and part-time teachers were used in the study.
As stated previously, forward, backward, and stepwise
procedures were used to determine the parameter estimates of
the linear equation. After these estimates were determined,
two separate linear equations were developed using stepwise
regression with two separate dependent variables. The
dependent variables that reflected the successes or outputs
of the two equations were the total number of individuals who
either passed the GED or received the Adult High School
Diploma.
After the two production equations were solved simul¬
taneously, a nonlinear formulation was attempted. By using
the PROC NONLIN command with SAS, the program used the Newton
method of elimination to develop the nonlinear formulation,
which best describes the process of adult education funding.
The PROC NONLIN does not guarantee that such a developed
equation is truly representative. Furthermore, an

78
examination of the results of the PROC NONLIN procedure
should not be used unless the estimated model demonstrates a
strong significance with the dependent variable.
As was stated previously, since some of the nonlinear
equation calculations demanded nonanalytical solutions, the
parameter estimates required the numerical solutions of
nonlinear equations. Furthermore, the need to increase the
number of variables based on further hypothesized effects
required the use of analytical procedures. However, as will
be seen in Chapter 4, linear models developed with multiple
regression appeared to be the best equations for the purposes
of this study.
Collection of Data
Data from the Florida Department of Education were used
to construct and pre-analyze the proposed formula. Data
about funding levels, GED and ABE performance, and related
information were collected from directors of adult education
programs in Florida, and the annual report, which is
submitted to the federal government, was used for analysis of
the developed formula. The annual report is not broken down
by local education agencies. However, the reports that were
produced by the individual local education agencies were
summarized, so that specific data concerning each agency were
obtained. Therefore, summary reports were used to develop
the 90 observations that were discussed in the section titled
"Research Design" (see p. 68). The numbers in these reports

79
were correlated using multiple regression techniques to
determine the parameters of the mathematical models.
Interviews from adult education administrators and expert
faculty of adult education were also used to determine the
funding effects and the estimate of the constants in the
production function.
Although many of the experts interviewed in this study
mentioned that transportation and child care would improve
the success rates of adult education centers, these possible
additions to adult education funding were not included.
Because Florida political leaders have voiced strong
opposition to transportation and child-care costs, these
factors were not considered feasible as state expenditures.
The emphasis was on feasibility of legislative approval of
the factors included. Based on current information, it was
decided that transportation and child care are not likely to
be adopted now, or in the near future, by federal or state
politicians. The emphasis in this study was on optimal
outputs under existing legislation. Furthermore, because
every effort is made to locate the adult classes as close to
the residential areas of the pupils as possible,
transportation was not considered a factor in the funding of
adult education.
Analysis of Data
First, the data were analyzed using PROC MEANS and PROC
CORR procedures on the SAS system. Because of the low ratio

80
of observations to variables, the most prominent variables
were selected for study. The 5-to-l ratio of observations to
variables is a strongly recommended minimum ratio in research
using multiple regression. According to Stevens (1992),
"Many of the popular rules suggest that sample size be
determined as a function of the number of variables being
analyzed, ranging anywhere from two subjects per variable to
20 subjects per variable. And indeed, in the previous
edition of this text, I suggested 5 subjects per variable as
the minimum needed" (p. 384). In discussing stepwise
discriminant analysis, Stevens wrote, "The F's to enter and
the corresponding significance tests in stepwise discriminant
analysis must be interpreted with caution, especially if the
subject/variable ratio is small sav < 5" (p. 284).
Two major assumptions must be met when using multiple
regression analysis to determine a regression model.
According to Chatterjee and Price (1991), "The assumptions
are (1) the explanatory variables are nonstochastic, that is,
the values of the x's are fixed or selected in advance, and
(2) the x's are measured without error. These assumptions
cannot be validated, so they do not play a major role in the
analysis. However, they do influence interpretation of the
regression results" (p. 67). Once these assumptions have been
accepted, then the researcher can follow certain steps to
determine variable selection.

81
The major procedures usually employed by researchers to
develop a mathematical model for testing are the forward
selection method, the backward elimination method, and the
stepwise method. The forward selection technique was
employed first. In the forward selection technique, the F
statistics are calculated for each of the independent
variables. The results of the forward selection procedure
revealed the variables which would give the largest F
statistic and R squared. Chatterjee and Price (1991)
reported,
The forward selection procedure starts with an equation
containing no explanatory variables, only a constant
term. The first variable included in the equation is
the one which has the highest simple correlation with
the dependent variable y. If the regression coefficient
of this variable is significantly different from zero it
is retained in the equation, and a search for a second
variable is made. The variable that enters the equation
as the second variable is one which has the highest
correlation with y, after y has been adjusted for the
effect of the first variable, that is, the variable with
the highest simple correlation coefficient with the
residuals form step 1. The significance of the
regression coefficient of the second variable is then
tested. If the regression coefficient is significant, a
search for a third variable is made in the same way.
The procedure is terminated when the last variable
entering the equation has an insignificant regression
coefficient or all variables are included in the
equation, (p. 236)
The backward elimination method is described by Agresti
and Finlay (1986) as follows:
The backward elimination procedure works in the reverse
direction from the forward selection method. In
backward elimination, we begin by placing all of the
independent variables under consideration in the model.
If they all make significant partial contributions, then
that model is the final one. Otherwise, the independent
variable having the least absolute partial correlation

82
with Y, controlling for the other independent variables,
is removed from the model. Next, for the model with
that variable removed, the partial correlations with Y
and each Xi (controlling for the other variables still
in the model) are recomputed. If they are all
significant, that model is the final model. The process
continues until each remaining independent variable
makes a significant partial contribution to explaining
the variability in Y. (p. 379)
The stepwise procedure was performed in addition to
forward and backward elimination. According to Chatterjee
and Price (1991),
The stepwise method is essentially a forward selection
procedure but with the added proviso that at each stage
the possibility of deleting a variable, as in backward
elimination, is considered. In this procedure a
variable that entered in the earlier stages of selection
may be eliminated at later stages. The calculations
made for inclusion and deletion of variables are the
same as FS and BE procedures. Often, different levels
of significance are assumed for inclusion and exclusion
of the variables from the equation, (p. 237)
In order to select the proper variables needed in the
model, the researcher determined the theoretical significance
to the model. In other words, common sense, past research,
or sometimes just plain guessing was used to determine the
variables that should be included in the model.
The summarized results of the backward elimination
method listed the variables that were considered by the
stepwise method. Although the original ratio of observations
to variables was 8 to 1, the true ratio of observations to
variables was much higher because the final summary of the
backward elimination method included only the variables
considered in either the forward selection method or the

83
stepwise method. Therefore, the final ratio of observations
to variables became much higher than 10 to 1.
Even though there is a need to address theoretical
considerations and to choose the best method of variables
selection, the major purpose of this study was exploratory.
Agresti and Finlay (1986) concluded, "In exploratory
research, on the other hand, the goal is not to explain
relationships among variables so much as it is to find a good
set of predictors" (p. 380). Thus, the purpose of this study
was to predict the optimized cost of adult education funding
in Florida.
According to experts in adult education, the measures of
success, for which data were considered most reliable, were
graduation rates on the General Education Development (GED)
test and completion rate for the Adult High School diploma,
as defined by the Florida's Program and Plan for Adult
Education (State of Florida, Department of Education,
Division of Vocational, Adult, and Community Education, 1989-
1993). These success variables were treated as dependent
variables in order to determine if changes in adult education
funding affected success variables.
The constraint on maximization of outcomes was the
funding level of adult education based upon the total
expenditures for adult education from all 90 local education
agencies for fiscal years 1991-1992 and 1992-1993. The two
regression equations were determined using the several

84
variables stated above. The B coefficients were estimated
using multiple regression analysis, and the final optimized
formula was determined using both linear and nonlinear
programming techniques, as discussed below. The production
model (first model) is stated as follows:
Y1 = LI * (B1)X1 + L2 * (Bn)X2 + ... Ln * (Bn)Xn.
The above production function was determined from the
stepwise regression performed on the first dependent variable
Y1 and the 12 independent variables stated previously. This
production function was solved subject to the expenditure
model (second model):
01 > LI * (B1)X1 + L2 * (B2)Xn + ...Ln * (Bn)Xn.
The above constraint was determined by using the
coefficients which were calculated using stepwise regression
for the variable Y2 and the corresponding 12 independent
variables. The variable 01 was the total expenditures for
adult education for fiscal year 1992-1993 and the total
expenditures for the 5 selected LEAs for fiscal year 1991-
1992. This total was then adjusted for possible errors of
truncation.
Equation symbols were defined as follows:
Yl = The amount of the outcome based upon the
performance of a local education agency (passing the GED,
receiving the Adult High School Diploma).

85
01 = The total expenditures for adult education for
Florida divided by 1,000. [The division by 1,000 is required
to scale the total expenditures in order to prevent
truncation errors ($1 = $1000).]
Ln = The unit measure of the effect in a nonlinear
function.
Bn = The magnitude of the relationship or the
coefficient obtained by using stepwise regression.
Budgetary constraints were based on the funding
(expenditures) of each district in Florida. The equation of
the funding of budgetary constraints was as follows:
Tn > Xn > Mn.
Tn = The minimum level of the respective effect.
Mn = The maximum level of the respective effect.
Xn = The variable representing the amount of the respective
effect.
Since the above equations were generic to the many
outcomes of the simulation, a more specific listing of the
several outcomes was revealed, and the result of the
simultaneous equations was one final production equation.
The final equation for the production model was as follows:
Y1: Completion of the GED and Adult High School Diploma.
The equation would be as follows:
Y1 = Z1 * PI +... Zn * Ln.

86
The symbols for the above-stated equations were as
follows:
Pn = Vector of student or school factors to the nth
local education agency.
Ln = Vector of school factors by the ith local education
agency.
Zn = The nonlinear effect of each of the above vectors.
The mathematical model states the outputs of an individual
(nth) LEA equal the profile of the student Pn and the LEA'S
contribution to education Ln.
Development of Vectors to Determine
Effects and Magnitude of Effects
The variables used in the least-squares equations were
the many data items obtained from Florida's Adult Education
Annual Performance Report. Fiscal Year 1993. These variables
were grouped by their effects of community inputs, school
inputs, student ability inputs, and the endowment position of
the student. Since this study required that nonlinear
programming be used to optimize adult education funding, a
review of the techniques to determine the production model's
parameters was necessary. The estimations of a model's
parameters were performed using either analytical or
numerical techniques. Much of the research, particularly in
engineering and science, has emphasized numerical techniques.
However, the social sciences have used more analytical
techniques, such as the stepwise regression method. McAfee

87
(1972) used such stepwise regression techniques in his study-
on K through 12 funding. According to Darlington (1990),
The first method is stepwise regression. Standard
computer programs for stepwise regression differ from
each other more than do standard programs for ordinary
regression, so we shall describe the method only in
general terms. Both "forward" and "backward" versions
exist. (p. 165)
In this study the stepwise regression model was used
because of its simplicity. Furthermore, any additional
predictions for production function parameters used the
stepwise regression method.
The SAS computer program was utilized to determine the
parameters or fitting of the nonlinear relationships of the
production functions. Darlington (1990) stated,
There are some very general methods for fitting curves
or curved surfaces to data, as represented, for
instance, in SAS PROC NLIN or the STSTAT program NONLIN.
These are sometimes called nonlinear regression methods.
However, they are in fact not based on regression
methods, so we might better call them general curve-
fitting methods. (p. 279)
The estimates of the coefficients of the production
function were estimated by using multiple regression
analysis. After the production function was determined, the
production function was solved with the budgetary constraints
by using mathematical programming. A software program using
the SAS statistical package was used to solve simultaneous
equations. The results of the simulations are presented in
Chapter 4.

CHAPTER 4
PRESENTATION OF THE DATA
Introduction
As stated previously, the purpose of this study was to
develop and analyze a mathematical model to optimize the
funding for adult education programs in Florida. The
simultaneous solution of linear and nonlinear formulations
was attempted to develop the mathematical model. The final
mathematical model created by the procedures in this study
was formulated using raw data concerning adult education.
Because the data used for development of the model were so
crucial to its final appearance, an extensive analysis of the
data was completed in order to ensure that all statistical
assumptions governing the model had been satisfied.
Analysis of Data
The SAS statistical program on the University of
Florida's main frame was used to analyze the data. The data
set was then examined by looking at the listings of these
procedures.
The data set included a total of 5 observations for
fiscal year 1991-1992. An additional total of 85
observations were noted in the second data set representing
fiscal year 1992-1993. As was stated in Chapter 3, the 5
88

89
observations in fiscal year 1991-1992 were not duplicated in
fiscal year 1992-1993. Therefore, these 5 observations were
independent of the 85 observations in the fiscal year of
1992-1993. The total of 90 observations were then available
to develop a model from regression analysis. The total list
of LEAs used in this study is presented in Appendix B.
Since most researchers adhere to the rule of thumb that
no more than 10% of the number of observations for each
variable may be missing, the total number of missing data
items allowable for this study would approximate nine for the
combined observations of fiscal years 1991-1992 and 1992-
1993. One of the contributing factors in selecting variables
was the presence or absence of data items. However, if the
variables were considered important, then, regardless of the
"shape" of the data items, these variables were included in
the model.
The data base was fairly complete for almost all of the
variables. However, some of the local agencies either failed
to turn in their report or were delinquent in doing so. As
shown in Table 3, for fiscal year 1992-1993, Local Education
Agency (LEA) A was missing all items of data for all of the
variables except the costs expended for adult education.
Because of this omission, the complete records for LEA A for
fiscal year 1991-1992 were used in its place. Of the four
observations in 1991-1992 (excluding LEA A), LEA D also was
void of any data items except for costs data items. Again,

there is no explanation for the absence of data from either
LEA A or LEA D.
90
Table 3
Accumulated Missing Items
Total observations in analysis
Observations with missing data:
90
Data Missing
LEA A
(1992-1993)
-1
All data items
except costs.
LEA B
(1992-1993)
-1
Correctional
facilities.
Legalized aliens.
LEA C
(1991-1992)
-1
Full-time & part-
time teachers,
counselors, &
full-time para-
professionals .
Volunteer teachers.
LEA D
(1991-1992)
-1
All data items
except costs.
LEA E
(1991-1992)
-1
Receiving Public
Assist. All
teaching, counselor
& paraprofessionals
LEA F
(1991-1992)
-1
Full-time teachers,
counselors, para-
professionals .
Volunteer teachers.
Total missing items -6
Other missing data items restricted the researcher's
ability to maintain a data base that included all school
districts in the study. For example, many of the

91
observations of fiscal year 1991-1992 were incomplete as to
variables relating to teaching. Thus, the part-time teaching
variable contributed to the total of missing variables
because of missing data items for LEA C and LEA E. Another
organization (LEA B) was missing data items for the variable
of X5 (Participants in Correctional Institutions). Finally,
the absence of a data item for RP (Receiving Public
Assistance) for LEA E created another missing data item.
The accumulation of missing data items, therefore,
contributed to the information presented in Table 3 (of items
missing) during the researcher's development of a
mathematical model.
Although the number of missing items was high compared
to the total number of observations, the absence of any
reports from LEA A and LEA D made at least two missing items
inevitable. Fortunately, the missing observations were less
than 9% or 10% of the total observations. Because of the
absence of these data items, the number of variables to be
examined was restricted to 12.
Also, influential outliers were not found, even though
the plots of studentized residuals versus the dependent and
predicted dependent variable did show four outliers. This
was not influential because from Cook's D (Appendix C) it was
noted that all of the observations had more or less the same
values, and only two of them were greater than or equal to
unity, hence indicating that none of the outliers were

92
influential and needed to be deleted. Furthermore, the
observations which were missing data items were omitted from
the analysis. The outliers identified by Cook's D procedure
were as follows:
Observation for Department of Corrections
Observation for LEA A and D
Observations for LEA C, LEA E, and LEA F
were missing so many items that they were not
evaluated by Cook’s D.
The observation of the Department of Corrections was kept in
the analysis because the Department of Corrections would
always appear to be unusual, based upon funding and number
and types of participants. Observation 90 is an
unexplainable outlier. Perhaps the fact that the observation
came from fiscal year 1991-1992 explains its values. The
observations of LEAs B, C, E, and F were utilized in the
regression analysis because these observations were not
missing data items included in the final model. However, the
conclusion was reached that both observations should be
included in the analysis.
Discussion of Administrative and Instructional Variables
Since the administrative and instructional variables for
the observations for fiscal year 1991-1992 were so
incomplete, only the variable of part-time teaching was
included in the study. Although fiscal year 1992-1993 had a
complete set of items for these variables, concern as to

93
their relevance to this study was questioned. First, the
large number of voluntary administrators, teachers,
paraprofessionals, and counselors opens up the question as to
whether this study or any other study could judge the effect
of full-time or part-time instruction. For instance, in
fiscal year 1992-1993, there were 2,999 voluntary teachers
compared to only 886 full-time teachers. Even though many
dedicated volunteers may be as good or better instructors
than their full-time counterparts, there are no factors that
indicate volunteers' quality or enthusiasm. Such a lopsided
ratio toward volunteers raises several questions of teaching
quality, which could not be addressed in this study.
Furthermore, there were 7,671 part-time teachers with 491
part-time paraprofessionals and 190 full-time
paraprofessionals who may or may not be trained to teach
adults or adult education courses. Since there were so few
full-time teachers, it was assumed that teaching quality in
adult education is questionable and may not be verifiable.
Thus, the examination of the administrator/instructional
variables was done with caution. Chances are that the
success of adult education students is based less on teaching
or administration than it is on the students' own
characteristics, as discussed in Chapter 3.
Qualitative Reasons for Variable Selection
The variables most emphasized in this study were the
variables describing the economic, social, and ethnic status

94
of the adult education students. Throughout much of the
educational research on student achievement, the research
emphasis has been on the students' social economic status
(SES). Apparently, the influence of the students' background
and demographics has a tremendous effect on the students'
achievement in school. According to Edwards and Young (1992,
September),
The importance of parent involvement in children's
schooling has been a persistent theme in the research
and school reform efforts of the last three decades.
Studies point to higher student achievement when parents
participate in school activities, monitor children's
homework, and otherwise support the extension into the
home of the work and values of the school" (p. 91).
Although the students in this study were adults, their
parents might have influenced their motivation to earn a GED
or Adult High School Diploma. The types of research that
supports the importance of parental involvement include all
levels of social demographics.
The influence of the father's or mother's education on
the adult student appears to be undeniable. Even if the
goals of parents of different educational levels are the
same, their ability to help their children still differs.
Epstein (1987) stated,
The main differences among parents are: their knowledge
of how to help their children at home; their beliefs
that the teachers want them to assist their children at
home; and the degree of information and guidance from
their children's teachers in how to help their children
at home. These factors create more or less school-like
families, (p. 135)

95
Another example of the problems faced by the influence
of families has been revealed in the difficulties experienced
in school by minority students. Several studies have
demonstrated the importance of the ethnic background of the
student in determining success in school. For example,
according to Hyland (1992),
Currently, Hispanics have the highest dropout rate of
all major population subgroups at approximately 36%,
more than doubling the dropout rate of the white
population. In addition, Hispanic children tend to be
excessively represented in remedial tracks, to be
underrepresented in gifted programs, and to exhibit low
academic achievement levels overall. (p. 127)
Cibulka (1992) gave this analysis of the achievement of
different ethnic groups:
Longitudinal National Assessment of Educational Progress
(NAEP) data show some improvement in the scores of
minority youth over time and a closing of the gap
between white and minority youth. But these national
trends, as Peterson (1991) points out, may mask poor
performance by central city districts, an interpretation
that would seem to be supported by anecdotal evidence of
high minority dropout rates in central city schools.
(pp. 37-38)
Thus, the importance of the student's family background
appears undeniable. However, because of the nature of adult
education, the variables of the different minority groups
could not be tested. Too many of the observations were
grouped by racial or ethnic background (i.e., Hispanic
Unity). Therefore, the testing of the effects of minority
status on GED success could not be tested. However, because
of the presence of so many female single parents in adult

96
education, the variable of the percentage of the females was
included.
Quantitative Reasons for Variable Selection
Before the forward selection, backward elimination, or
stepwise procedures were used, the degree of multi-
collinearity among the variables was analyzed. If the
variables were highly correlated with each other, then some
of the variables would have to be either eliminated or
combined. According to Chatterjee and Price (1991),
A thorough investigation of multicollinearity will
involve examining the value of R squared that
results from regressing each of the explanatory
variables against all others. The relationship
between the explanatory variables can be judged by
examining a quantity called the variance inflation
factor (VIF).... Values of variance inflation factors
greater than 10 are often taken as a signal that the
data have collinearity problems. (pp. 189-191)
Again, the results supported the argument that the
regression model did not have a problem of multi¬
collinearity. Thus, the model appeared to be a good
predictor of the dependent variables without multi¬
collinearity problems. Chatterjee and Price (1991) continued
by stating,
In absence of any linear relationship between the
explanatory variables (i.e., if the explanatory
variables are orthogonal), R squared would be zero and
VIF would be equal to unity. The deviation of VIF value
from 1 indicates departure from orthogonality and
tendency toward collinearity. The reciprocal of (1 - R
squared) also measures the amount by which the variance
of the variable with other explanatory variables
relative to the variance that would result if Xi were
not related to them linearly. This explains the naming
of this particular diagnostic, (p. 192)

97
An examination of the computer printout showed a VIF
that was very close to unity, as can be seen by the variance
inflation values given in Tables 4 and 5.
Table 4
Variance Inflation Values With Dependent Variable Y1
Variable Description DF
Inflation
DF
Variance
XI
Enrolled in other education
1
1.19352620
X2
Students who were female
1
1.97635076
X3
Students who were handicapped
1
1.16480345
X4
Percent of legalized aliens
1
1.90371644
X5
Students in correctional
facilities
1
1.73200666
X6
Students who were employed
1
1.58505721
X7
Receiveing public assistance
1
1.27358665
X8
Part-time teachers
1
1.64587154
X9
Full-time teachers
1
1.78693057
X10
Costs of teacher salaries
1
2.20240015
XI1
Costs of support servies
1
1.14407238
X12
Costs of supplies and
materials
1
1.13920911
The
variance inflation demonstrated
that
there were no
problems of multicollinearity among the variables. Since
this study required two major dependent variables, an

98
analysis of the relationship among the variables including
the total cost per student was also prepared. This
relationship is presented in Table 5.
Table 5
Variance Inflation Values With Dependent Variable Y2
Variable
DF
Variance Inflation
XI
1
1.18302597
X2
1
1.98366601
X3
1
1.15601750
X4
1
1.83514954
X5
1
1.73330361
X6
1
1.57619122
X7
1
1.22614245
X8
1
1.70755591
X9
1
1.83141705
XI0
1
2.11952896
Xll
1
1.14209078
X12
1
1.13356466
Two major assumptions must be met when using multiple
regression analysis to determine a regression model.
According to Chatterjee and Price (1991), "The assumptions
are (1) the explanatory variables are nonstochastic, that is,
the values of the x's are fixed or selected in advance, and

99
(2) the x's are measured without error. These assumptions
cannot be validated, so they do not play a major role in the
analysis. However, they do influence interpretation of the
regression results" (p. 67). Once these assumptions have
been accepted, then the researcher can follow certain steps
to determine variable selection.
The major procedures usually employed by researchers to
develop a mathematical model for testing are the forward
selection method, the backward elimination method, and the
stepwise method. The first procedure that was employed in
this study was the forward selection technique. In the
forward selection technique, the F statistics are calculated
for each of the independent variables. The variables are
stated as follows:
X10--The ratio of state instructional salary
expenditures over total expenditures. This was calculated by
dividing the total instructional salary expenditures for each
LEA cost by the total expenditures by LEA. The total
expenditures included the expenditures of both state and
federal monies for instructional salaries, contracted
services or other personnel services, other expenses, and
equipment.
Xll--The ratio of state support personnel services or
contracted services expenditures over total expenditures by
LEA. This was calculated by dividing the total cost of other
personnel services by the total expenditures by LEA. The

100
total expenditures included the expenditures of both state
and federal monies for instructional salaries, contracted
services or other personnel services, other expenses, and
equipment.
X12--The ratio of state expenses of material and supply-
expenditures over the total expenditures by LEA. This was
calculated by dividing the total cost of other expenses by
the number at each LEA by the total expenditures by LEA. The
total expenditures by LEA included the total expenditures of
both state and federal monies for instructional salaries,
contracted services or other personnel services, other
expenses, and equipment. No other variables were significant
at the alpha level of .05.
A summary of the forward selection procedure for the
dependent variable GD and Adult High School or achievement of
the GED or Adult High School Diploma is shown in Table 6.
The results of the forward selection process appeared
encouraging. All three of the variables which included costs
were now significant for the dependent variable of Y1. These
variables were then included in the model. No other vari¬
ables were significant to the success on the GED examination.
The results of the forward selection procedure were that
the selected variables of X12 (percentage of state
expenditures on materials and supplies) and X10 (instructor
salaries) and Xll (support costs) were significant when
associated with the number of students passing the GED exam.

101
Table 6
Summary of Forward
Selection
Procedure for
the Deoendent
Variable of Y1
Variable
Entered/
Prob>F
Partial R2
Model R2
F Value-
X12
.0024
.1083
.1083
9.8399
X10
.0027
.0954
.2037
9.5872
Xll
.0328
.0449
.2486
4.7190
The fact that the partial R squares for both X10, Xll, and
X12 were low revealed minute problems of multicorrelation,
which permitted interpretation of the forward selection
process without concern about the influence of the other
variables. Finally, the F values for the X10, Xll, and X12
variables had significance.
The backward elimination method is described by
Chatterjee and Price (1991) as follows:
The backward elimination procedure starts with the full
equation and successively drops one variable at a time.
The variables are dropped on the basis of their
contribution to the reduction of error sum of squares.
The first variable deleted is the one with the smallest
contribution to the reduction of error sum of squares.
This is equivalent to deleting the variable which has
the smallest t ratio (the ratio of the regression
coefficient to the standard error of the coefficient) in
the equation. If all the t ratios are significant, the
full set of variables is retained in the equation.
Assuming that there are one or more variables that have

102
insignificant t ratios, the procedure operates by-
dropping the variables with the smallest insignificant t
ratio. The equation with the remaining (q - 1) variables
is then fitted and the t ratios for the new regression
coefficients are examined. The procedure is terminated
when all the t ratios are significant or all but one
variable has been deleted, (p.236)
A summary of the results of the backward elimination
procedure for the dependent variable Yl is shown in Table 7.
Table 7
Results of Backward Selection Procedure
Variable
Removed
Prob>F
Partial R2
Model R2
F Value
X4
.9247
.0001
.2861
.0090
X9
.8044
.0006
.2854
.0618
X5
.8311
.0005
.2850
.0458
XI
.6682
.0018
.2832
.1852
X6
.6324
.0022
.2809
.2307
X8
.5893
.0028
.2781
.2940
X7
.5169
.0040
.2741
.4240
X3
.4101
.0065
.2676
.6861
X2
.1589
.0190
.2486
2.0227
The results of the backward elimination procedure
reaffirmed the importance of the variables of X10 (percentage

103
of state funding used for instructional salaries), Xll
(percentage of state funding used for other personnel
services or contractual services), and X12 (percentage of
state funding for materials and supplies). However, the
most disappointing result was the weakness of the variable X5
or the percentage of students who were incarcerated.
Theoretically, the students in correctional institutions
should have had a higher passing rate on the GED because
these students are not allowed to take the GED exam until
they have completed all course work. The reasons for the
weakness of variable X5 are explained further in Chapter 5.
However, the fact this variable had a p value of only .8311
revealed that the inclusion of X5 would have jeopardized the
model's integrity and allowed for more guessing as to the
actual effect or influence on the GED passing quantities.
The stepwise procedure was performed for both forward
and backward selection (elimination). Agresti and Price
(1986) wrote,
The stepwise regression procedure is a modification of
the forward selection procedure that drops variables
from the model if they lose their significance as other
variables are added. The general approach is the same
as in the forward selection procedure except that at
each step, after entering the new variables, we drop
from the model any variables whose partial contributions
are no longer significant. With this procedure, a
variable entered into the model at a particular stage
may eventually be eliminated because of its strong
relationship to other variables entered at later stages,
(pp. 378-379)

104
The results of the stepwise method for the dependent
variable GD or the acquisition of the GED and Adult High
School Diploma are shown in Table 8.
Table 8
Results of the Stepwise Method for the Dependent Variable Yl
Variable
Entered/
Prob>F
Partial R2
Model R2
F Value
X12
.0024
.1083
.1083
9.8399
X10
.0027
.0954
.2037
9.5872
Xll
.0328
.0449
.2486
4.7190
Again, the stepwise procedure confirmed the results of
both the forward selection and backward elimination
procedures. Obviously, the X10, Xll, and X12 variables
should be included in the final model with the dependent
variable Yl or the number passing the GED or earning the
Adult High School Diploma.
Evaluation of the Selection Procedures
and their Results
In order to select the proper variables needed in the
model, theoretical significance to the model must be

105
determined. In other words, common sense, past research, or
sometimes just plain guessing may be used to determine the
variables that should be included in the model.
Finally, researchers do not always agree on which method
is best at determining the proper model. For example, many
researchers believe the backward elimination method is
superior to both the forward selection method and the
stepwise procedure. Chatterjee and Price (1991) commented,
We recommend the BE [backward elimination] procedure
over the FS [forward selection] procedure for variable
selection. One obvious reason is that in BE procedure
the equation with the full variable set is calculated
and available for inspection even though it may not be
used as the final equation. Although we do not
recommend the use of stepwise procedures in a collinear
situation, the BE procedure is better able to handle
multicollinearity than the FS procedure, (p. 237)
Since the variables appeared not to reveal multi¬
collinearity, the stepwise procedure was believed to be the
appropriate method to determine the best variables and their
corresponding parameter estimates. Furthermore, the backward
elimination method was used to monitor the variables entered
into the stepwise approach. However, even by using all three
of the methods, the researcher's judgment will always affect
interpretation of the results.
There is a need to consider theoretical possibilities
and to choose the best method of variable selection; however,
the major purpose of this study was exploratory. However,
Agresti and Finlay (1986) stated, "The goal is not to explain
relationships among variables so much as it is to find a good

106
set of predictors" (p. 380) . This study was designed to
predict the optimized costs of adult education funding in
Florida. Therefore, the selection of a combination of
variables that appeared to be important and most significant
to the study was believed to be the best procedure.
The results from the stepwise procedure were surprising.
The absence of variable X5, or the percentage of incarcerated
participants, nullified the argument that the sometimes
mandatory enrollment in GED or Adult High School programs was
a major factor in the success of these participants. All
GED students cannot be thrown in jail for the sake of
education, and there is little evidence as to success rate
of mandatory programs external to state correctional
facilities.
The variable Xll, which related the total costs per
student of other personnel or contractual services, was
important in the model. The costs of paraprofessionals and
teachers’ aides may play an unseen benefit toward success in
adult education. One adult education administrator commented
that many classes may be "taught" by a paraprofessional or an
absent teacher with the help of self-study workbooks. The
state mandate that all adult education teachers be certified
may look good on paper, but the reality is that adult
education teaching is made up of an assortment of part-
timers, volunteers, and whoever-may-be-interested-in-teaching

107
types of personnel. The reader may only contemplate as to
the quality or presence of teaching.
Thus, the results of the study point to the three main
variables of instructional salaries, other personnel
services, and the costs of other expenses of supplies and
materials. The question remains, however, as to how to deal
with the other variables that remained unselected. The
obvious explanation may be that the connection or
relationship of many of the variables was either nonexistent
or weak at best. Because of the extreme dropout rate
experienced in adult education (over 40%), any success with
passing the GED would seem a high achievement. Furthermore,
the weakness in the data may reflect the complexity of
dealing with adult students rather than children in pre-K
through 12. Adults may have their own agenda, and only a
minority of enrolling adult education students have the GED
or Adult High School Diploma as a goal. The reasons are
many. Some want to learn to read only simple sentences or
just read the Bible. Others are there because their friends
are enrolled. Whatever the reasons, the variables selected
could be improved with some method of accurately determining
the reasons why some leave and why some stay. Other reasons
for the weakness in the variable relationship might be due to
the lack of available data. Although this study was a
population study, many of the local education agencies were

108
not listed. The agencies which were not listed may be found
in Appendix D.
Determination of Significance of Variables in Model
The second major step in the study was to determine the
significance of the selected variables to the regression
model. Thus, the PROC REG procedure in SAS was invoked for
the regression model of Yl = X10 + Xll + X12 (Table 9).
Table 9
Results of Applying Model Y1=X10, Xll. X12 on SAS System
Source
DF
Sum of Squares
F Value
P Value
Model
3
.08652
9.021
.0001
Error
83
.26535
Total
86
.35188
R square
.2459
Variable
DF
Parameter Estimate
T value for
Ho: P
Intercept
1
. 027077
1.922
.0581
X10
1
.061260
3.122
.0025
Xll
1
.206600
2.219
.0292
X12
1
.192165
3.389
.0011
Since
the
above model could be
improved, a
continued
investigation was made of nonlinear and curvilinear
formulations, such as adding quadratic artificial variables
or adding interaction variables to reflect the effects of

109
the interaction of the variables. The results of developing
quadratics were disappointing. Many of the quadratic
formulations may have increased overall R square and the F
value, but they left the parameters of the variables
themselves insignificant. Furthermore, the use of quadratics
beyond the third power is usually not helpful in social
research modeling. However, attempts were made to develop a
quadratic formula for the variables X10, Xll, and X12. The
tests of interactions were not promising either. By
including an artificial variable representing the square of
the interaction between the two selected variables, the R
square was improved but the significance of the parameter
estimates allowed p value of much higher than the acceptable
.05. Thus, the final model that was determined for the
analysis of the first dependent variable of GED and Adult
High School is as follows:
Yl = .027077 + .061260 * X10 + .206600 * Xll + .192165 * X12.
The results of running the above model using the SAS system
proved fruitful. Some of the attempts at improving the
model's fit may be examined in Table 10. However, as can be
seen from the results, the best model that could be obtained
was the one stated above.
The data in Table 10 reveal that the R-square was
increased by including the interaction of variables X10 and
X12. However, the t value and the probability of the

110
Table 10
Results of Applying Model on SAS System
Source
DF
Sum of Squares
F Value
Prob > F
Model
4
.09983
8.120
.0001
Error
82
.25204
Total
86
.35188
R square
.2837
Variable
DF
Parameter Estimate
T Value for
Ho: P
Intercept
1
.023937
1.722
.0888
X10
1
.083046
3.792
.0003
Xll
1
.177412
1.921
.0582*
X12
1
.509796
3.138
.0024
X10 * X12
1
-.711330
-2.081
.0406
parameter estimate of Xll exceeded the .05 significance
level. Therefore, the increase in R squared was
not large. The significance of the increase in R squared was
tested using the equation as follows:
F = -
2 2
( P-rtn.r. Rrpti ) / ( df full — df / red ,
( 1 — RfULL ) / df ERR
F =
( .2837- .2459) / 1 .0378
(1- .2837) / 82 " .008735
â–  = 4.327
3.96
F significant

Ill
The F statistic of 4.327 was significant. However, the
interaction of variables X10 and X12 were omitted from the
final model. After examining the data using Cook's D for
X10, Xll, and X12, three observations were found to have
standard deviations greater than 2.00. Although these
observations did not have standard deviations of greater than
3.00, these observations might have been potential outliers.
Therefore, observations 44, 56, and 65 were omitted from the
analysis. After deleting the above-mentioned outliers, the
interaction of X10 and X12 were found to be no longer
significant as follows:
X10 * X12 T for Ho = -1.909, Prob>T = .0599
Upon returning to the final model, at first glance, the
results of the model on the SAS system revealed a rather
unuseable model, considering the weakness of the R squared
statistic. However, certain aspects of the model should be
discussed. First, the model reflects the strong emphasis on
variable X12 since the parameter estimate and significance to
Yl was very strong. Furthermore, the model had an F value of
9.021 and was therefore useable for testing purposes.
Tests of Partial Correlations of the Model's Variables
Once the final model was selected, a test of the
Squared Semipartial Correlation Type II was prepared, and
also prepared was a test of the Squared Partial Correlation

112
Type II. The analysis of these partial correlationsis
presented in Table 11.
Table 11
Partial and Semioartial Correlations
Variable
DF
Squared Semipartial
Correlation
Squared Partial
Correlation
X10
1
.08857093
.10510575
XI1
1
.04473449
.05599878
X12
1
.10432154
.12152533
The semipartial and partial correlations did not reveal
a problem of multicollinearity. Therefore, the model must be
a good representation of the relationship with the GED exam.
Problems of Determining Funding
The funding of adult education programs was difficult to
trace. Although most of the funding was through the pre-K
through 12 Florida Education Finance Program (FEFP) or the
Community College Program Fund fCCPF), much of the funding at
the remote sites--such as Hispanic Unity, the Urban League,
or volunteer organizations--came from federal funds or
donations. Because information concerning the donations
was difficult to trace or unavailable, these monies were
ignored in the analysis. However, an attempt to examine the
costs of federal funding was done in order to examine the

113
influence of this funding. One must realize, however, that
the bulk of the federal funding made up only 3.7% of the
total funding for adult education. Many organizations
received donations which exceeded their federal grants.
Thus, the examination of federal grants must be done with
some reservations.
As was discussed in Chapter 3, the same 12 variables
were used in forward selection, backward elimination, and
stepwise methods while using the total cost per student as
the dependent variable (Y2). The results are shown in Table
12.
Table 12
Results of the Forward Selection Process
Variable
Entered/
Prob>F
Partial R2
Model R2
F Value
X9
.0001
.2672
.2672
29.5319
XI
.0227
.0464
.3135
5.4021
X5
.0317
.0392
.3527
4.7832
The results revealed that the variables X9 (percentage
of full-time teachers), XI (percentage of participants who
were in other educational programs), and X5 (percentage of

114
participants who were in correctional institutions) were most
significant with the dependent variable Y2. The explanations
for this are unclear. The reasons these variables were
significant are discussed in more detail in Chapter 5.
However, the fact that full-time teachers are paid greater
salaries in addition to benefits might explain the presence
of variable X9. Also, the FEFP does allow for greater
allotments for handicapped students. Perhaps these findings
demonstrate that the changes in funding are related to these
types of participants.
The presence of variable X5 is not surprising. Since
this variable was fairly strong in its significance in the
regression using the GED and Adult High School Diploma, it
seemed to remain strong when funding was a consideration.
More funds were spent on education of individuals in
correctional facilities than for the general public.
The results of the backward elimination procedure
supported the results of the forward selection method. These
results are presented in Table 13.
Again, the backward elimination confirmed the final
result of the forward selection procedure. With only the
variables of XI, X5, and X9 remaining in the model, the
stepwise procedure resulted in the same conclusion. The
results of the stepwise procedure are displayed in Table
14.

115
Table 13
Results of the Backward Elimination Procedure
Variable
Removed
Prob>F
Partial R2
Model R2
F Value
Xll
.9135
.0001
.3940
. 0119
X2
.6953
.0013
.3926
.1547
X10
.6731
.0015
.3911
.1794
X7
.5505
.0030
.3881
.3597
X8
.5154
.0035
.3846
.4271
X12
.4185
.0054
.3792
.6618
X6
.4356
.0050
.3741
.6142
X4
.4869
.0040
.3702
.4881
X3
.1456
.0174
.3527
2.1602
Table 14
Results of the
Steowise
Procedure
Variable
Entered/
Prob>F
Partial R2
Model R2
F Value
X9
.0001
.2672
.2672
29.5319
XI
.0227
.0464
.3135
5.4021
X5
.0317
.0392
.3527
4.7832

116
The results demonstrated the same final variables.
However, one may note that the X5 variable made only
a weak contribution to the final model for dependent
variable Y2. The weakness of this variable in being
significant to the analysis may be seen by the results of
the model developed by the SAS system, as shown in Table
14.
Test of Partial Correlations and Analysis of Final Model
Another test of the partial correlations for the model
with the dependent variable Y2 (total costs per student) was
prepared. The results of this test are also presented in
Table 15.
Table 15
Partial and Semioartial Correlations
Variable
DF
Squared Semipartial
Correlation
Squared Partial
Correlation
XI
1
.06057333
.08557391
X5
1
.03919084
.05709076
X9
1
.32254306
.33258107
The semipartial and partial correlations did not reveal
a problem of multicollinearity. Even though the partial and
semipartial correlations were high for variable X9 (above
.30), they were not high enough to justify the exclusion of
X9 from the proposed model. Therefore, the model must be a

117
good representation of the relationship with the total costs
per student.
The variable X5 was retained in the analysis. The final
model for the dependent variable Y2 was as follows:
Y2 = .426911 - 1.131003 * XI - .89414 * X5 + 1.949522 * X9.
The results of the analysis of variance are shown in Table
16. The R squared of .3527 was fairly high considering the
circumstances surrounding adult education. From past
experience with the variables, it was difficult to
discover any variables that showed a strong relationship with
either the dependent variable Yl or Y2. The parameter
estimates are shown in Table 16.
After the variables had been selected with the above-
mentioned procedures, scatter plots of the residuals and
studentized residuals were plotted against each of the
variables thought to be critical in determining student GED
achievement.
Examination of the scatter plots of residuals and
studentized residuals against the independent variables and
predicted dependent variables revealed a fairly strong model.
The plots are fairly evenly scattered, which would infer that
the independent variables are not additive and that there is
an absence of multiplicative or interaction effects. The
scatter plots of the residuals and studentized residuals

118
Table 16
Results of the Model Developed by the SAS System
Source
DF
Sum of Squares
F Value
P
Model
3
7.56649
14.350
.0001
Error
Total
R Squared
Variable
79 13.88503
82 21.45152
= .3527
DF Parameter Estimate
T Value for Ho:
P
Intercept
1
.426911
5.837
.0001
XI
1
-1.131003
-2.719
.0080
X5
1
- .894140
-2.187
.0317
X9
1
1.949522
6.274
.0001
plotted against the dependent variables Y1 and Y2 reveal a
movement from left to right in an upward direction. This
result would be expected since variables Y1 and Y2 should
increase with the increase in residuals.
The following two equations were then solved
simultaneously using the pertinent constraints:
Maximize:
Yl= .027077 + .061260 * X10 + .206600 * Xll + .192165 * X12

119
Subject to:
01 > .426911 - 1.131003 * XI - .89414 * X5 + 1.949522 * X9
01 = ($228,606,358.00 + $634,768.00) / 100,000,000
The $228,606,358.00 was the total expenditures for
adult education for fiscal year 1992-1993, and the
$634,768.00 was the total expenditures for LEA C, LEA D, LEA
E, and LEA F.
The following constraints were utilized:
.08 < XI < .10
.05 < X5 < .15
.05 < X9 < .10
0 < X10 < .98
0 < Xll < .39
0 < X12 < .60
0 < X10 + Xll + X12 <1.00
These constraints were determined by examining the
typical magnitudes of the variables in real life. For
example, the prison population (X5) should not exceed 15% of
the total participants. Finally, the variable X9, or the
total percentage of full-time teachers, will probably not
exceed 10% of the total teaching staff of the LEA. The
material given in Table 17 clarifies the decision to select
the above-mentioned constraints.

120
Table 17
Support for the Constraints
Fiscal
Years
Description
1989-90
1990-91
1991-92
1992-93
Percentage in
other programs
8.0834
6.1184
8.836
9.617
Percentage of
students in
prison
12.3936
11.4933
8.007
8.965
Percentage of
full-time
teachers
7.2852
7.6046
6.625
6.969
Range i
of Percentages
Percentage of cost
of instructional
salaries (X10)
0
.9767897092
Percentage of cost
of services (Xll)
0
.388105579
Percentage of cost
of other expenses
(X12)
0
.602050413
Results of the Solution of Simultaneous Equations
The mathematical program of Mathematica was used to
solve the equations simultaneously. According to Wolfram
(1991), "Mathematica can solve any set of simultaneous linear
equations. It can also solve a large class of simultaneous
polynomial equations. Even when it does not manage to solve

121
the equations explicitly, Mathematica will still usually
reduce them to a much simpler form" (p. 97) . Since the
variables in the above equations were not repeated,
Mathematica in essence would only combine the equations by
altering the parameter estimates in reaction to the
individual variables.
A specific model using simultaneous equations was
difficult to determine. According to Hillier and Lieberman
(1974), "If the rank of A [total number of equations] is less
than n [total number of unknowns], then there will exist an
infinite number of solutions" (p. 766). Since the above two
equations for variables Y1 and 01 did not share any common
variables, the solution of these two equations would be
considered meaningless. Since the equation for 01 could not
be used as a constraint for the equation for Yl, there is no
budgetary or cost constraint for the maximization procedure.
Therefore, there was not a specific simultaneous solution
available for the two equations. According to Wolfram
(1991), "There are some equations, however, for which it is
mathematically impossible to find explicit formulas for the
solutions" (p. 96).
The possible use of the first equation might be to give
the budgeting officer an allocation method which results in
the greatest success for the adult education student. This
first model is restated as follows:

122
Yl= .027077 + .061260 * X10 + .206600 * Xll + .192165 * X12.
The possible uses of the above-stated equation are discussed
in Chapter 5.
Summary
Twelve variables were used in the multiple regression
analysis. Of these 12 variables, the variables that had the
greatest effect on student success with the GED were the
state's expenditures on teacher salaries, the costs of other
support services, and the costs of materials and supplies.
Furthermore, three variables were found to be significant
statistically to the increase in cost of adult education.
These variables were the percentage of full-time teachers,
the percentage of students involved in other educational
programs, and percentage of students who resided in
correctional facilities. Since the variables which affected
success on the GED did not coincide with the variables that
affected total costs of adult education, a specific solution
using simultaneous equations was not meaningful or possible.
However, the study did conclude that the use of the formula
developed from success on the GED may be useful for
determining the proper allocation of funds.

CHAPTER 5
CONCLUSIONS AND RECOMMENDATIONS
Introduction
The purpose of this study was to develop and analyze a
mathematical model to optimize the funding for adult
education programs in Florida. Although a simultaneous
solution of linear and nonlinear formulations was attempted,
the solution of the two equations was not possible.
Therefore, the development of a comprehensive model that
encompassed the variables that affected both the success rate
of the GED or Adult High School Diploma and the total costs
per student was not possible. However, the first equation
representing the relationship of the variables to the GED and
Adult High School Diploma may be used to estimate the
percentage allocations of the separate spending categories of
adult education funding. For example, the final equation
developed from multiple regression techniques was as follows:
Yl = .027077 + .061260 * X10 + .2066 * Xll + .192165 * X12.
The above model could be used to estimate the allocation
of the categories of instructor salaries (variable X10),
other personal services or support costs (variable Xll), and
123

124
the costs of other expenses or instructional supplies
(variable X12). Thus, a state agency could use the above
formula to allocate the above costs based on the parameter
estimates. However, one word of caution must be made. The
above equation, which had an R squared of only .25, was
considered low for prediction purposes. Therefore, the
weakness in the correlation of the model to the success
factors would need to be included in any budgeting process
before a final funding allocation was initiated.
Problems and Limitations of the Study
Unforeseen difficulties were encountered during the
execution of the study, the most troublesome of which was the
occurrence of missing or incomplete data. In addition to the
6 observations that were omitted because of missing data for
the independent variables and the 1 observation omitted
because of the missing dependent variable, 14 observations
did not have complete data for the variables of XI0 (state
instructional costs), Xll (state support costs), and X12
(state supply and material costs). These 14 observations
were funded solely by federal monies or outside donations
from charity organizations. Since there was no state funding
of these 14 LEAs, the variables of X10, Xll, and X12 were
assumed zero for all of these observations. However, the
final results of the multiple regression might not have been
representative of these variables because of these omissions.
Because the state cannot control the amount or categorical

125
distribution of federal dollars or contributions, the forcing
of these variables to equal zero was unavoidable. Thus only
the county districts and community colleges could demonstrate
the actual magnitude of variables X10, Xll, and X12.
One variable that could have been included in the study
was the variable of the percentage of minorities for each
LEA. Unfortunately, due to the nature of adult education,
many of the LEAs were unintentionally segregated by race and
ethnic group because of the demographics of society. Since
most adult education centers attempt to offer courses in
locations where the courses are needed, many local LEAs were
representative of only one minority group such as Hispanics
for the Hispanic Unity organization, etc. Thus the inclusion
of the variable of minorities would have allowed for too few
observations for regression analysis. If the data had been
arranged to accommodate the different ethnic groups, then
this variable could have been included. Finally, the fact
that the minority students made up a majority of the student
body caused the information gained from such a variable to be
of little value.
Other difficulties were also revealed when the
regression equation involving the dependent variable of total
cost per student was analyzed. Four of the community
colleges share the costs for adult education for four of the
reported districts. However, these colleges did not report
any statistics for adult education. Instead, the county

126
districts reported the actual adult education statistics for
the colleges. The unreported community colleges and their
respective county districts are shown in Table 18.
Table 18
Unreoorted Community Colleges and their Respective Countv
Districts
Community College
County School District
Santa Fe
Alachua County
Miami-Dade
Dade County
Seminole
Seminole County
Hillsborough
Hillsborough County
The only solution available to solve this reporting problem
was to add the costs of the community colleges to those of
the districts and use the combined totals for analysis.
The other major problem encountered in this study was
that a true GED passing rate was not available per LEA on a
fiscal year basis. No statistics were available as to how
many of the adult education students who actually sat for the
GED exam actually passed. Since the GED exam was designed to
enable the student to pass regardless of whether the student
had taken any of the adult high-school-level courses, the
percentage of the total students enrolled in adult education
was considered relevant to the study. Furthermore, since the
GED as a success factor was considered equivalent to the

127
Adult High School Diploma, the percentage of all adult
education students who had earned the Adult High School
Diploma was also considered a valid success factor for this
study. Of course, the limitations of such assumptions might
have affected study results. To be sure, there may have been
students who had attended only a GED prep course and passed
the GED exam in one calendar year. Furthermore, some
students had repeated several grades and had attempted the
GED several times without success. Finally, some students
may have taken the exam several times and passed only in the
fiscal year in which the study was made. Thus, with all
these reservations, a GED passing rate may not have been any
more valid than the percentage of the total student body that
had achieved these goals.
Other difficulties dealing with the costs related to the
Department of Corrections were encountered in the study.
Since the Department of Corrections was treated as one
observation, all of the individuals in this observation were
included in variable X5, or those students who were in
correctional facilities. Attempts at excluding this
observation were futile because more than 25% of the total
number of individuals in correctional facilities were
included in this one observation. Thus this observation was
included in the analysis. These costs were not available by
category for the variables of X10, Xll, and X12.

128
The observations that included Native American (Indian)
tribes did not indicate the exact allocation of costs for
variables X10, Xll, and X12. However, upon advice from
Department of Education staff, these costs were allocated to
the variable X10, or the total costs of instruction.
By eliminating the observations of LEAs that received no
state dollars and by eliminating any community college that
had received federal dollars, an alternative analysis was
obtained. This analysis involved the regression of the
controllable variables of X10, Xll, and X12 against the
dependent variable of GED and resulted in a fairly usable
model for funding only these entities. Also, the federal
costs of one district were added to one community college
observation because of lack of information.
The final concern that many observers of this study
would be quick to point out is the problem of definition of
the separate categories for variables X10, Xll, and X12.
Although the definitions of instructional salaries for the
community college, school districts, and other not-for-profit
agencies were similar, the treatment and magnitude of fringe
benefits were very different. The districts appeared to have
the most costs related to teacher benefits. However, at the
other extreme, the not-for-profit agencies had the least
benefits. The effects of these differences on the data were
uncertain and need to be studied further. Again, the
definitions of the other personnel services were similar, but

129
the use of these temporary staff members ranged from office
work to support as teachers' aides. The differences in these
allocations were considered nonconsequential. Finally, the
differences in the allocation of other expenses and equipment
purchases were confusing. Regardless of the determination of
whether costs should be considered equipment or expense, the
final results were probably unaffected by these decisions.
Concluding Remarks Concerning the Mathematical Model
The results of the multiple regression of the 12
independent variables with the dependent variable of the GED
were not surprising. The variables of X10 (the percentage of
state adult education costs spent on instructional salaries),
Xll (the percentage of state adult education costs spent on
other personnel services or support services), and X12 (the
percentage of state funding designated for materials and
supplies) were the only variables found to be significant.
The variables will be discussed in order of their
significance to the passing of the GED exam or the
achievement of the Adult High School Diploma.
The relationship of variable X12 (the percentage of
state funding that was contributed to materials and supplies)
and the GED may be explained by observing the typical
organization of the adult education facility. Because of
high student-teacher ratios (sometimes exceeding 60 to 1),
many LEAs have resorted to using certified teachers combined
with paraprofessionals. Because of this inadequacy, many

130
adult educators have turned to the "workbook approach" to
education. The teacher acts as an overseer by helping the
students complete workbooks on an individual or independent
basis. Finally, the course materials of many of the GED
preparation courses and similar programs of instruction make
liberal use of study guides, workbooks, and sample tests in
order to teach the students how to pass the GED.
Variable X10 (the percentage of state funding spent on
instructional salaries) appeared next in importance in the
model. The presence of X10 confirmed the position that the
cost of instructors in adult education was a major factor in
success in adult education. Although the cost of instruction
was secondary to the costs of materials and supplies, the
need for individuals to guide the studies of these adults was
most evident. However, the determination of whether emphasis
should have been placed upon part-time or full-time
instructors was not determinable. The variables X8
(percentage of part-time teachers) and X9 (percentage of
full-time teachers) were not significant and were eliminated
from the model. Perhaps future studies could help answer
these questions.
The need for teachers has presented itself in several
studies. The existence of variable Xll (the percentage of
state funding spent on other contractual services) may be due
to the fact that so many of the support staff helped in the
instruction of the students in adult education. As stated

131
earlier, because the teacher-to-student ratio was low, as
compared to pre-K through 12 or even higher education, the
presence of support personnel may be pertinent to the success
or achievement of the adult education student.
The purpose of this study was not to judge the quality
of the above approaches toward adult education instruction.
However, the importance of materials and supplies in the
study of adult education will be more and more appreciated.
Unfortunately, the study did not encompass the effect of
equipment purchases on the performance of adult education
students. Since these costs made up only 5% of the total
costs of adult education, they were ignored in the study.
However, as education moves from a paper-based textbook-
workbook approach to a paperless system of self-pace computer
programs, these equipment costs may be much more important to
the determination of the number of students passing the GED
or earning the Adult High School Diploma.
Discussion of the Variables of the Cost Model
The results of the second model involving the total cost
per student as the dependent variable were also easily
explained. The second model may be stated as follows:
Y2 = .426911 - 1.131003 * XI - .089414 * X5 + 1.949522 * X9
The independent variable X9 (percentage of full-time
teachers) contributes significantly to the total costs of

132
educating students. Payment of full-time teachers requires
not only higher wages than those earned by part-time teachers
or volunteers but also includes payment of fringe benefits.
The fringe benefits of the districts alone make up almost 30%
of the total salary costs for instruction. Any increase in
full-time teachers would result in large budget increases for
teaching adult education students with limited results in
passing the GED or earning the Adult High School Diploma.
The variable XI (percentage of students in other
educational programs) may be explained by the relationship
adult education has with other academic programs in the
state. Many individuals who pursued the GED or Adult High
School Diploma were not greatly involved in other state-
sponsored programs, such as vocational education in the many
vocational centers across the state and community college
programs leading to certificates in vocational or academic
disciplines. Thus the negative relationship of the variable
XI revealed that Adult Education programs were experiencing
some economies of scale by offering more adult education
programs and, therefore, reducing overhead costs associated
with each student. Certainly, the legislature's emphasis on
the current proposal for the Enterprise Florida program is
evidence of the importance of the goal toward gainful
employment of Florida's residents.
The variable X5 (percentage of students in correctional
facilities) was also revealing. The strength of the

133
relationship of this variable to the total cost per student
should have been positive because more funds are spent on the
adult education of prisoners than are spent on the general
population. Regardless of the fairness of this fact, state
law guarantees residents access to a high school education.
Because so many prisoners may be required to sit in GED
preparation courses to satisfy judicial requirements, these
students are provided more funds to meet statuory
requirements. However, because of the negative parameter
estimate, the above relationship was not realized.
Conclusions and Remarks
The results of the study point toward the need to place
more funding emphasis on support materials and instructional
supplies for adult education. These recommendations were
found in other studies on adult education. Porter and Kissam
(1990, July 23) stated, "This value-added approach has
reportedly influenced the type of curricula taught, the way
curricula are implemented, and the frequency and content of
ancillary support such as faculty advising. It has helped
generate pressure for more resources for students deficient
in skills, and more remediation" (p. 25). Review of the
several models reveals the positive benefits of competency-
based learning, incentive programs for improving learning
deficiencies, and promotions for program improvements.
Porter and Kissam (1990) concluded with a rather positive
view of a nontraditional approach to adult education. They

134
stated that instruction should allow for "any-time, any¬
place, and on-demand" instruction. For instance, adult
education programs should have computer-assisted instruction
and televised courses, tutoring and on-the-job training, and
collaborative programs with businesses and manufacturers.
Porter and Kissam (1990) also listed the following
recommendations:
Adopt the Independent Study Approach as the Basis for
Non-traditional Adult Education.
Develop A Cafeteria Plan of Reimbursement Options.
Develop a Statistically Reliable Model for Measuring
Increased Learner Competencies.
Develop a Fee-for-services Incentive Model.
Develop a Standardized Funding Model Based on Value-
Added .
Experiment With a Cafeteria Plan of Reimbursement
Options. (p. 75)
Suggestions for Further Research
The statistical weakness of the final equation for the
success of the GED and Adult High School Diploma points to
the need for further investigation. Although it appears that
the costs of instruction (variable X10), support services
(variable Xll), and other expenses (variable X12) were
important to success, the low R squared was somewhat
disappointing. However, the study could be repeated under
the following circumstances:
1. The study should be performed in a state that
records data by LEAs where there are more LEAs than this

135
study's 85. Many states have more than 150 different school
districts which might provide the means to increase the
number of observations available to the researcher, resulting
in more estimates.
2. The inclusion of a variable recording the costs
and/or depreciation of electronic equipment (i.e., computers)
used to assist in teaching. Unfortunately, for the purposes
of this study, this information was either unavailable or the
local LEA did not have much electronic equipment.
3. The need to examine the effects on achievement of
different ethnic or racial groups should be included in
future studies. There were too few observations to use for
this variable. However, a better organized data base might
allow for this investigation.
4. The investigation of the differences in achievement
among the three major LEAs could be examined in future
studies. For example, the three major types of LEAs were the
school districts, the community colleges, and the not-for-
profit agencies supported by federal grants and other
donations. By investigating the differences in achievement
among these groups, different states could determine which
type of LEA would be most successful in achievement of the
GED or the Adult High School Diploma.
5. An emphasis on the study of adult education
curriculum should be made. The advantages or disadvantages
of GED prep courses versus traditional GED or adult high

136
school courses should be studied. The benefits of these
different approaches would be helpful in determining the
final allocation of adult education funding.
6. One further avenue of research would be to divide
the funding into different levels. For instance, because of
the existence of many unpaid volunteers and smaller LEAs, the
amount of funding ranged from a high of $3,000 per student
down to approximately $75 per student. Another study that
allows for the division of the funding into different levels
would be very useful for determining future funding. Hager
(1994), the codirector of the Center for Applied Optimization
at the University of Florida, recommended this approach for
future studies.
Final Conclusion
The presentation and analysis of the data and the
resulting recommendations were an attempt to quantify the
successes of adult education. The critical need for an
educated populace cannot be refuted. If the United States is
to continue to compete in a global economy, more studies
should be pursued in an attempt to maximize student success
and educate a more trainable society.

02
03
04
05
06
07
08
09
10
11
12
13
14
15
16
17
18
19
APPENDIX A
PRESENTATION OF RAW DATA
GED
AHS
MALE
FEMALE
0
0
18
48
56
4
1213
1580
86
0
168
221
65
37
795
1037
88
0
232
272
853
186
3566
3315
3160
37
30011
35085
12
0
198
309
12
16
51
90
262
0
578
857
71
14
449
431
6
0
25
73
210
12
727
1056
5
0
52
73
404
0
3203
2913
54
3
206
309
1117
0
9370
660
3024
546
54898
63411
1161
109
4451
3475
137

20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
138
39
0
405
363
140
38
1424
1451
57
50
212
279
682
202
9467
9919
28
8
62
116
19
0
516
492
10
0
27
45
4
9
125
145
2
0
64
85
42
0
253
269
47
2
399
244
133
1
967
1307
0
0
92
23
1897
220
13570
14591
0
0
62
92
382
37
5823
5817
108
0
450
431
57
2
559
554
0
0
102
80
20
1
129
230
16
0
76
64
59
0
116
214
80
19
493
661
666
4
1361
1521
2
0
162
202

46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
139
300
15
2746
3190
6
5
142
176
10
2
69
57
1
2
71
49
2
0
29
28
331
8
1834
1690
217
24
844
1096
159
1
1242
973
2
0
20
24
189
0
416
493
310
0
566
600
0
0
74
70
20
0
171
266
39
0
126
241
69
0
280
954
11
0
57
66
1743
66
19600
10459
344
2
1245
1408
0
0
126
119
374
0
11361
12054
761
28
2643
3572
147
221
1863
1984
923
25
6776
8626
344
21
2895
4203
49
3
544
537
521
29
1873
1805

72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
140
734
143
1923
2436
4
0
27
36
203
38
1305
1632
151
9
510
424
122
1
513
623
40
0
151
162
1
2
84
143
0
0
64
139
15
5
24
108
31
8
220
286
7
0
38
44
46
0
174
276
4
8
63
52
54
0
131
288
32
0
262
112
0
0
26
0
•
•
21
32
0
0
12
23

02
03
04
05
06
07
08
09
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
141
EMPLOYED
UNEMPLOYED
ON
PUBLIC
ASSIST.
HANDICAPPED LIMITED
ENGLISH
RURAL
26
25
0
0
6
0
533
2260
0
206
404
177
125
264
47
60
0
0
337
1495
186
145
266
38
187
317
92
80
1
504
3165
3715
310
365
606
268
15701
44946
2385
1734
20971
0
232
275
200
0
181
0
29
112
0
13
1
136
205
1230
0
73
210
0
140
740
0
152
0
671
12
86
98
1
8
0
1088
695
8
20
218
141
73
52
39
0
108
125
5571
4723
128
185
1144
774
74
441
146
85
15
292
0
0
0
0
0
0
17124
101185
124
4487
56208
•
2378
5548
317
623
547
476
178
590
0
285
119
0
1182
1693
100
182
82
318
173
318
0
59
21
42
9150
12031
2906
1300
2007
0
49
129
0
9
0
108

25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
225
149
0
324
0
115
1128
0
1127
207
583
70
74
330
115
0
26
0
171
21
0
46
34
12
107
31
202
313
525
92
12724
0
2194
373
220
136
0
18
77
359
1113
102
1711
166
0
101
0
974
0
334
26
60
0
0
0
163
0
31
0
118
21
0
0
320
0
32
50
330
0
0
314
1749
128
201
51
23
60
0
115
15437
0
921
4043
42
0
0
154
9446
684
81
1763
508
153
21
173
893
0
544
18
46
9
15
3
359
0
0
0
122
0
0
29
253
12
0
0
795
50
49
7
1089
0
179
543
35
0
20
141
4225
106
1055
314
152
0
41
0
126
0
0
0
19
0
2
88
0
0
0
13

51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
13
71
1
44
0
lili
143
437
0
252
0
219
17
37
1640
5219
1419
2
0
216
38
262
41
2937
0
1136
1219
2305
10
124
968
128
1775
0
172
119
693
1522
0
142
725
4
40
18
0
6
0
904
0
42
238
453
713
181
74
10
80
64
30
29
80
218
219
121
105
2
91
276
0
0
135
463
862
299
21
343
27
96
0
30
13
12032
21612
4646
1432
6359
764
1889
0
183
781
143
102
0
22
0
6062
17353
726
701
13239
1659
4556
0
211
126
563
3129
541
328
375
6245
9157
70
2833
2513
1358
5740
0
2514
818
201
880
108
55
10
1077
2601
0
183
781
1656
2703
959
218
1437
24
39
0
0
19
2203
734
1322
206
657
375
1029
0
156
100
272
728
0
115
50

77
78
79
80
81
82
83
84
85
86
87
88
89
90
313
61
0
10
506
58
194
115
369
53
0
53
35
45
268
0
29
1
66
161
0
4
0
146
27
8
0
0
22
42
25
0
0
456
250
146
0
0
39
43
0
0
0
98
192
150
95
91
50
65
0
0
0
102
317
187
38
2
46
328
182
23
6
0
26
0
0
0
21
•
•
3
14
10
20
2
0
0

02
03
04
05
06
07
08
09
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
10
567
38
258
17
247
4202
0
82
59
201
5
371
26
139
0
0
6091
72
68
944
113
1199
0
34
IN CORR.
FAC.
IMMIGRANT
OTHER
INST.
LEGAL
ALIEN
HOMELESS
0
6
0
0
0
77
0
52
3
0
0
0
9
0
0
0
0
56
0
0
0
0
0
0
0
193
41
2
124
27
5449
2336
1331
1317
727
0
0
0
181
0
0
0
0
0
0
13
5
0
5
0
0
0
18
0
0
0
0
0
0
0
0
0
0
0
0
0
51
0
47
0
122
325
0
634
0
0
5
0
0
0
10030
0
0
0
0
2460
35184
1750
2066
1649
2457
507
0
41
0
0
0
0
0
0
141
21
10
6
0
2
0
0
1
0
1967
635
1552
572
247
0
0
0
0
0
0
0
237
0
0

26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
13
29
31
21
520
1
4280
0
2507
40
57
45
0
31
0
353
0
41
720
165
1
12
0
368
0
0
0
1
129
0
4189
0
129
0
0
0
0
0
0
158
35
302
0
0
0
3
187
0
0
0
12
0
114
25
0
549
55
0
0
15
0
0
0
53
0
0
0
88
13
7
11
0
0
0
0
0
439
0
17
14
4
5
0
0
0
0
0
0
104
0
0
0
0
0
0
0
0
82
0
38
5
0
155
0
0
0
0
0
2
0
0
0
o
o
81
0
210
0
0
0
0
0
20
0
0
23
0
0
2
0
0
0
0
0
5
0
0
0
0
0
0

52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
167
244
0
177
248
0
23
2
76
31
5425
629
0
3197
1344
95
2129
1476
223
662
218
0
81
187
0
65
0
1
83
4
0
76
1
25
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
80
29
80
0
59
-
70
0
0
0
0
0
0
0
21
72
0
186
0
0
0
0
0
0
8130
4214
419
597
202
40
0
100
0
0
0
0
0
0
0
0
13262
161
1022
101
358
32
97
48
0
656
58
11
9
14
87
2285
710
4
0
4
0
0
0
0
0
0
45
0
0
4
205
25
36
0
242
610
128
13
0
0
0
0
0
0
352
540
587
114
0
53
0
0
0
0
53
0
0
38
0
0
0
0
0
0

78
79
80
81
82
83
84
85
86
87
88
89
90
4
0
118
1
51
14
67
122
0
15
2
0
0
0 0 0
0 0
0 0 0
0 0
0 0 0
0 0
0 0 0
0 0
0 0 0
0 0
0 0 93
0 0
0 0 0
0 0
0 0 0
0 0
0 0 7
0 191
0 0 0
0 0
2 14
14
0 0 0
0 0

149
LEA
PART-TIME
ADMIN.
PART-TIME
TEACHER
PART-TIME
COUSELOR
PART-TIME
PARAPROF.
PART-TIME
ADMIN.
FULL-TIME
TEAC.
01
0
0
0
0
2
0
02
3
52
0
1
4
5
03
1
6
0
0
0
1
04
0
26
0
4
1
9
05
0
13
2
0
1
1
06
8
166
25
3
14
9
07
0
1041
22
77
43
138
08
23
74
10
2
12
11
09
0
3
1
0
1
3
10
2
8
0
1
1
1
11
0
18
1
1
4
8
12
7
5
3
3
0
0
13
0
29
0
0
4
0
14
0
5
0
4
1
0
15
5
193
0
12
4
4
16
0
35
3
0
1
0
17
0
0
0
0
25
120
18
25
2278
52
84
128
102
19
4
110
0
0
6
2
20
0
6
0
1
3
7
21
1
78
9
3
5
8
22
1
11
0
0
2
6
23
8
331
3
11
18
12
24
1
8
0
4
0
0
25
0
19
2
4
2
11

26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
3
0
3
0
5
0
42
0
5
0
15
1
3
2
0
6
1
0
13
0
4
0
0
9
0
1
1
0
3
2
12
2
0
1
0
0
1
1
o
o
1
3
1
0
1
1
1
o
8
5
5
51
64
0
655
2
117
23
7
3
8
2
20
25
32
0
72
9
3
0
1
65
0
0
1
0
3
1
36
1
0
1
0
o
1
o
o
o
o
o
o
o
o
o
o
o
o
1
o
2
o
o
45
0
88
6
0
0
0
0
0
0
0
0
22
0
0
0
1
10
1
0
6
2
10
0
27
1
4
2
2
1
2
0
1
1
7
1
8
3
0
1
0
4

52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
9
18
2
0
3
0
0
0
1
2
98
2
1
38
12
21
51
17
8
3
5
0
3
1
1
0
1
2
0
3
0
3
0
1
0
0
25
5
0
5
1
9
0
3
0
0
5
2
0
0
0
o
41
10
0
28
8
2
9
11
27
3
265
19
0
471
138
79
237
341
17
49
49
4
43
52
17
30
0
1
0
1
1
0
0
0
0
0
27
5
0
15
6
0
38
7
2
1
0
0
o
1
o
1
4
0
0
0
3
0
0
2
0
0
0
4
0
20
0
18
0
12
0
9
0
1
7
14
0
3
8
8
2
3
2
0
1
1
2
1
29
3
4
32
10
6
16
6
2
3
5
0
2
1
1
1

152
78 1 4
79 1 1
80 1 0
81 0 4
82 1 4
83 0 4
84 1 0
85 0 9
86 0
87
88 1 1
89 3
90 0 2
0 0 2
0 10
2 10
0 0 1
0 0 0
0 0 1
0 0 0
0 2 1
1
1 1
0 0 1
2
0
2
3
0
2
2
3
0

153
LEA
FULL-TIME
COUNSELOR
FULL-TIME
PARAPROF.
VOLUNTEER
ADMIN.
VOLUNTEER
TEACHER
VOLUNTEER
COUNSELOR
VOL
PAR
01
0
0
0
43
0
0
02
1
1
0
71
0
0
03
0
1
0
0
0
18
04
1
1
0
0
0
59
05
0
1
0
3
0
2
06
2
5
3
2
0
258
07
20
16
0
4
1
211
08
6
0
0
0
0
0
09
0
1
0
0
0
0
10
0
0
175
0
0
0
11
3
0
0
0
0
40
12
0
0
0
0
0
0
13
1
0
0
0
0
66
14
0
0
0
0
0
0
15
0
2
0
128
0
0
16
0
0
0
1
0
1
17
25
23
0
8
0
0
18
60
49
2
22
0
4
19
0
0
0
415
0
0
20
1
0
0
12
0
0
21
0
4
0
1
0
6
22
1
3
9
0
0
68
23
4
0
0
4
0
0
24
0
0
0
0
0
0
25
0
0
0
2
0
4

154
26
0
0
0
0
0
0
27
•
•
•
•
•
•
28
0
1
0
2
0
0
29
0
0
0
0
0
4
30
1
0
0
2
0
0
31
0
4
0
9
0
0
32
0
0
0
0
0
0
33
0
0
0
0
0
1
34
8
3
0
39
0
4
35
0
0
2
0
0
0
36
0
3
0
0
0
0
37
0
1
0
1
0
0
38
1
10
0
30
0
0
39
0
0
0
0
0
2
40
0
1
0
0
0
2
41
0
0
0
0
0
0
42
0
0
•
21
0
0
43
1
0
0
0
0
0
44
1
0
0
45
0
0
45
0
0
26
331
0
0
46
3
6
0
463
0
0
47
0
0
0
3
0
0
48
0
4
0
0
0
0
49
0
0
130
0
0
0
50
0
0
12
43
0
26
51
1
1
0
0
0
54

52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
0
0
0
0
8
0
0
74
0
282
2
0
0
0
57
150
0
103
142
169
0
0
0
15
0
2
1
0
0
o
o
o
o
1
o
23
1
0
3
2
3
3
2
1
1
0
0
1
1
0
o
3
7
1
0
3
1
0
0
0
o
o
o
o
6
3
2
4
0
0
1
0
0
o
5
0
0
2
0
0
3
0
0
0
0
0
0
0
0
2
0
o
1
139
0
0
0
4
0
0
0
0
0
22
3
0
0
20
11
0
0
0
0
0
0
245
228
447
1
194
12
0
0
0
0
78
0
0
20
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
o
o
o
o
o

156
78 1
79 O
80 0
81 1
82 0
83 1
84 1
85 0
86
87
88
89
2
0
0
4
0
0
2
5
3
0
6
0
0
0
0
0
0
0
6
0
0
0
0
0
6
71
90
0
0
0
0
0
0
0
0
0
0
2
1
0
o
36
0
0
0 0

157
LEA/
SALARY
OTHER
OTHER
MATERIALS
CAPITAL
FRINGE
SERVICE
EXPENSE
SUPPLIES
OUTLAY
01
0
0
0
0
0
0
02
518952
14694
39390
274163
3468
99952
03
69320
2660
3090
7355
0
20738
04
500877
5862
16632
11154
18825
152667
05
23002
4404
1993
974
983
6826
06
819004
409818
758377
0
7315
0
07
12523414
907061
681821
768
843121
2433865
08
0
0
0
0
0
0
09
59254
1100
1937
0
0
17072
10
114536
4686
37600
246628
1261
42045
11
242968
4115
18814
3379
14457
72310
12
0
0
0
0
0
O

158
13
36013
119936
3652
13474
0
536
14
0
0
0
0
0
0
15
410556
1150190
31852
75244
674135
46747
16
23902
78173
3044
1603
81
240
17
0
8375752
96820
536305
0
52375
18
9019871
27080752
9358577
527521
9497
153764
19
0
1525658
461486
141108
0
5254
20
99443
292612
13456
11205
4766
8205
21
212117
694258
3147
10316
70480
10188
22
93797
284371
96992
30399
58485
43196
23
0
2850516
428699
134007
0
0
24
10704
28830
568
3585
272
234
25
373413
8633
8287
39
4482
117555

2992
2714
32653
2535
58649
28077
89079
0
02683
0
0
48781
23573
0
73
105
149
3555
86
5253
0
11115
0
3419
7981
48787
9872
119
698
0
11234
460
630
0
91001
5498
5580
0
16646
996
1169
124
185324
12782
13281
27913
119965
742
9338
41041
288885
7473
25744
53335
0
0
0
0
4671391
81194
90479
91653
0
0
0
0
1165544
344311
104488
0
137011
5502
7763
4164
1577687
37123
28036
175497

160
39
0
0
0
0
0
0
40
111238
2540
15418
887
2066
32166
41
16654
222
1756
467
1424
4216
42
80290
73990
4729
0
9090
0
43
259251
18650
15931
8481
12274
80862
44
1336979
11660
32172
22717
20748
249980
45
0
0
0
0
0
0
46
1381378
41827
88738
35723
54452
400126
47
49971
882
510
19
0
9410
48
278821
160
442
4719
1
82945
49
0
0
0
0
0
0
50
0
0
0
0
0
0
51
539521
7979
7660
20833
61034
150747

161
52
204794
633822
44706
91870
11567
4736
53
321424
892248
78830
90625
232344
25790
54
0
48960
0
0
0
0
55
22790
66371
6546
8358
101052
0
56
13886
51872
9275
9848
25767
10846
57
0
0
0
0
0
0
58
0
22818
25651
8325
0
725
59
13601
45863
759
2026
610
546
60
0
219017
0
5056
0
0
61
32275
114945
2027
7570
2349
3348
62
1146111
4969160
86171
62909
25284
13922
63
62459
188907
3123
1012
66183
410
64
0
0
0
0
0
O

162
65
1031279
2880417
136100
525291
1704679
184612
66
207610
705477
44016
22092
13146
18279
67
0
1606599
107934
132259
0
8068
68
1115436
3807441
45108
90772
23412
88388
69
547165
1713118
31348
70329
84779
6551
70
44458
148805
2133
9748
21372
4620
71
211673
1063622
14816
9235
0
42024
72
0
1419779
105034
116098
0
97168
73
0
48960
0
0
0
0
74
0
555307
61461
23741
0
779
75
71366
200154
25155
22975
6584
36943
76
0
152174
30170
31685
2427
251093
77
32597
1108
4932
23667
372
9504

27491
O
O
35028
5215
37993
6190
54719
0
1885
0
1397
1691
0
47
16577
0
3549
692
5043
0
0
0
193
7703
91325
3640
2192
16525
0
0
0
0
48140
0
22781
2810
124651
2980
9081
132
17488
262
1260
0
119893
3447
6469
1196
20637
352
217
1283
179491
12091
13118
772
0
0
0
0
6944
547
465
0
880194
0
0
0
4275
781
327
173
6759
35
1562
0

02
03
04
05
06
07
08
09
10
11
12
13
14
15
16
17
18
19
20
21
22
23
164
STATE AND FEDERAL
COSTS FOR DISTRICTS
AND
STATE COSTS FOR
COMMUNITY COLLEGES
FEDERAL GRANTS
FOR COMMUNITY
COLLEGES AND
OTHER LEAS OTHER
THAN DISTRICTS
0
40451.20
1024375
0
130531
0
768400
0
46230
0
2525651
406368.88
17463428
0
96468
0
472100
0
446143
0
0
0
173743
0
0
11042.77
2407365
0
133436
0
9061252
595489.22
47455378
0
2394480
122109.42
452817
0
1059685
0
674297
0
3436774
497412.39

24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
165
49757
0
606178
0
13681
0
25025
0
150011
0
23708
0
336989
0
211979
0
503032
0
0
61941.10
6033986
0
0
45000.00
1617762
69873.91
239842
0
2459413
0
0
87905.65
228865
0
31834
0
177538
13106.00
454862
0
1771910
0
0
60794.99
2065060
0
60792
0
377903
0
0
36448.28

50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
166
0
913049
1063635
1641261
48960
234746
128940
0
57519
77938
230276
178497
6391471
336253
0
6800736
1103375
1854873
5397400
2683511
257499
1399266
2043059
48960
641288
413105
0
0
0
0
51790.04
0
0
147949.37
23985.38
0
97054.65
0
0
0
0
0
0
54894.07
0
0
0
0
125781.53
65944.31
46642.75
0

76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
167
251093
37120.00
85478
0
173704
0
0
46190.24
79258
65849.04
205419
0
36971
0
204225
0
29371
0
485109
37864.15
0
63090.12
9841
0
880194
0
7146
25176.97
23667
0

APPENDIX B
LISTS OF LOCAL EDUCATION AGENCIES
Name LEA Number
For Fiscal Year 1992-1993
Bay County Public Library 01
Alachua County School District 02
Baker County School District 03
Bay County School District 04
Bradford County School District 05
Brevard Community College 06
Broward County School District 07
Broward Employment and Training Administration 08
Calhoun County School District 09
Charlotte County School District 10
Citrus County School District 11
City of Ft. Lauderdale (Gateway) 12
Clay County School District 13
Collier County Housing Authority 14
Collier County School District 15
Columbia County School District 16
Correctional Education School Authority 17
Dade County School District 18
Daytona Beach Community College 19
168

169
DeSoto County School District 20
Escambia County School District 21
Flagler County School District 22
Florida Community College at Jacksonville 23
Franklin County School District 24
Gadsden County School District 25
Gilchrist County School District 26
Glades County School District 27
Gulf County School District 28
Hamilton County School District 29
Hardee County School District 30
Hendry County School District 31
Hernando County School District 32
COFFO/SDIA 33
Hillsborough County School District 34
Hispanic Unity of Florida, Inc. 35
Indian River Community College 36
Indian River County School District 37
Jackson County School District 38
Jacksonville Public Library 39
Jefferson County School District 40
Lafayette County School District 41
Lake City Community College 42
Lake County School District 43
Lee County School District 44
Leon County Public Library 45

170
Leon County School District 46
Levy County School District 47
Liberty County School District 48
Literacy Volunteers--Monroe 49
Literacy Volunteers--Washington 50
Manatee County School District 51
Marion County School District 52
Martin County School District 53
Miccousukee Indians 54
Monroe County School District 55
Nassau County School District 56
North Florida Education Development 57
North Florida Junior College 58
Okaloosa County School District 59
Okaloosa-Walton Community College 60
Okeechobee County School District 61
Orange County School District 62
Osceola County School District 63
Palm Beach County Library System 64
Palm Beach County School District 65
Pasco County School District 66
Pensacola Junior College 67
Pinellas County School District 68
Polk County School District 69
Santa Rosa County School District 70
Sarasota County School District 71

171
Seminole Community College 72
Seminole Indians 73
South Florida Community College 74
St. Johns County School District 75
St. Johns River Community College 76
Sumter Community School District 77
Suwannee County School District 78
Florida Endowment Fund 79
Tampa--Hillsborough Urban League 80
Taylor County School District 81
Union County School District 82
Wakulla County School District 83
Walton County School District 84
Washington-Home Vocational School 85
For Fiscal Year 1991-1992
ACTION, INC. 86
Dixie County School District 87
Glades County School District 88
Dozier Schools of Florida 89
Washington County Council on Aging, Inc.
90

APPENDIX C
ANALYSIS OF COOK'S D PRINT-OUT
DEPENDENT VARIABLE Y1
Cook's
Obs -2-1-0 12 D
1
1
★ I
0.011
2
1
★ * ★ ★ I
0.039
3
1
I ★ ★ ★ *
0.016
4
1
★ I
0.001
5
1
I ★ *
0.008
6
1
1 *
0.007
7
1
1 1
0.000
8
1
1 1
0.000
9
1
I ★ * *
0.114
10
1
1 1
0.006
11
1
1 1
0.001
12
1
1 1
0.002
13
1
1 1
0.001
14
1
1 1
0.001
1 The SAS System
4
172

15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
173
17:10 Monday,
5, 1994
Cook's
-2-1-0 12 D
★ 1
0.018
1 1
0.002
1 *
0.106
★ 1
0.013
1 *
0.012
1 1
0.003
★ 1
0.002
1 ★ * ★
0.034
★ 1
0.004
1 * ★ ★
0.023
★ 1
0.010
1 *
0.002
★ 1
0.002
★ ★ ★ 1
0.017
1 1
0.000
1 1
0.002
★ 1
0.003
1 1
0.000
1 1
0.001
0.003

36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
174
0.056
0.002
0.006
0.003
0.005
0.027
0.000
0.050
0.002
0.008
0.028
0.000
0.021
0.001
0.000
0.000
0.007
0.011
0.032
0.061
0.000
0.101
0.001
0.007
0.000

62
63
64
65
66
67
68
:>er
>bs
69
70
71
72
73
74
75
76
77
78
79
175
★ 1
0.003
1 1
0.000
1 1
0.000
★ ★ ★ ★ 1
0.031
1 1
0.001
1 1
0.000
1 1
0.001
The SAS
System
5
1994
-2-1-0 1 2
Cook's
D
17:10 Monday,
★ I
0.004
★ I
0.004
I ★ ★
0.007
| ★ * ★
0.017
1 1
0.001
★ I
0.008
I * * ★
0.015
1 1
0.000
1 1
0.000
* ★ ★ 1
0.015
0.005

176
80
1
1 *
1
0.019
81
1
1
1
0.003
82
1
1
1
0.002
83
1
1
1
0.000
84
1
1
1
0.000
85
1
1 *
1
0.005
86
•
87
•
88
•
89
•
90
1
★ ★ |
|
0.010
Sum of Residuals
Sum of Squared Residuals
Predicted Resid SS (Press)
0
0.2410
0.3216
Dependent Variable: T
Obs -2-1-0 1 2
Cook's
D
1
2
3
4
0.013
0.001
0.001
0.001
0.004
5

6
7
8
9
10
11
12
13
14
Der
>bs
15
16
17
18
19
20
21
22
23
177
1 1
0.002
1 1
0.001
1 1
0.004
1 1
0.001
*1 1
0.002
*1 1
0.048
1 1
0.000
1 1
0.002
The SAS
System
4
17:12 Monday,
1994
Cook 1s
-2-1-0 1 2
D
1 1
0.005
★ I
0.003
1 *
0.116
1 1
0.000
1 1
0.001
* ★ I
0.021
1 *
0.002
I * * ★
0.027
0.000

24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
178
0.002
0.028
0.000
0.001
0.000
0.001
0.000
0.000
0.027
0.000
0.002
0.001
0.000
0.251
0.003
0.065
0.005
0.000
0.001
0.001
0.001
0.014
0.350
0.043

50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
179
★ ★
★
★ ★ ★
★
★
★ ★
★ ★
★
5
0.032
0.001
0.000
0.006
0.097
0.005
0.002
0.029
0.000
0.002
0.004
0.013
0.002
0.000
0.026
0.000
0.001
0.000
0.001
The SAS System
17:12 Monday,
5, 1994
Cook's
-2-1-0 12 D

180
69
1
1 1
70
!
★ ★ I
71
1
1 1
72
1
1 1
73
1
I ★★★★★★ I
74
1
1 1
75
1
1 *
76
1
★ I
77
1
78
1
1 1
79
1
1 1
80
1
1 1
81
1
82
1
1 1
83
1
★ * I
84
1
★ ★ ★ I !
85
1
I * ★ ★
86
87
88
89
90 | I** |
Siam of Residuals
Sum of Squared Residuals
Predicted Resid SS (Press)
0.001
0.005
0.000
0.000
0.098
0.000
0.002
0.002
0.001
0.000
0.002
0.002
0.000
0.001
0.010
0.050
0.033
0.008
0
12.9985
19.2050

APPENDIX D
LOCAL EDUCATION AGENCIES
NOT INCLUDED ON FEDERAL REPORT
University of Florida 01
Florida Atlantic University 02
Florida State University 03
Literacy Volunteers of America 04
Florida Literacy Coalition 05
University of South Florida 06
181

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BIOGRAPHICAL SKETCH
The author of this disseration is Ralph Bradley
Kimbrough, Jr. His educational background includes a
Bachelor of Science in Business Administration (1976), a
Master's of Accounting (1980), and a Specialist of Education
(1993)--all three degrees were earned at the University of
Florida in Gainesville. Mr. Kimbrough's work experience
includes 3 years of industrial experience as an auditor in
public accounting and as a management auditor with Associated
Coca-Cola Bottling Company, 7 years of teaching experience
with Embry-Riddle Aeronautical University, and 5 years of
experience with the University of Florida as an auditor and
accounting coordinator. At the time of the completion of
this dissertation he was a Graduate Research Assistant in the
Department of Educational Leadership.
189

I certify that I have read this study and that in my
opinion it conforms to acceptable standards of scholarly
presentation and is fully adequate, in scope and quality,
a dissertation for the degree of Doctor of Philosophy.
, /Jnair
Crimes L. Wattenbarger
distinguished Service
Professor of Educational
Leadership
as
I certify that I have read this study and that in my
opinion it conforms to acceptable standards of scholarly
presentation and is fully adequate, in scope and quality, as
a dissertation for the degree o^lpoctor Philosophy.
pavro S. ¿Hone^ínan, Cochair
ssociate Professor of
Educational Leadership
I certify that I have read this study and that in my
opinion it conforms to acceptable standards of scholarly
presentation and is fully adequate, in scope and quality, as
a dissertation for the degree of Doctor of Philosophy.
Carl A. Sandeen
Professor of Educational
Leadership
I certify that I have read this study and that in my
opinion it conforms to acceptable standards of scholarly
presentation and is fully adequate, in scope and quality, as
a dissertation for the degree of Doctor of Philosophy.
Eiigene A. Todd
Professor of Instruction and
Curriculum

I certify that I have read this study and that in my
opinion it conforms to acceptable standards of scholarly
presentation and is fully adequate, in scope and quality, as
a dissertation for the degree of Doctor of Philosophy.
M. David Miller
Associate Professor of
Foundations of Education
This disseration was submitted to the Graduate Faculty
of the College of Education and to the Graduate School and
was accepted as partial fulfillment of the requirements for
the degree of Doctor of Philosophy.
December 1994
Dean, Graduate School

LO O
1780
199^
UNIVERSITY OF FLORIDA
3 1262 08556 9696