Evidence for the usefulness of task performance, job dedication, and interpersonal facilitation as components of performance

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Title:
Evidence for the usefulness of task performance, job dedication, and interpersonal facilitation as components of performance
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v, 131 leaves : ill. ; 29 cm.
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English
Creator:
Van Scotter, James R
Publication Date:

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Subjects / Keywords:
Performance   ( lcsh )
Performance technology   ( lcsh )
Management thesis Ph.D
Dissertations, Academic -- Management -- UF
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bibliography   ( marcgt )
non-fiction   ( marcgt )

Notes

Thesis:
Thesis (Ph. D.)--University of Florida, 1994.
Bibliography:
Includes bibliographical references (leaves 123-130).
Statement of Responsibility:
by James R. Van Scotter.
General Note:
Typescript.
General Note:
Vita.

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University of Florida
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All applicable rights reserved by the source institution and holding location.
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oclc - 33003060
notis - AKL5096
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Full Text
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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


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


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
XI0 .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 Stepwise P. rocedur*

Variable Entered/ Prob>F Partial R2 Model R2 F Value
X9 .0001 .2672 .2672 29.5319
XI .0227 .0464 .3135 5.4021
X5 .0392 .3527 4.7832
.0317


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


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.


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


APPENDIX A PRESENTATION OF RAW DATA
LEA
GED
AHS
MALE
FEMALE
01
0
0
18
48
02
56
4
1213
1580
03
86
0
168
221
04
65
37
795
1037
05
88
0
232
272
06
853
186
3566
3315
07
3160
37
30011
35085
08
12
0
198
309
09
12
16
51
90
10
262
0
578
857
11
71
14
449
431
12
6
0
25
73
13
210
12
727
1056
14
5
0
52
73
15
404
0
3203
2913
16
54
3
206
309
17
1117
0
9370
660
18
3024
546
54898
63411
19
1161
109
4451
3475
137


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


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 1 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


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


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


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


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


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


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


62
63
64
65
66
67
68
? ? ?
0.003
0.000
0.000
0.031
0.001
0.000
0.001
1
The SAS System
5
September 5, 1994
Cook's
17:10 Monday,
Obs
-2-1-0 1 2
D
69
0.004
70
0.004
71
* *
0.007
72
* *
0.017
73
0.001
74
0.008
75
? *
0.015
76
0.000
77
0.000
78
? ? *
0. 015
79
0.005


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


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 of the College of Education and to the was accepted as partial fulfillment of the degree of Doctor of Philosophy.
the Graduate Faculty Graduate School and the requirements for
December 1994
Dean, Collegepof Education
Dean, Graduate School


188
Stevens, J. (1992). Applied mulitvariate statistics for the social sciences (2nd ed.). Hillsdale, NJ: Lawrence Erlbaum Associates, Publishers.
Stock, A. (1992). Looking back and looking forward: 25 years of adult education. Convergence, 2.5(4), 28-33.
Sultan, A. (1993). Linear programming. Boston: Academic Press, Inc.
Texas State Council on Vocational Education. (1988,
December). Literacy and training: Priorities for Texas. Biennial report to the governor and legislature. Austin,
TX: Author.
Thompson, D. C, Wood, R. C., & Honeyman, D. S. (1994).
Fiscal leadership for schools: Concepts and practices. New York: Longman.
Utah State Office of Education. (1990, December). Cost
effectiveness of the state adult basic education and adult high school program FY 1989-1990 (Statistical data). Salt Lake City, UT: Author.
Webster's third new international dictionary of the English language unabridged. (1986). P. B. Gove (ed.). Springfield, MA: Merriam-Webster Inc. Quorum Books.
Wolfram, S. (1991). Mathematica: A system for doing
mathematics bv computer (2nd ed.). Reading, MA: Addison Wesley.
Wood R. C. & Honeyman, D. S. (1992). Rapid growth and unfulfilled expectations: Problems for school finance in Florida. In J. G. Ward & P. Anthony (Eds.), Who pays for student diversity? Population changes and educational policy (pp. 160-179). Newbury Park, CA: Corwin Press, Inc.


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.


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


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)


(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.


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
Unreported Community Colleges and their Respective County 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


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


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,


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 multicollinearity. Thus, the model appeared to be a good predictor of the dependent variables without multicollinearity 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)


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


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


187
Phelps, J. L. (1992, March). A simultaneous equation model of resource allocation in education. Unpublished manuscript, Michigan Department of Education, Ann Arbor, MI.
Porter, D., & Kissam, E. (1990, July 23). Funding for innovation performance: Working paper on strategic recommendation 2. Unpublished Advisory Review Draft submitted to the Adult Education Unit Youth, Adult and Alternative Educational Services Division, California Department of Education, Sacramento, CA.
Rickards, J. M. (1993, September). Multiple option
instructional program for adult high school completers. Garfield County School District, Panquitch, UT. (ERIC Document Reproduction Service No. ED244072)
Rose, R. M. (1990) Determinants of success in adult basic education among mothers receiving public assistance: A symbolic interactionist perspective (Doctoral State University of New York at Albany, 1990). Dissertation Abstracts International, 51(4), 1104A.
Rothenberg, J. (1975). Cost-benefit analysis: A
methodological exposition. In M. Guttntag & E. L. Struening (Eds.), Handbook of evaluation research (Vol. 2). Beverly Hills, CA: Sage Publications.
SAS Institute, Inc. (1988). SAS/STAT User's Guide: Release 6.03 edition. Cary, NC: SAS Institute, Inc.
Seppanen, L. (1991, March). Adult basic education in Washington community colleges Unpublished manuscript, Washington State Board for Community College Education, Olympia, WA.
State Board of Education. (1992, April). What has happened to
Iowa's ged graduates?: A two-,five-, and ten-year follow-
study (Research Rep.). Des Moines, IA: State Board of
Education. (ERIC Document Reproduction Service No. ED 344 047)
Steele, S. M. (1971, July). Cost-benefit analysis and the adult educator: A literature review. Unpublished manuscript, Washington, DC: Adult Education Association of U.S.A. (ERIC Document Reproduction Service No. ED056287)
Stern, B. (1989) The California adult education system: Background paper on the response of adult education institutions to the needs of Californians. Unpublished manuscript, Sacramento, CA: Pacific Management and Research Associates.


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
XI0 .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


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


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


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


26
9872
119
698
0
0
2992
27
11234
460
630
0
73
2714
28
91001
5498
5580
0
105
32653
29
16646
996
1169
124
149
30
185324
12782
13281
27913
58649
31
119965
742
9338
41041
86
28077
32
288885
7473
25744
89079
33
0
0
0
0
0
0
34
4671391
81194
90479
91653
11115
1002683
35
0
0
0
0
0
0
36
1165544
344311
104488
0
3419
0
37
137011
5502
7763
4164
7981
48781
38
1577687
37123
28036
175497
48787


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.


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


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


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


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


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.


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


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
? ?
? ? ?
? ? ? ? ?
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
49
0.043


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)


0
32166
4216
0
80862
249980
0
400126
9410
82945
0
0
150747
160
39
0
0
0
0
0
40
111238
2540
15418
887
2066
41
16654
222
1756
467
1424
42
80290
73990
4729
0
9090
43
259251
18550
15931
8481
12274
44
1336979
11660
32172
22717
20748
45
0
0
0
0
0
46
1381378
41827
88738
35723
54452
47
49971
882
510
19
0
48
278821
160
442
4719
1
49
0
0
0
0
0
50
0
0
0
0
0
51
539521
7979
7660
20833
61034


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


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.


101
Table 6
Summary of Forward Selection Procedure for the Dependent Variable of Yl
Variable Partial R2 Model R2 F Value-
Entered/ Prob>F
X12 .1083 .1083 9.8399
.0024
X10 .0954 .2037 9.5872
.0027
Xll .0449 .2486 4.7190
.0328
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


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:
2 2
(R FULL RED ) / (df
FULL df /RED )
F =-
2
(1-Rfoll) / df
err
F
^ ( .2837-.2459) / 1 .0378 A ,or7 F = ---=-=4 327
(1- .2837) / 82 .008735
3.96 = F significant


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


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.


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Alamprese, J., & Koloski, J. (1992, March). Direct and equitable access collaborative opportunities under the national literacy act: Report of a workshop. Washington, DC: National Adult Education Professional Development Consortium.
Arthur, J. (1989) The nonmonetary costs of adult education. (Doctoral dissertation, Syracuse University, 1989). Dissertation Abstracts International, 51,(1) 52A.
Beder, H. (1991). Adult literacy: Issues for policy and practice. Malabar, FL: Krieger Publishing Company.
Bronfenbrenner, U.(1979). The ecology of human development; Experiments by nature and design. Cambridge, MA: Harvard University Press.
Burket, L. (1992). Socioeconomic profiles of Georgia's counties: A needs-based framework for allocating public support for adult education. (Doctoral dissertation, University of Georgia, 1992). Dissertation Abstracts International. 53(7), 2203A.
Campen, J. T. (1986). Benefit, cost, and beyond. Cambridge, MA: Ballinger Publishing Company.
Chatterjee, S., & Price, B. (1991). Regression analysis by example (2nd ed.). New York: John Wiley & Sons, Inc.
Cherem, B. (1990). Adult education: A searching stepchild. Adult Learning 2(1), 23-26.
Cibulka, J. A. (1992). Diversiy in urban schools. In J. G. Ward & P. Anthony (Eds.), Who pays for student diversity? Population changes and educational policy. Newbury Park, CA: Corwin Press, Inc.
182


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 Yl 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:


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


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


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


185
Hayes E. (1991, December). Follow-up study of 1989 GED recipients in Wisconsin (Research Rep.) Madison, WI: University of Wisconsin-Madison, Department of Continuing and Vocational Education.
Heath, S. B., & McLaughlin, M. W. (1987). A child resource policy: Moving beyond dependence on school and family. Phi Delta Kappan, pp. 57 6-80.
Henderson, A. T. (Ed.) (1987). The evidence continues to grow: Parent involvement improves student achievement. Columbia, Md: National Committee for Citizens in Education.
Hillier, F. S., & Lieberman, G. J. (1974). Operations research (2nd ed.). San Francisco: Holden-Day, Inc.
Hodgkinson, H. L. (1988). Florida: The state and its educational system. Washington, DC: Institute for Educational Leadership.
Holtmann, A. G. (1970, August 3). Cost-benefit analysis
in adult literacy programmes. Paper presented at the Third Meeting of the Panel for the Evaluation of Experimental Literacy Projects. Paris, France: United Nations Educational, Scientific, and Cultural Organization.
Hough, J. R. (1987). Education and the national economy. London: Crom Helm in association with Methuen, Inc.
Huffman, G. W. (1992). The relationship of selected cost variables to the performance rating of postsecondary vocational-technical programs. (Doctoral dissertation, The University of Southern Mississippi, 1992). Dissertation Abstracts International, 53 (8), 2623A.
Hyland, C. R. (1992). Rising Hispanic enrollments: A new challenge for public schools. In J. G. Ward & P. Anthony (Eds.), Who pays for student diversity: Population changes and education policy. Newbury Park, CA: Corwin Press, Inc.
Johns, R. L. (1976, Fall). The evolution of the equalization of educational opportunity in Florida, 1926 to 1976. Gainesville: University of Florida, Institute for Education Finance.
Kaestle, C. F., Damon-Moore, L. C, Stedman, K. T. &
Trollinger, W. V. (1991) Literacy in the United States: Readers and reading since 1880. New Haven and London: Yale University Press.


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


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 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


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


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


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


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


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


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 .2672 .2672 29.5319
.0001
XI .0464 .3135 5.4021
.0227
X5 .0392 .3527 4.7832
.0317
The results r of full-time teach' evealed that ers), XI (pei the variables rcentage of pe > X9 (percentage irticipants who
were in other educational programs), and X5 (percentage of


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


51 1219 2305 10 124 968 13
52 128 1775 0 172 119 71
53 693 1522 0 142 725 1
54 4 40 18 0 6 44
55 0 904 0 42 238 0
I
56 453 713 181 74 10 1111
57 80 64 30 29 80 143
58 218 219 121 105 2 437
59 91 276 0 0 135 0
60 463 862 299 21 343 252
61 27 96 0 30 13 0
62 12032 21612 4646 1432 6359 219
63 764 1889 0 183 781 17
64 143 102 0 22 0 37
65 6062 17353 726 701 13239 1640
66 1659 4556 0 211 126 5219
67 563 3129 541 328 375 1419
68 6245 9157 70 2833 2513 2
69 1358 5740 0 2514 818 0
70 201 880 108 55 10 216
71 1077 2601 0 183 781 38
72 1656 2703 959 218 1437 262
73 24 39 0 0 19 41
74 2203 734 1322 206 657 2937
75 375 1029 0 156 100 0
76 272 728 0 115 50 1136


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
Vll


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.


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 3 6%, 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


170
Leon County School District 46
Levy County School District 47
Liberty County School District 48
Literacy Volunteers--Monroe 49
Literacy VolunteersWashington 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


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)


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


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,


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,


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


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.


STATE AND FEDERAL
FEDERAL GRANTS
COSTS FOR DISTRICTS FOR COMMUNITY
AND
STATE COSTS FOR COMMUNITY COLLEGES
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


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
X10 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


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


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,


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


25
34
974
0
334
26
627
26
12
60
0
0
0
0
27
28
107
163
0
31
0
29
31
118
21
0
0
149
30
202
320
0
32
50
0
31
313
330
0
0
314
324
32
1749
128
201
51
0
33
92
23
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0
115
115
34
12724
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0
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35
0
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0
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154
0
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9446
684
81
1763
1127
37
373
508
153
21
173
207
38
220
893
0
544
18
583
39
136
46
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0
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0
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18
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0
0
29
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42
77
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0
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330
43
359
795
50
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1113
1089
0
179
543
0
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0
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4225
106
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314
0
47
166
152
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0
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88
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50
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0
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0
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46


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


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)


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 3 0
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 3 6
Indian River County School District 37
Jackson County School District 38
Jacksonville Public Library 3 9
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


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:


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"


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


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


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


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


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


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


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


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


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


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 Yl
Variable Inflation Description DF 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 corre facilities ctional 1 1 .73200666
X6 Students who were employed 1 1 .58505721
X7 Receiveing public assistance 1 1 .27358665
X8 Part-time teacher s 1 1 .64587154
X9 Full-time teacher s 1 1 .78693057
XI0 Costs of teacher salaries 1 2 .20240015
Xll Costs of support servies 1 1 .14407238
X12 Costs of supplies materials and 1 1 .13920911
The v ariance inflation demonstrated that the: re were no
problems of multicollinearity among the variables. Since this study required two major dependent variables, an


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),


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


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.


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


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


78
1
2
0
0
0
0
79
0
0
6
6
0
2
80
0
0
0
0
0
1
81
1
4
0
0
0
0
82
0
0
0
0
0
0
83
1
0
0
0
0
36
84
1
2
0
0
0
0
85
0
5
0
6
0
0
86
3
87
88
9
71
90
0
0
0
0
0
0


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


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.


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


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.


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


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


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,


LEA/
FRINGE
SALARY
OTHER
OTHER
MATERIALS CAPITAL
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
0


(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


APPENDIX C ANALYSIS OF COOK'S D PRINT-OUT
DEPENDENT VARIABLE Yl
Cook1s
Obs
-2-1-0 1 2
D
1
2
3
4
5
6
7
8
9
10
11
12
13
14
? ? ?
? ? ? *
? *
* ? ?
0.011
0.039
0.016
0.001
0.008
0.007
0.000
0.000
0.114
0.006
0.001
0.002
0.001
0.001
1
The SAS System
4
172


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.


184
Fingeret, A. (1984). Adult literacy education: Current and future directions. Columbus, OH: Eric Clearinghouse on Adult, Career and Vocational Education.
Florida Administrative Code, S 6A-14.0713. (1991).
Florida Administrative Code, S 6A-14.076. (1991).
Florida Department of Education. (1988) The Florida adult literacy plan. Tallahassee, FL: Bureau of Adult and Community Education, Division of Vocational, Adult, and Community Education.
Florida Department of Education. (1989-1993). Florida's program plan for adult education. Tallahassee, FL: Bureau of Adult and Community Education, Division of Vocational, Adult, and Community Education.
Florida Department of Education. (1992, Fall). The fact book: Report for Florida community colleges. Tallahassee, FL: Division of Community Colleges.
Florida Department of Education. (1992-1993). Statistical and cost reports. Unpublished manuscript. Tallahassee, FL: Author.
Florida Department of Education. (1993a). Maior
accomplishments fiscal year 1991-92. Tallahassee, FL: Bureau of Adult and Community Education.
Florida Department of Education. (1993b). Summary report: Needs Assessment. Tallahassee, FL: Author.
Florida Department of Education. (1993, May). 1993-1994 Florida education finance program: Statistical report. Tallahassee, FL: Division of Public Schools.
Florida State Statute, Sec. 239.117.
Gordon, E. E., Ponticell J. A., & Morgan, R. R. (1991).
Closing the literacy gap in American business: A guide for trainers and human resource specialists. New York: Quorum Books.
Hager, W. (1994, Fall). Private consultations concerning optimization of adult education funding. Gainesville, FL: Center for Applied Optimization for the Deparment of Mathematics at the University of Florida


145
IN CORR FAC.
IMMIGRANT OTHER
INST.
LEGAL ALIEN
HOMELESS
OTHER EDU.
0
6
0
0
0
10
77
0
52
3
0
567
0
0
9
0
0
38
0
0
56
0
0
258
0
0
0
0
0
17
193
41
2
124
27
247
5449
2336
1331
1317
727
4202
0
0
0
181
0
0
0
0
0
0
0
82
13
5
0
5
0
59
0
0
18
0
0
201
0
0
0
0
0
5
0
0
0
0
0
371
0
51
0
47
0
26
122
0
634
0
139
0
5
0
0
0
0
10030
0
0
0
0
0
2460
35184
1750
2066
1649
6091
2457
507
0
41
0
72
0
0
0
0
0
68
141
21
10
6
0
944
2
0
0
1
0
113
1967
572
247
1199
0
0
0
0
0
0
0
0
237
0
0
34


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


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.


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


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
? *
* *
* *
* *
* *
* *
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


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


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 X10 (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 cateaorical


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


87
148
78
0
0
0
0
0
0
79
0
0
0
0
0
4
80
0
0
0
0
0
0
81
0
0
0
0
0
118
82
0
0
0
0
0
1
83
0
0
93
0
0
51
84
0
0
0
0
0
14
85
0
0
0
0
0
67
86
0
0
7
0
191
122
88
0
0
0
0
0
0
89
2
14
14
15
90
0
0
0
0
0
2


183
Costa, M. (1988). Adult literacy/illiteracy in the United States. Santa Barbara, CA: ABC-Clio, Inc.
Daniels, S. J., & Hess, C. (1992, March 12-13). Adult literacy: An evaluation of a successful program. Paper presented at the Annual Meeting of the Midwest Regional Reading and Study Skills Converence, Kansas City, MO.
Darlington, R. B. (1990). Regression and linear models. New York: McGraw-Hill.
Division of Vocational, Adult, and Community Education. (1991-1992). Manor accomplishments. Tallahassee, FL: Author.
Division of Vocational, Adult and Community Education.
(1992-1993). Summary report: Needs assessment. Presented to the Accountability Commission, Tallahassee, FL: Author.
Donald, J. (1991). How illiteracy became a problem (and literacy stopped being one). In C. Mitchell & K. Weiler Eds.), Rewriting literacy: Culture and the discourse of the other (pp. 211-228) New York: Bergin & Gravey.
Dorfman, R., Samuelson, P. A., & Solow R. M. (1986). Linear programming and economic analysis. New York: Dover Publications, Inc.
Drennan, A. P. (1980). Adult basic education and English as a second language: A critique. In E. J. Boone, R. W. Shearon, E. E. White, & Associates (Eds.), Serving personal and community needs through adult education (pp. 97-128). San Francisco: Jossey-Bass Publishers.
Dubay, T. (1978). Philosophy of the state as educator. Westport, CT: Greenwood Press.
Edwards, P. A., & Young, L. S. J. (1992, September). Beyond parents: Family, community, and school involvement. Phi Delta Kappan, pp. 72-81.
Epstein, J. L. (1987). Toward a theory of family--School connections: Teacher practices and parent involvement. In K. Hurrelmann, F. Kaufmann, & F. Losel (Eds.), Social intervention: Potential and constraints. New York: Walter de Gruyter.
Fagerlind, I., & Saha, L. J. (1989). Education and national development: A comparative perspective (2nd ed.). Elmsford, NY: Pergamon.


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


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.23 6)
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 Prob>F Partial R2 Model R2 F Value
Removed
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


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.
es Wattenbarger, /mair istinguished Service Professor of Educational
ip
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
Philosophy.
an, Cochair sociate 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.
Todd
Professor of Instruction and Curriculum


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.


149
LEA PART-TIME PART-TIME PART-TIME PART-TIME PART-TIME FULL-TIME
ADMIN.
TEACHER COUSELOR PARAPROF.
ADMIN.
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


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 multicollinearity, 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


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)


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


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


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


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


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


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


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


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)


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


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


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)


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


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


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


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)


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.


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.


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


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


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.


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


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 79 13.88503
Total 82 21.45152
R Squarec i = .3527
Variable DF Par ameter 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 c igainst the dependent variables Yl and Y2 : reveal a
movement from left to right in an upward direction This
result would be exp ected since variables Yl 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


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 Yl=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


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 Semipartial Correlations
Variable DF Squared Semipartial Squared Partial
Correlation 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


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)


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


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


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


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


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


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


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


52
2
3
2
22
1
53
1
7
0
3
0
0
54
0
1
0
0
0
0
55
0
0
3
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56
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59
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74
61
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282
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245
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6
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228
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66
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3
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447
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3
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0
57
68
3
4
139
194
1
150
69
2
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103
71
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169
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87
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268
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0
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89
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90
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35


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.


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


LD :
1780
.199.
UNIVERSITY OF FLORIDA
ii i mini ii ii ii
3 1262 08556 9696


(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


September 5, 1994
Cook's
17:10 Monday,
Obs
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D
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
? *
* *
? *
0.018
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0.106
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0.012
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0.010
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0.002
0.017
0.000
0.002
0.003
0.000
0.001
0.003


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


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


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).


26 0 0 0 0 0 16
27
28 0 0 11 0 0 13
29 0 0 0 0 0 29
30 0 0 0 0 0 31
31 1 12 0 82 0 21
32 129 0 0 0 0 520
33 0 114 0 38 20 1
34 4189 25 439 5 0 4280
35 0 0 0 0 0 0
36 129 549 17 155 23 2507
39
37 0 55 14 0 0 40
38 0 0 4 0 0 57
5 2 45
40 0 0 0 0 0 0
41 0 15 0 0 0 31
42 0 0 0 0 0 0
43 0 0 0 2 0
44 158 0 0 0 0 0
45 35 53 0 0 5 41
46 302 0 104 0 0 720
47 0 0 0 0 0 165
48 0 0 0 0 0 1
49 0 88 0 81 0 12
50 3 13 0 0 0 0
51 187 7 0 210 0 368


112
Type II. The analysis of these partial correlationsis presented in Table 11.
Table 11
Partial and Semipartial Correlations
Variable DF Squared Semipartial Squared Partial
Correlation Correlation
X10 1 .08857093 .10510575
Xll 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 (CCPF), 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


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


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


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


6
7
8
9
10
11
12
13
14
0.002
0.001
0.004
0.001
0.002
0.048
0.000
0.002
1
The SAS System
4
September 5, 1994
Cook's
17:12 Monday,
Obs
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0.005
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0.000


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


134
stated that instruction should allow for "any-time, anyplace, 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


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),


186
Kirsch, I. S., Jungeblut, A. Jenkins, L., & Kolstad, A.
(1993, September). Adult literacy in America: A first look at the results of the National Adult Literacy Survey. Washington, DC: National Center for Education Statistics.
Knapp, J. P. (1991) The benefits of consumer education: A survey report. (Tech. Rep.). Ypsilanti, MI: Eastern Michigan University. (ERIC Document Reproduction Service
No. ED329772)
Kulich, J. (1992). Adult education through a rear view
mirror: The changing face of adult education over the last 25 years. Convergence, 25(4), pp. 42-46.
Kutner, M. A., Furey, S., Webb, L., & Gadsden, V. (1990, November). Adult education programs and services: A view from nine programs. Washington DC: U.S. Department of Education, Office of Planning, Budget, and Evaluation.
Kwon, D. (1990). Adult education/business partnership in
education and trainingThe social context. Paper presented at the meeting of the American Association for Adult and Continuing Education, Salt Lake City, UT.
Levin, H. M. (1983). Cost-effectiveness: A primer. London: Sage.
Luenberger, D. G. (1989). Linear and nonlinear programming (2nd. ed.). Menlo Park, CA: Addison Wesley.
Marson, A. A. (1977, July). Cost benefit model development. Final report. Washington, D C: Office of Education (DHEW).
Mason, R. (1988). Adult education and the future of work.
Studies in Continuing Education, 10(1), 4-18. (ERIC Document Reproduction Service No. EJ378460)
McAfee, J. K. (1972). A mathematical model for allocation of school resources to optimize a selected output. (Doctoral dissertation, University of Florida, 1972). Dissertation Abstracts International, 96A.
Nakamura, S. (1993). Applied numerical methods in c. Englewood Cliffs, NJ: PTR Prentice Hall.
Natale, J. A. (1992, October). Growing up the hard way. The American School Board Journal, 179(10), 20-27.
National Education Association Search. (1987). Understanding state school finance formulas. Washington, DC: Author.


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 Yl. These variables were then included in the model. No other variables 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.


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


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


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


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


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


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


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


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


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)


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


141
LEA EMPLOYED UNEMPLOYED
ON PUBLIC ASSIST
HANDICAPPED LIMITED RURAL
ENGLISH
01
26
25
0
0
6
0
02
2260
0
206
404
177
03
264
47
60
0
0
04
337
1495
186
145
266
38
05
187
317
92
80
1
504
06
3165
3715
310
365
606
268
07
15701
44946
2385
1734
20971
0
08
232
275
200
0
181
0
09
29
112
0
13
1
136
10
205
1230
0
73
210
0
11
140
740
0
152
0
671
12
12
86
98
1
8
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1088
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8
20
218
141
14
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52
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108
125
15
5571
4723
128
185
1144
774
16
74
441
146
85
15
292
17
0
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0
0
0
18
17124
101185
124
4487
56208
19
2378
5548
317
623
547
476
20
178
590
0
285
119
0
21
1182
1693
100
182
82
318
22
173
318
0
59
21
42
23
9150
12031
2906
1300
2007
0
24
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129
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9
0
108


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


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


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