RELATIONSHIP OF
SELECTED SOCIOECONOMIC FACTORS TO
SCHOOL FISCAL POLICY
By
JULIAN M. DAVIS
A DISSERTATION PRESENTED TO THE GRADUATE COUNCIL OF
THE UNIVERSITY OF FLORIDA
IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE
DEGREE OF DOCTOR OF EDUCATION
UNIVERSITY OF FLORIDA
April, 1967
ACHNOWLEDGMENTS
The writer wishes to express his appreciation to Dr. R. L. Johns, the chairman of his doctorial committee, for his guidance in formulating the general approach to the study, particularly with regard to relating the statistical approaches to the needs of education. To Dr. C. M. Bridges, the writer is particularly grateful for advice and new ideas regarding specific statistical techniques, for locating and adapting for the use of this study computer programs which would not otherwise have been available, and for serving as a liaison with the staff at the computing center in times of difficulty.
Special thanks are extended to Dr. R. B. Kimbrough, whose suggestion and encouragement led the writer to undertake this particular study. The other members of the graduate committee, Dr. W. A. LaVire and Mr. R. B. Jennings, have also been helpful, both through suggestions concerning the research and furnishing related texts and materials.
Dr. D. E. Scates and Dr. E. A. Tood attended the seminar for
planning the techniques for this study, and both made suggestions which have been helpful in reaching meaningful results.
For invaluable assistance in typing and editing, the writer extends sincere thanks to Mrs. J. B. Parkell.
TABLE OF CONTENTS
Page
ACKNOWLEDGMENTS ..... ............................. ii
LIST OF TABLES ......... ......................... ... vi
LIST OF FIGURES ............ ......................... ix
CHAPTER
1. INTRODUCTION ......... ....................
Need for the Study ..... .................. .. 1
Relationship to Cooperative Research Project 2..... 2 Statement of the Problem ....... ............... 5
Hypotheses ........... ...................... 6
Deliminations ......... .................... 6
Definition of Terms ........ ................. 6
Review of Related Research ....... .............. 7
Organization of the Study .... .............. 14
II. PROCEDURES ........ ....................... ... 16
Size of Sample ...... .................... .... 16
Sources of Data ................................... .. 17
Socioeconomic variables .... .............. ... 17
Financial effort ..... ................. ... 19
Elasticity of demand for education ........ 19 Revenue receipts per pupil ... ............ 20
Statistical Procedures ........ ................ 21
Comparability of data between states ... ....... 21 Consistency of effort and elasticity ... ....... 21
Relationship of (a) financial effort to (b)
fiscal response to income change .. ......... ... 22
Multiple regression technique .. ........... ... 22
Significance test ..... ................. ... 24
Illustration of computer output .. .......... ... 26
Removal of interdependency between independent
variables ................. .......... .. 39
Alternative significant test .... ........ 48
TABLE OF CONTENTS (Continued)
Page
III. ANALYSES AND INTERPRETATIONS OF DATA .. .......... 51
Consistency of Effort and Elasticity ......... 53
Relationship of (a) Financial Effort to (b) Fiscal
Response to Income Change .... .............. ... 59
Relationship of Socioeconomic Factors to Local
School Financial Effort .... ............... ... 62
Relationship of 1950 socioeconomic factors
to financial effort E5 ... ............. ....63
Relationship of 1960 socioeconomic factors
to financial effort E7 ...................... 72
Relationship of Socioeconomic Factors to Local
Elasticity of Demand for Education ............. 82
Relationship of 1950 socioeconomic factors
to elasticity of demand D3 ... ............ ... 83
Relationship of 1960 socioeconomic factors
to elasticity of demand D5 .................. 88
Relationship of Socioeconomic Factors to Local
School Revenue Receipts per Pupil .. .......... ... 97
Test of equation transformations .... ......... 106
Correction for sample size ...... ............ 107
IV. SUMMARY AND CONCLUSIONS
Purpose of the Study ....... ................ ...110
Selection of Sampleand Variables ... ........... ... O110
Statistical Procedures ....................... Ill
Consistency of effort and elasticity ....... ...
Relationship of financial effort to income
responsiveness .. ................. .. 1
Multiple regression techniques ... ..........Ill
Significance test ........ ................. 112
Refinement of regression equations .... ........ 113
Implications of the Findings ...... ............. 113
Hypothesis 1: Most school districts follow
consistent patterns of financial effort and elasticity, yet some make marked changes in
relatively short periods of time .... ......... 113
Hypothesis 2: High effort districts are more
responsive to changes in per capita personal
income than are low effort districts, such that
they invest in education a greater portion of
increases in their personal income. ............ 114
Hypothesis 3: There is little association
between socioeconomic factors and local
school financial effort to support public
schools .......... ..................... 115
TABLE OF CONTENTS (Continued)
Page
Hypothesis 4: There is little association
between socioeconomic factors and elasticity
of demand for education .... ............. ... 116
Hypothesis 5: Local Financial support per pupil
is significantly related to personal income
per capita but not to other socioeconomic
variables ....... .................... .117
General Comments ........................... .......... 118
Effect of significance tests ... ........... ... 118
Effect of interdependency between independent
variables ....... .................... ... 118
Effect of using larger sample .... ......... ... 118
Conclusion ......... .................. .... ... 119
APPENDIX A ............. ........................ ... 122
APPENDIX B ............ .......................... ... 124
APPENXIX C ........... ........................... ... 132
BIBLIOGRAPHY ........... .......................... ... 136
BIOGRAPHICAL SKETCH ........ ....................... ....140
LIST OF TABLES
Table Page
1. Illustration of Computer Output When Using Multiple
Correlation Program. Elasticity D5 Regressed against
1960 Socioeconomic Variables. Page 1, Heading and
Constant Tables ......... ...................... ... 27
2. Illustration of Computer Output When Using Multiple
Correlation Program. Elasticity D5 Regressed against
1960 Socioeconomic Variables. Page 2, Correlation Matrix 28
3. Illustration of Computer Output When Using Multiple
Correlation Program. Elasticity D5 Regressed against
1960 Socioeconomic Variables. Page 4, Step I of
Multiple Correlation ........ .................... ... 30
4. Illustration of Computer Output When Using Multiple Correlation Program. Elasticity D5 Regressed against
1960 Socioeconomic Variables. Page 5, Step 2 of
Multiple Correlation ....... ..................... ...31
5. Illustration of Computer Output When Using Multiple
Correlation Program. Elasticity D5 Regressed against
1960 Socioeconomic Variables. Page 6, Step 3 of
Multiple Correlation .......... ..................... 32
6. Illustration of Computer Output When Using Multiple Correlation Program. Elasticity D5 Regressed against
1960 Socioeconomic Variables. Page 7, Step 4 of
Multiple Correlation ......... ................... ....33
7. Illustration of Computer Output When Using Multiple
Correlation Program. Elasticity D5 Regressed against
1960 Socioeconomic Variables. Page 8, Summary Table ........ 34
8. Correspondence between Computer Identification Numbers and Variance Symbols ....... ..................... ....37
9. Rankings of 1960 Financial Effort (E7), and Changes in Rank Since 1950 ........ ....................... ....55
10. Rankings of 1960 Elasticities of Demand (05), and Changes in Rank Since 1950 ........ ...................... ... 57
I1. Summary of E5 Regression Analysis Based Upon Raw Data .. 65
LIST OF TABLES (Continued)
Table Page 12. Summary of E5 Regression Analysis Based Upon Z Values. 66 13. Comparison of Coefficients of Separate Determination for Socioeconomic Variables Found to be Significant in
Predicting Financial Effort E5' **..................... ..73
14. Summary of E7 Regression Analysis Based Upon Raw Data . 74 15. Summary of E7 Regression Analysis Based Upon Z Values .. 75 16. Comparison of Coefficients of Separate Determination for Socioeconomic Variables Found to be Significant in
Predicting Financial Effort E7' ................ 77
17. Summary of E Regression Analysis Without ttest, Based Upon Raw Datd... ..... ........................ ...80
18. Summary of E Regression Analysis Without ttest, Based Upon Z Value?... ...... ....................... ..81
19. Summary of D3 Regression Analysis Based Upon Raw Data . 85 20. Summary of D3 Regression Analysis Based Upon Z Values . 86 21. Comparison of Coefficients of Separate Determination for Socioeconomic Variables Found to be Significant in
Predicting Elasticity of Demand D3 .... ............ ...87
22. Summary of D5 Regression Analysis Based Upon Raw Data . 89 23. Summary of D5 Regression Analysis Based Upon Z Values . 90 24. Comparison of Coefficients of Separate Determination for
Socioeconomic Variables Found to be Significant in
Predicting Elasticity of Demand D5. **.............. 93
25. Summary of D Regression Analysis Without ttest, Based
Upon Raw Data... .......................... .. 95
26. Summary of D Regression Analysis Without ttest, Based
Upon Z Value ... ...... ........................ ...96
27. Summary of R4 Regression Analysis Based Upon Raw Data . 98 28. Summary of R4 Regression Analysis Based Upon Z Values . 99 29. Comparison of Coefficients of Separate Determination for
Socioeconomic Variables Found to be Significant in
Predicting Local Revenue Receipts per Pupil R4' 1........02 vii
LIST OF TABLES (Continued)
Table
30 Summary of R4 Regression Analysis Without ttest, Upon Raw Data ....... ..................
31. Summary of R 4 Regression Analysis Without ttest, Upon Z Values ....... ...................
32. Summary of Symbols ...............
33. Raw Data for Dependent and Independent Variables, Florida, 1960 ....... ...................
34. Raw Data for Dependent and Independent Variables, Georgia, 1960 ........ .................
35. Raw Data for Dependent and Independent Variables, Kentucky, 1960 . . . . .
36. Raw Data for Dependent and Independent Variables, Illinois, 1960 . . . . .
37. Raw Data for Dependent and Independent Variables, Florida, 1950 ........ ..................
38. Raw Data for Dependent and Independent Variables, Georgia, 1950 ....... ...................
39. Raw Data for Dependent and Independent Variables, Kentucky, 1950 . . . . .
40., Raw Data for Dependent and Independent Variables,
Illinois, 1950 . . . . .
41. First Order Correlation Matrix of 1950 Variables
Expressed in Raw Form* ..... ..............
42. First Order Correlation Matrix of 1960 Variables
Expressed in Raw Form ..... ...............
43. First Order Correlation Matrix of 1950 Variables
Expressed as Z Values ..... ...............
44. First Order Correlation Matrix of 1960 Variables
Expressed as Z Values ..... ...............
Page
Based Based
. 104
viii
.... 105
. 122 .... 124
.... 125
.... 126
.... 127
.... 128
.... 129
.... 130
.... 131
.... 132
. 133 .... 134
.... 135
LIST OF ILLUSTRATIONS
Figure Page
1. Gross Regression Versus Net Regression ... ........... ... 42
CHAPTER I
INTRODUCTION
Need for the Study
Recent research (Schultz 1961, and Fabricant 1959) has shown that growth in the national economy is directly related to increased investment in education. Obviously it is extremely important that educators and other leaders become familiar with those factors which are associated with optimal school fiscal policy.
According to Norton (1965), there need be no uncertainty about the nation's ability to finance the kind and amount of education we need. "Our economy is fabulously productive. We can pay for anything we really believe is important .... Dr. Norton points out that new economic insights have been developed regarding the productivity of education. In the past, educational expenditures were looked upon as a levy upon the economy, and cuts in school budgets as "savings." Economists today see that the concept of capital formation must be broadened to include education as an addition to human capital.
Johns (1961) expressed a similar opinion in even stronger terms:
...we can make our economy of trained people one of plenty
instead of one of scarcity by adequate investment in the
education of people, and the evidence is clear that we can do this without depriving the private economy of the funds
needed for investment in physical capital. National progress
and national survival in the future may well depend upon
which of the following policies we follow:
We can minimize the investment in education and provide a
minimum quality and quantity of education or we can invest
I
what is needed in education to maximize national progress
and the chances of national survival.
Furthermore, Johns and orphet (1960) have shown that the quality of the instructional program in the schools is strongly related to the financial support of the educational program.
A review of recent research concerned with influences upon school fiscal policy reveals that the determining variables fall into two general categories: (a) socioeconomicthose which are inherent in the society, the culture, and the economic system of the district; and
(b) leadershiprelatedthose which are based upon leadership traits of influentials, decision making processes, value systems of the informal power structure, typology of the power structure, and leadership of the superintendent and other educational officials. It is essential that educational administrators know the importance of each group of variables if they are to effectively plan strategies for bringing about desirable change.
Relationship to Cooperative Research Proiect 2842
This is one of several studies conducted or planned to meet the objectives of United States Office of Education Research Project Number 2842, "The Relationship of Socioeconomic Factors, Educational Leadership Patterns, and Elements of Community Power Structure to Local School Fiscal Policy." The directors of this project, Professors Roe L. Johns and Ralph B. Kimbrough, of the College of Education, University of Florida, selected the states of Florida, Georgia, Kentucky, and Illinois for an intensive threeyear study. They have brought together in one design methods for investigating the interrelationships of socioeconomic factors, educational leadership, and community power structure, and the relationship of these factors to local fiscal policy.
The various studies in the overall project seek to answer the
following questions:
(a) Have most school districts in the selected states
followed relatively consistent patterns of local school fiscal policy as measured by local effort in relation to ability and elasticity of demand
for education?
(b) What socioeconomic factors are associated with effort
in relation to ability and elasticity of demand?
(c) What unusual changes in fiscal policy have occurred
through time in school districts in the selected
states?
(d) Are such factors as social power exchanges, economic
changes, and changes in educational leadership activities related to changes in local school fiscal policy?
(e) What relationships do the characteristics of community
power structure (e.g., monopolistic, competitive,
pluralistic) have with the level of local financial
effort?
(f) What relationships do the characteristics of educational leadership have with observed variation in
effort?
(g) How are certain socioeconomic beliefs among the population, power wielders, and teachers in selected
school districts related to financial effort?
(h) Do economic beliefs have a closer relationship than
educational beliefs to liberal or conservative fiscal
policies among selected school districts?
This study deals with the first three of these questions. It
followsup four separate studies of socioeconomic factors associated
with patterns of school fiscal policy in Florida, Georgia, Kentucky, and
Illinois, respectively (Hopper, King, Adams, and Quick, each 1965). The
present study deals with the same four states as a composite rather than
separate entities. The combination should provide more suitable samples
for statistical analysis.
It is not suggested that findings from this composite fourstate
area can be generalized for either the region or the nation, but it is felt that such findings will be of national interest and importance. Probably no set of individual states could be selected such that a study of the effects of socioeconomic factors, power structure, and leadership in decision making with respect to local school fiscal policy would produce a valid basis for generalizations with national applications. Patterns of behavior with respect to fiscal policy decisions in local districts vary widely for different states and different regions. As James, Thomas, and Dyck (1963) pointed out, "The pattern of relationship between expenditures and our measures of wealth and aspiration seems to vary significantly from state to state, not only in the level of expenditures but also in the strength of the effects of the different explanatory variables."
The four states included in this study do, however, provide a variety of characteristics which might, either directly or indirectly, have some bearing upon decisions with respect to local fiscal policy. Florida is a rapidly growing state with an exclusive county unit school system. It has only 67 school districts, is the wealthiest state in the southeast, and has an emerging twoparty system. Kentucky, on the other hand, is a relatively poor state, and it has a mixed county unitindependent city school system, with a total of 206 school districts. Geographically, it is a border state, and it has a twoparty political system.
Georgia is average in wealth for the southeast and is more representative of the old South. It has a mixed county unitindependent city school system organization, with 197 school districts. It continues to maintain a oneparty political system. Illinois was selected from the
5
midwest because of its citydistrict type of organization with a sufficient number of districts suitable for study. Its per capita personal income was above the national average in 1960, and it has a two party political system.
Statement of the Problem
Since the quality of our instructional programs are dependent upon adequate financial resources, one of the primary objectives of educational administrators should be shaping the school fiscal policies of their districts. In fact,.a great amount of time and energy is already being expended for this purpose, but a major portion of this energy will be ineffective unless these administrators know what factors determine fiscal policy. Which categories of determinants are effective and to what degree? Educational leaders must know this in order to develop adequate strategies for needed change.
If fiscal policy is shaped primarily by socioeconomic factors, then administrators will be limited as to how much impact they can bring upon it, for characteristics of the society and the economic system are slow to change. There is little that educational leaders can do within a limited number of years, for example, to markedly change the population density, the employment structure of the community, personal income levels, etc. School administrators need to know which socioeconomic factors are effective and to what degree.
But if socioeconomic variables are not the major cause of variance in school fiscal policy, then educators should look to other factors as possible determinants, such as the leadershiprelated variables mentioned on page two. These factors, if effective, would lead to quite
different strategies of improvement, and would likely indicate more openness to change. It is, therefore, urgent that school administrators know which variables influence school fiscal policy and to what degree.
Hypotheses
1. Most school districts follow consistent patterns of financial effort and elasticity, yet some make marked changes in relatively short periods of time.
2. High effort districts are more responsive to change in per capita personal income than are low effort districts, such that they invest in education a greater portion of increases in their personal income.
3. There is little association between socioeconomic factors and local school financial effort to support public schools.
4. There is little association between socioeconomic factors and elasticity of demand for education.
5. Local financial support per pupil is significantly related to personal income per capita but not to other socioeconomic variables.
Delimitations
Only districts with populations of 20,000 or more (U. S. Bureau of the Census, 1961) from the states of Florida, Georgia, Kentucky, and Illinois, are included in the study. There are a total of 122 of these districts.
Definition of Terms
Socioeconomic factors.Characteristic measures of the society, the culture, and the economic system.
School fiscal policy.Level of support of the public schools.
In this study it is analyzed from three aspectsfinancial effort, elasticity of demand for education, and financial support per pupil.
Pupil.Defined in terms of average daily attendance for the purpose of this study.
Fincial effort.Local school revenue receipts divided by net effective buying income of the school district.
Local school revenue receipts.All school financial receipts from local sources, including city, county, and district revenue, whether earmarked for specific purpose (debt service, etc.) or unrestricted.
Net effective buying income.Total income received by individuals, including salaries, wages, profits, property income, and other personal income, less all tax payments to federal, state, and local governments. This is the same factor defined by the U. S. Department of Commerce as "disposable personal income."
Elasticity of demand for education.The ratio of percentage
change in per pupil revenue receipts to percentage change in per capita net effective buying income. When greater than one, it is referred to as being elastic; less than one, inelastic. A formula somewhat more sophisticated than the above ratio was used in the study. However, it produces essentially the same result. It is described in Chapter II, under "Sources of data."
Review of Related Research
Numerous research studies have sought to identify the causes of variations in school fiscal policy, both from district to district and from one period of time to another. Yet an adequate explanation has not been found.
The research approaches to this problem have varied greatly.
Many studies have related financial support to personal income. Hirsch (1959), for example, found that 76 per cent of the variation in per pupil expenditure for 1900 through 1958 was explained by changes in per capita personal income, when the urbanization factor and the ratio of high school enrollment to total enrollment were held constant.
As an alternate approach, he correlated total current expenditures against the following four variables and found that they accounted for 99.8 per cent of the variance from year to year:
1. High school enrollment as a per cent of total enrollment
2. Average daily attendance as a per cent of 5to 19yearold
population in urban areas
3. Average annual salary of instructional staff members
4. Number of principals, superintendents, and consultants
per 1,000 pupils in average daily attendance
Shapiro (1962) also used per capita personal income as an independent variable, in analyzing educational expenditures among different states for the years 1920, 1930, 1940, and 1950. He found it to be highly significant in explaining variations in per pupil expenditure in all areas except in the south, where no significant relationship could be found.
Brazer (1959) used median family income rather than personal per capita income in analyzing the variance in educational expenditures between different urban areas. The following independent variables were used:
1. City population
2. Population growth rate
3. Population density
4. Ratio of school enrollment to total population
5. Ratio of manufacturing employment to total employment
6. Median family income
7. Revenue from state and federal agencies
Only population density and ratio of school enrollment to total
population proved to be significant. Although it had been expected that population and manufacturing employment would be important factors, they were found to be relatively immaterial.
Brazer (1959:35) recognized other factors as probably being important influences upon educational expenditures, such as cultural and ethnic background of population elements, climate and topographical features, tax and debt limits, political patterns, etc. And despite the lack of correlation in the above study, he felt educational expenditures are being increasingly influenced by the size of population, both through diseconomies of scale and because of association "with other factors, such as income and population density, which in turn account for the apparent association between per capita expenditures and city size."
Norton (1965) has expressed a similar concern over the effects of city size:
Many things have caused overall expenditures to rise rapidly in big cities. One of the most potent factors
has been termed 'bigcity overburden.' It refers to
the fact that the need for public services accelerates as the density of the population rises. The concentration of population increases old needs and spawns new
ones. Police and fire protection, traffic control,
waste removal, sanitary and health facilities, control
of air and water pollution, and welfare measures increase
in amount and cost. Some of these services, less needed in rural areas, have an immediate and sharp impact in the
crowded city. They cannot be put off. The adequate
education of children can be put offor at least this is
often the short sighted decision that is made.
He further pointed out that the lack of fiscal independence often places big city schools at a serious disadvantage in securing needed local revenue. Furthermore, cities often receive smaller allocations of state aid funds per pupil than do other parts of the state.
There has been a growing awareness that metropolitan areas present special fiscal problems which have a strong bearing on educational fiscal policy. Margolis (1961) made comprehensive analyses of such fiscal problems in several metropolitan centers; Lindman (1963) formulated an approach to educational fiscal policy which related educational costs to other governmental costs; and Johns (1963) provided statistical information relating to educational finance in certain urban areas.
Lohnes (1958) investigated the relationship of educational expenditures to size of school and to rate of growth in enrollments. He found that increases in spending were greater in systems with 500 to 1,199 pupils than in smaller or larger systems and the rate of growth in expenditures correlated positively with rate of growth in enrollments.
Wolfbein (1962) found that the occupational structure of the district had a strong relationship to investment in education. Three forces that were found to be particularly influential were (a) continued structural changes in the economy which bring about growth in the service sector, (b) marked increase in professional and technical employment, and (c) substantial rise in productivity, causing relative increases in employment in the service sector and relative decreases in employment in goodsproducing enterprises.
There appears to be an inevitable poor fit between the skills and competencies produced by education and the needs of business, industry, and other societal activities. Hanson (1962) found that one of the most
pressing shortages was in the number of qualified teachers, a fact that has profound implications for education. He suggested that insight into the causes of teacher shortages requires an understanding of (a) factors that affect the demand for education, (b) factors that affect teacher supply, and (c) changes in these factors.
Kershaw and McKean (1962) suggested the abvisability of modifying the single salary schedule in order to meet the competition of business and industry in critical areas. Unless education successfully competes for the available supply of key personnel, a circular process will work against the financing of our schools. Low quality of teaching discourages the public from providing an adequate supply of funds, and inadequate financing in turn leads to obtaining poorer teachers.
Some researchers found that the amount of state aid revenue had a substantial effect upon expenditures per pupil. Renshaw (1960:172), for example, found a significant association between these two variables.
James, Thomas, and Dyck (1963) also studied the effects of state spending upon local support. The usual purpose of statesupported programs is the attainment of equality imong school districts, both in per pupil expenditures and in sacrifice required of each taxpayer. They found that this objective was not generally being met because other objectives were leading to conflicting results. Such conflicting objectives include the shifting of revenue demands away from the property tax, and directing expenditures into specified educational activities.
They further hypothesized that demand for education is related to
(a) financial ability of the community, (b) aspirations for education among citizens, and (c) the degree of freedom of expression of preferences
by members of the community. Multiple regression techniques reflected that the level of wealth was the factor most closely associated with the rate of educational expenditure. Fiscal independence bore some relationship to local expenditure levels in the different states and in the composite sample, but other governmental variables were rather inconsistently related. When wealth and other variables were held constant, expenditures by state educational agencies proved to be highly influential on local support.
Miner (1963) found that total educational expenditures, including state aid, varied positively with the wealth of the state, the relative number of children, the proportion of pupils in the secondary grades, and the salary level of beginning teachers. Total expenditures were negatively related to population density, fiscal dependency of school agencies, and location in a metropolitan area. Local expenditures varied directly with ability to pay for education and with the costs of services provided.
Roos (1957) analyzed all consumer expenditures rather than just educational ones, and he saw nonincome factors as being of primary importance. He found that outlays for science were increasing and that greater proportions of consumer income were being spent for insurance, medical care, education, and other services.
McMahon (1958), in analyzing the 1956 school expenditures in
several states, found that 52 per cent of the variations between states were associated with three nonincome variables as follows:
1. Proportion of nonwhites
2. Proportion of the population consisting of school age children
3. Proportion of children not attending public schools
Many educators have felt that the values and accomplishments of parents constitute perhaps the strongest influence upon the family's demand for education. Brazer and David (1962) used educational attainment of children as the dependent variable, representing the demand for education, in attempting to prove this hypothesis. Using multiple correlation procedures, they found that approximately 40 per cent of the variance in attainment were caused by parental values and accomplishments.
Gentry (1959) chose independent variables such as social climate, years of formal schooling completed by adults, and population change. These accounted for only 30 per cent of the variation in school financial effort, but he suggested other factors observed in his study which may be significant.
Adams, Hopper, King, and Quick (each 1965) chose socioeconomic factors to explain the variability in school fiscal policy between school districts of Kentucky, Florida, Georgia, and Illinois, respectively. Each concluded that none of the following variables: effort, level of support per pupil, and elasticity of demand could be adequately explained by socioeconomic factors. They suggested, however, that other factors may be more influential. These include leadership of the superintendent, typology of the informal power structure, political organization for decision making, etc.
Johns and Morphet (1960) suggested that variations in support
levels are caused by a combination of cultural factors and qualities of educational leadership. In line with this suggestion, recent studies have been directed toward community leadership and its related power systems as well as toward cultural elements.
When Hirsch (1959) related school financial support to per capita personal income, as discussed above, he found a nationwide tendency for
the two variables to increase or decrease together. The ratio of percentage change in pupil financial support to percentage change in per capita income is called elasticity of demand for education. Hirsch's study of the period 1900 through 1958 found the elasticity for the nation as a whole to be 1.09. Fabricant (1959), on the other hand, found the state to state elasticity for the United States to be only .78 in 1942. McLoone's (1961) study, however, agrees much more closely with that of Hirsch. He made a statetostate analysis for the years 1929 through 1958 and found the elasticity to be .99. He made a similar study for the period 1947 thr6ugh 1958 and found an elasticity of 1.34, indicating increasing interest in education. James (1961) studied almost identical years, 1946 through 1958, and made findings that confirmed McLoone's latter figure.
Burk (1958) cautions the reader that placetoplace data generally produce an elasticity coefficient which is slightly lower than one computed with time series data. This may account for some of the difference between Hirsch's coefficient and those of Fabricant, McLoone and James. Futhermore, the coefficients produced by the latter two tend to confirm each other, providing confidence in the results.
Although the above research has added greatly to our knowledge of school fiscal policy determinants, it has also given evidence that further research is needed.
Organization of the Study
Chapter I includes the introduction to the study, an explanation of the relationship of this study to Cooperative Research Project 2842, the statement of the problem, hypotheses, delimitations, definition of
15
terms, review of related research and the organization of the study.
Chapter II covers the procedures followed, including the selection of the sample size, the sources of data, and the statistical procedures.
Chapter III describes the analyses made, gives interpretations of the data, and brings out conclusions regarding hypotheses.
Chapter IV summarizes the study and suggests implications for education.
CHAPTER II
PROCEDURES
Size of Sample
Hopper, King, Adams, and Quick (each 1965) studied the socioeconomic factors associated wi.th the patterns of school fiscal policy in Florida, Georgia, Kentucky, and Illinois, respectively. Using only those districts with 1960 populations of 20,000 or over in each of the four states, rather small samples were used as follows:
State Number of Districts Studied
Florida 32 Georgia 33 Kentucky 29 Illinois 28
The results of these individual state studies were both inconclusive and inconsistent. For example, Hopper commented as follows:
The evidence presented.. .on the relationship of socioeconomic variables to local school effort is quite inconclusive. Socioeconomic variables leave a large part of the variation in local effort unexplained. Furthermore, in the same state at different points in time, different
socioeconomic variables were not common to the fourstate
study. The evidence indicates clearly that regression
equations to predict local financial effort for schools,
using socioeconomic factors as independent variables, are
quite unstable; that is, it is impossible to generalize
through time in any given state on the relationship with
any particular set of socioeconomic variables to local
school effort. Nor is it possible to generalize from statetostate, on the evidence presented in this study.
Similar difficultues were experienced with respect to elasticity of demand for education and for financial support per pupil, and these problems were common to all four studies. An evaluation of the statistical procedures used in these studies has led to the opinion that a composite study of the fourstate area may provide a more suitable sample and generate more definite evidence.
Sources of Data
Socioeconomic variables
After reviewing previous research, a panel of doctoral students and faculty members selected 22 variables on the basis of their relevance to school fiscal policy and their suitability for statistical treatment. These were the 22 variables used in the studies of Florida, Georgia, and Kentucky, with the following five factors being unavailable for Illinois: federal revenue receipts per pupil, population per square mile, per cent rural nonfarm population, per cent rural farm, and per cent of 619yearolds attending school. The loss of these factors from the composite study has been considered carefully and for the following reasons judged not to materially damage the validity. None of these five factors was shown in the original studies to be significantly related to either financial effort or to local revenue per pupil for the year 1960 in any state studies. Also only federal revenue receipts per pupil was significant with respect to elasticity. Even this relationship was very slight and negative in effect.
The 17 remaining variables are used in this study as listed below. They are numbered so as to be consistent with the symbols in
the previous studies, the elimination of the five listed independent variables accounting for the numbering gaps.
X, Average daily attendance in public schools
X2 Per capita net effective buying income
X3 ..Average daily attendance as a per cent of total population
X5 State revenue receipts per pupil
X6 Per cent of civilian labor force employed
X7 Per cent of families with income of $10,000 or more
X8 Per cent of population that is nonwhite
U:X12 Per cent of 1417:yearolds attending public or private
schools
X13 Median school years completed by 25ormoreyearolds
X14 Per cent of 14ormoreyearold females in labor force
X15 Per cent of employed persons engaged in manufacturing
X16 Per cent of population comprised of 25ormoreyearolds
with four years of college education
X17 Median Family income
X18 Per cent of married couples not owning homes
X19 Per cent of population comprised of 65ormoreyearolds
X21 Population of district
X22 Per cent increase in population over the past decade
These data were available only for decennial years,being dependent upon the federal census (U. S. Bureau of the Census, 1952, 1961). They were collected for 1950 and 1960, for all districts having 1960 census populations of 20,000 or more. The decision to restrict the study to nonrural districts was based primarily on the fact that data on net effective buying income were available only for districts having
populations as great as 20,000. There is, however, an additional advantage to this restriction, in that extraneous effects upon the relationships being studied might otherwise be caused by the sparcity of population in smaller districts, effects with which the original researchers chose to eliminate from consideration. Financial effort
Financial effort has been defined earlier as total local school revenue receipts divided by net effective buying income. Data for the former factor were obtained from the biennial rr?orts of the state educational superintendents of the respective states. Data for the latter were found in Sales Management Magazine (1950, etc.). Information from both of these sources was summarized in the four independent state studies by Hopper, King, Adams, and Quick (each 1965), where the respective effort computations were made. In order to eliminate the effects of fluctuations from year to year, three year averages were computed for each district: (a) 1949, 1950, and 1951; and (b) 1959, 1960, and 1961. The results of these computations became the sources of data for the present study. To be consistent with the previous studies, E5 and E7 are used to symbolize these respective three year averages. Elasticity of demand for education
This factor was computed by relating change in per pupil local school revenue to change in per capita net effective buying income. The revenue information was obtained from biennial reports of the respective chief state school officers, and the data regarding buying income were available from Sales Management (1950, etc.). Brazer (1959), Fabricant (1959), and Hirsch (1959) have each suggested using a formula for computing elasticity which readily lends itself to statistical
analysis. It consists of the regression coefficient of the independent variable multiplied by the ratio of the mean of the independent variable to the mean of the dependent variable, as follows: [ XY E X) (1Y)
Elasticity N X by.xX
of demand = 2 i
N
X represents the independent variable, which in this case is per capita net effective buying income, and Y represents the dependent variable, per pupil revenue receipts.
When inspecting data for the respective districts from year to year, the original researchers observed a tendency for increases in school revenue to lag increases in personal income. Furthermore, there were fluctuations in revenue from year to year which would cause elasticities of demand trends from year to year to be very erratic. It became obvious that to obtain meaningful coeffecients of elasticity, it would be necessary to base the computations on extended periods of time rather than on single years. Therefore, elasticities of demand for education were computed for nineyear periods, 1945 through 1954, and 1953 through 1962, for which symbols D3 and D5 were chosen to represent the respective values. The same symbols are used in the current study, and the. elasticity values computed there provide one of the primary sources of information for the present study. Revenue receipts per pupil
Receipts per pupil were calculated for the year 1960 and summary rized in the separate studies by Hooper, King, Adams, and Quick. The results of their calculations are used in this study, and the symbol R4
is used here to represent this quotient, as was done in the prior studies.
Statistical Procedures
Comparability of data between states
There was considerable discussion among the judges regarding the advantages of using raw data as opposed to using standardized deviate value equivalent data in the various correlations of the current study. There appeared to be advantages and disadvantages in each approach. Even though raw data provided a much broader range of dispersion, certain extraneous factors were permitted to influence the variables in some states while those in other states were unaffected, thus distorting the result. For example, legal restrictions upon levels of property taxation or fiscal dependence of school districts might have had the effect of lowering the effort levels in some states. Standardizing the data would tend to restrict the impact of such extraneous effects, but it would also narrow the range of dispersions caused by the independent variables, thus eliminating the very effects we are seeking to discover. For this study it was decided to compare the independent and dependent variables in both forms. The multiple correlations were computed first using raw data, and then using standardized data.
Consistency of effort and elasticity
Financial effort E which is a three year average for years 1959 through 1961, was compared with E5, a similar average for 1959 through 1961. The comparison was made by ranking E7 by district in descending order, and similarly ranking E5 in descending order. For
each county, the change in relative rank was calculated, and the results were summarized and interpreted in order to evaluate the consistency of effort over a period of years.
In an identical manner, elasticities of demand for education D5 and D3 were compared in order to evaluate consistency over a time base.
Relationship of (a) financial effort to (b) fiscal response to income change
The second hypothesis was tested by relating financial effort, as represented by E79 the average for years 1959 through 1961, to fiscal response to personal income change, as represented by elasticity of demand D the 19531962 average. Pearson r was calculated to determine whether response to change in personal income varied directly with variation in effort. This correlation was thus based on a space relationship rather than a time relationship. The computation was executed both using raw data and using standardized Z values. Each result was evaluated and the two were compared. Multiple regression technique
It was decided that in investigating the third through fifth hypotheses, a multiple regression analysis would be employed. More specifically, a stepwise multiple regression equations in a stepwise manner. In each step, one additional independent variable was brought into the computation for consideration.
In this program the first step involved selecting the independent variable which has the highest simple correlation with the dependent
variablc. In the second and in each subsequent step, the independent variable selected for inclusion was the remaining independent variable having the highest partial correlation with the dependent variable. Thus, in each step, the variable being brought into the computation was the one which made the greatest reduction in error in the analysis of variance, based upon the sum of squares of deviation. The variable selected in this manner was also the one which has the highest F ratio when brought into the regression equation. In fact, the value of the F ratio was used as the criteria for bringing in additional variables. In the present study, an F value of .001 was used as the cutoff point. Variables which, if brought into the computation, would have an F value lower than this, were omitted from the correlation equation.
The program also provided for the rejection of any variable which, after being accepted, experienced a drop in its F ratio down to some preselected level due to the effects of later variables being added. In this study the rejection level was established at .00001. This was found to be sufficiently low so that no variable, once having been accepted, was ever rejected. This was consistent with the practice in the studies by Hopper, King, Adams, and Quick (each 1965).
The output from this program included the following information:
1. Prior to computing regression stepsa. Mean of each variable
b. Standard deviation of each variable
c. Correlation matrix
2. During computation of each regression stepa. Multiple correlation after the most recent
addition or deletion
b. Standard error of estimate of the multiple
correlation
c. Analysis of variance table, showing the
following:
Degrees of freedom for both the included
and the excluded groups of variables
Sum of squares of deviations for each group
Mean square for each group
F ratio for included variables
d. For each included variable:
Regression coefficient
Standard error
F level at or below which deletion will occur
e. For each variable not included:
Partial correlation with the dependent variable
F level required for entry
Tollerance
3. After completion of all regression stepsSummary table identifying the variables entered and the ones removed, and giving the following information for each:
Multiple correlation after inclusion or deletio
Multiple correlation squared
The increase in the squared multiple correlatio
caused by entry or removal
The F value required for entry or removal
Significance test
Upon completion of the above computation, certain of the included variables were selected as being significant. Since the present study is a composite of the four previous studies of Florida, Georgia,
n
n
Kentucky and Illinois, with the composite results to be compared to those from such original studies, it was felt that the statistical procedures should be identical, at least up to the point where comparisons were to be made. For this reason, the .05 level ttest which was previously used, was similarly applied in the current study, as follows.
I
First the value of t was determined. Three of the degrees of freedom provided by the 122 cases in the sample had been consumed in computing the means, the standard deviations, and the simple correlations. Consulting a ttable, the t value corresponding to the remaining 119 degrees of freedom was found to be 1.98. Each step of the multiple correlation computation was examined in order, until one was found with a coefficient that failed to equal or exceed 1.98 times its standard error. That step and all subsequent ones were discarded. The variables in the previous step were accepted as being the only ones considered sufficiently significant for consideration. Furthermore, the equation used in such previous step was accepted as the most significant regression equation for predicting the dependent variable. This was the identical significance test applied in the original studies of the four states.
As an additional measure in testing significance, failure to
reduce the standard error of the dependent variable was also considered grounds for elimination. Again, this was a precaution applied in the four original studies. However, when it was applied in the current study, no eliminations were effected, for all steps which were otherwise significant did cause reductions in standard error of their respective dependent variables.
Illustration of computer output
Inasmuch as the computerized multiple correlation program was the heart of the procedure used for investigating the hypothesized relationships, the writer felt that the machine output from this program should be illustrated in sufficient detail to clearly show the progression of the computation and the arrangement of information furnished. Therefore, the next several pages are provided as an exact reproduction of a representative portion of the computer output.
Table I of the illustration identifies the program being used,
summarizes the numbers of cases, variables, and subproblems, and gives the code number for the time period involved. Then it lists the means and standard deviations fbr each of the dependent and independent variables. The reader will notice that 20 variables are included,whereas each computation involves only one dependent variable and 17 independent variables, a total of only 18. The reason for this is that the machine program consolidates the regressions of three different dependent variables against the same set of independent variables into one overall problem, having three subproblems.
For computation efficiency, the machine was programmed to compute simultaneously for all variables, including the three different dependent variables, those constants and relationships which could be handled jointly. The results of these calculations are shown on the first three pages of the illustration. Pages two and three tabulate the simple correlation (Pearson r) of each variable to all other variables. This tabulation is commonly called the correlation matrix and will be referred to accordingly in this report. These simple correlations
TABLE I
ILLUSTRATION OF COMPUTER OUTPUT WHEN USING MULTIPLE CORRELATION PROGRAM
ELASTICITY D5 REGRESSED AGAINST 1960 SOCIOECONOMIC VARIABLES HEADING AND CONSTANT TABLES
BSL070 STEPWISE REGRESSION VERSION OF JUNE 2, 1964 UNIVERSITY OF FLORIDA COMPUTING CENTER
PROBLEM CODE YEAR 6 NUMBER OF CASES 122 NUMBER OF ORIGINAL VARIABLES 20 NUMBER OF VARIABLES ADDED 0 TOTAL NUMBER OF VARIABLES 20 NUMBER OF SUBPROBLEMS 3
VARIABLE MEAN STANDARD DEVIATION
1.78354 18213.22119
1618.16393 20.05598
160. 14028
5.23852 10.5o491 15.o4o16 84.43030
9.83524
34.29835 22.88852
4.42o49 4746.67212 2.23443 9.54016 107892.30273
36.37048
1.12090
168.25732
1.06337
41724.51953
441.64314
4.39468
41.26210
2.22337 5.07090 13.24465 5.83733 1.34342 7.55683 13.06915 3.72405
1291.28027
0.73864 3.73092 336400.64063
54.77359 0.79375
132.00801
I
2
3
4
5
6
7
8
9 10
II
12 13 14 15 16 17 18 19
20
TABLE 2
ILLUSTRATION OF COMPUTER OUTPUT
WHEN USING MULTIPLE CORRELATION PROGRAM
ELASTICITY D5 REGRESSED AGAINST 1960 SOCIOECONOMIC VARIABLES CORRELATION MATRIX
VARIABLE
NUMBER 1 2 3 4 5 6 7 8 9 10
1 1.000 0.012 0.636 0.186 0.454 0.211 0.588 0.338 0.327 0.352
2 1.000 0.276 0.215 0.164 0.004 "0.261 0.121 0.083 0.207
3 1.000 0.318 0.710 0.444 0.871 0.230 0.341 0.706
4 1.000 0.291 0.184 0.171 0.014 0.154 0.264 5 1.000 0.291 0.629 0.235 0.120 0.284 6 1.000 0.472 0.138 0.369 0.367 7 1.000 0.220 0.422 0.715 8 1.000 0.074 0.154 9 1.000 0.48o 10 1.000
TABLE 2CONTINUED
VARIABLE NUMBER
1
2 3 4 5 6 7 8 9 10
11 12 13
14
15
11
0.199 0.147
0.538
0. 182
o,446
0.663 0.506 0.387 0.450 0.417 1.000
12
0.245
0.020 0.238
0.071
0.447
0.285 0.217
0.281 0.126
0.109
0.337 1.000
13
0.447
0.044 0.632
0.188
0.354
0.345 0.639
0.116 0.362
0.610 0.358
0.097 1.000
14
0.6c, 0. 159 0.837
0.166
0.685
0.495 0.874
0.347 0.384
O.6O4 0.492 0.440 0.489 1.000
15
0.543 0. 124
0.557 0.117
0.247 0.311
0.502 0.397
0.324
0.571
0. 145
0.069
0.459
0.540 1.000
16
0.444 0.002 0.220
0.149
0.086 0.109
0.079
0.125 0.239
0.107
0.026
0. 100
0.170 O.048
0.279 1.000
17
0.008
0.984 0.264
0.239
0.182
0.005
0.249 0.098
0.057
0.165 0.137 0.011
0.049 0. 162 0.101
0.020 1.000
18
0.03 1 0.115
0.131
0.103 0.139
0.235
0.240
0.027 0.191
0.514 0.101
0.188 0.077
0.144
0.215 0.077
0.056 1.000
19
0.057 0.034 0.106
0.000
0. 154
0. 311 0.114 0.031
0. 245 0.083 0.330 0.294 0.013 0.153
0.005 0.003 0.030
0.178 1.000
20
0.861 0.155
0.847
0.217
0.649
0.326
0. 749
0.333 0.300 0.520
0.346
0.237 0.637 0.730
0.578
0.418 0.170
0.016
0.007 1.000
TABLE 3
ILLUSTRATION OF COMPUTER OUTPUT
WHEN USING MULTIPLE CORRELATION PROGRAM
ELASTICITY D5 REGRESSED AGAINST 1960 SOCIOECONOMIC VARIABLES
STEP I OF MULTIPLE CORRELATION
SUBPROBLEM 2
DEPENDENT VARIABLE
MAXIMUM NUMBER OF STEPS FLEVEL FOR INCLUSION
FLEVEL FOR DELETION TOLERANCE LEVEL
STEP NUMBER I
VARIABLE ENTERED 11
MULTIPLE R STD. ERROR OF EST.
ANALYSIS OF VARIANCE
REGRESSION
RESIDUAL
0.001000
0.000010 0.001000
0.3300
0.7524
OF SUM OF SQUARES
1 8.304 120 67.932
VARIABLES IN EQUATION
MEAN SQUARE
8.304 0.566
F RATIO "i4.668
VARIABLES NOT IN EQUATION
VARIABLE COEFFICIENT STO. ERROR F TO REMOVE VARIABLE PARTIAL CORR. TOLERANCE F TO ENTER
(CONSTANT 0.06809)
11 0.03467 0.00905 14.6684 1 0.13285 0.9605 2.1378 2 0.01564 0.9783 0.0291 3 o.09o14 0.7110 0.9747 4 0.064o8 o.9670 0.4906 5 o.oo849 o.8o14 0.0086 6 0.13003 0.5604 2.0467 7 0.06567 0.7437 0.5155 8 0.11118 0.8501 1.4894 9 0.11475 0.7972 1.5877 10 0.06407 0.8258 0.4905
12 0.20572 0.8861 5.2589 13 0.11954 0.8717 1.7250 14 0.01154 0.7583 0.0158 15 0.04611 0.9791 0.2536 16 0.01168 0.9993 0.0162 17 0.01586 0.9813 0.0300 )8 0.15424 0.9897 2.9001 20 0.13667 0.8803 2.2652
TABLE 4
ILLUSTRAT10N OF COMPUTER OUTPUT WHEN USING MULTIPLE CORRELATION PROGRAM ELASTICITY D5 REGRESSED AGAINST 1960 SOCIOECONOMIC VARIABLES STEP 2 OF MULTIPLE CORRELATION
STEP NUMBER 2
VARIABLE ENTERED 12
MULTIPLE R 0.3829 STD. ERROR OF EST. 0.7394 ANALYSIS OF VARIANCE
DF SUM OF SQUARES MEAN SQUARE F RATIO REGRESSION 2 11.179 5.589 10.224
RESIDUAL 119 65.057 0.547
VARIABLES IN EQUATION VARIABLES NOT IN EQUATION
VARIABLE COEFFICIENT STD. ERROR F TO REMOVE VARIABLE PARTIAL CORR. TOLERANCE F TO ENTER
(CONSTANT 0.I0405)
11 0.02735 0.00945 8.3796 1 0.17969 0.9248 3.9371 12 0.01253 0.00546 5.2589 2 0.00017 0.9727 0.0000
3 0.10739 0.7074 1.3767 4 0.03587 0.9474 0.1520 5 0.06990 0.7018 0.5795
6 0.11516 0.5562 1.5859
7 0.07920 0.7413 0.7449
8 0.01568 0.6585 0.0290 9 0.12387 0.7964 1.8389 10 0.00435 0.7556 0.0022
13 0.07237 0.8183 0.6212 14 0.08711 0.6735 0.9022 15 0.05171 0.9786 0.3163 16 0.03239 0.9900 0.1239
17 0.00838 0.9800 0.0083 18 0.21364 0.9339 5.6436 20 0.16992 0.8639 3.5085
TABLE 5
ILLUSTRATION OF COMPUTER OUTPUT
WHEN USING MULTIPLE CORRELATION PROGRAM
ELASTICITY D5 REGRESSED AGAINST 1960 SOCIOECONOMIC VARIABLES
STEP 3 OF MULTIPLE CORRELATION
STEP NUMBER 3
VARIABLE ENTERED 18
MULTIPLE R 0.4308 STD. ERROR OF EST. 0.7254 ANALYSIS OF VARIANCE
DF SUM OF SQUARES MEAN SQUARE F RATIO REGRESSION 3 14.148 4.716 8.963
RESIDUAL 118 62.087 0.526
VARIABLES IN EQUATION VARIABLES NOT IN EQUATION
VARIABLE COEFFICIENT STD. ERROR F TO REMOVE VARIABLE PARTIAL CORR. TOLERANCE F TO ENTER
(CONSTANT 0. i46o8)
11 0.02336 0.00942 6.1498 1 0.18242 0.9247 4.0273 12 0.01564 0.00552 8.0361 2 0.01912 0.9655 0.0428 18 0.00296 0.00125 5.6436 3 0.13533 0.6985 2.1.828 4 0.04868 0.9446 0.2779 5 0.04229 0.6889 0.2096 6 0.06438 0.5202 0.4870 7 0.13780 0.6983 2.2648 8 0.01649 0.6441 0.0318 9 0.09290 0.7759 1.0186 10 0.12700 0.5765 1.9179 13 0.07072 0.8181 0.5881 14 0.13711 0.6450 2.2416 15 0.10232 0.9334 1.2378 16 0.02026 0.9866 0.0480 17 0.01633 0.9787 0.0312 20 0.16887 0.8634 3.4343
TABLE 6
ILLUSTRATION OF COMPUTER OUTPUT
WHEN USING MULTIPLE CORRELATION PROGRAM
ELASTICITY D5 REGRESSED AGAINST 1960 SOCIOECONOMIC VARIABLES
STEP 4 OF MULTIPLE CORRELATION
STEP NUMBER 4
VARIABLE ENTERED 7
MULTIPLE R 0.4484 STD. ERROR OF EST. 0.7215 ANALYSIS OF VARIANCE
DF SUM OF SQUARES MEAN SQUARE F RATIO REGRESSION 4 15.327 3.832 7.361
RESIDUAL 1.17 60.908 0.521
VARIABLES IN EQUATION. VARIABLES NOT IN EQUATION
VARIABLE COEFFICIENT STD. ERROR F TO REMOVE VARIABLE PARTIAL CORR. TOLERANCE F TO ENTER
(CONSTANT 0.18071)
7 0.02329 0.01548 2.2648 1 0.12604 0.5951 1.8725 11 0.03038 0.01047 8.4242 2 0.01014 0.9229 0.0119 12 0.01660 0.00553 9.0263 3 0.03859 0.2224 0.1730 18 0.00342 0.00128 7.1848 4 0.03639 0.9364 0.1538 5 O.G4949 0.4464 0.2848 6 0.08785 0.5075 0.9022 8 0.07180 0.4489 0.6011 9 0.12842 0.7366 1.9453 10 0.04631 0.3127 0.2494 13 0.01967 0.4999 0.0449 14 0.03714 0.1705 0.1602 15 0.04229 0.7228 0.2078 16 0.03473 0.9764 0.1401 17 0.01309 0.9354 0.0199
20 0.10057 0.3953 1.1852
TABLE 7
ILLUSTRATION OF COMPUTER OUTPUT
WHEN USING MULTIPLE CORRELATION PROGRAM
ELASTICITY D5 REGRESSED AGAINST 1960 SOCIOECONOMIC VARIABLES
NUMBER
STEP VARIABLE MULTIPLE INCREASE F VALUE TO OF INDEPENDENT NUMBER ENTERED REMOVED R RSQ IN RSQ ENTER OR REMOVE VARIABLES INCLUDED
1 11 0.3300 0.1089 0.1089 14.6684 1 2 12 0.3829 0.1466 0.0377 5.2589 2 3 18 0.4308 0.1856 0.0390 5.6436 3 4 7 0.4484 0.2011 0.0155 2.2648 4 5 9 0.4628 0.2142 0.0132 1.9453 5 6 5 0.4693 0.2203 0.0060 0.8920 6 7 6 0.4768 0.2273 0.0071 1.0437 7 8 15 0.4834 0.2336 0.0063. 0.9274 8 9 8 0.4904 0.2405 0.0069 1.0179 9 10 10 0.4953 0.2453 0.0048 0.7045 10 11 14 0.4988 0.2488 0.0034 0.5031 11 12 16 0.5002 0.2502 0.0015 0.2118 12 13 17 0.5012 0.2512 0.0010 0.1472 13 14 2 0.5019 0.2519 0.0007 0.0932 14 15 3 0.5022 0.2522 0.0003 0.0368 15 16 4 0.5023 0.2523 0.0001 b.0195 16 17 13 0.5023 0.2523 0.0000 0.0018 17
were retained in the memory of the computer and used for calculating partial correlations of each independent variable not yet brought into the multiple correlation equation. This provided a measure which enabled the machine to select the appropriate independent variable to next bring into the computation. The simple correlations, used to gether with the means listed on the first page of the illustration, were again used after completion of the machine computation of multiple correlation, in order to refine the significant multiple regression equation. This refinement is described in the next section of this chapter.
Tables 3 thru 6 of the computer output illustration portray the first four steps in the multiple correlation computation. The reader will notice that the illustration covers the second subproblem of the combined computation. The three subproblems were similar; nothing would be gained by showing all three. Subproblem number two, elasticity D5 regressed against socioeconomic variables for calendar year 1960, was chosen simply because fewer steps were required to reach the significant regression equation, using the significance test described above.
Step one (Table 3) identified the dependent variable as number 19, and stated the F level required for inclusion (0.001), the F level at or below which an included variable will be rejected (0.00001), and the tol*erance level (0.001). It then continued with the computation, printing as output the information listed above under the section "Multiple regression technique." Independent variable number 11 was brought into the regression equation in this step. Its partial correlation with the
dependent variable was not printed, but it was computed by the machine and compared to the partial correlations for all other independent variables. In order for variable 11 to be selected for inclusion, it had to have the highest partial correlation of all the outstanding independent variables, as well as having an F level as high as .001.
Of the remaining independent variables, number 12 had the highest partial correlation with the dependent variable, a value of .20572, and it was the variable selected for inclusion in step two. The reader should be aware that although variables I and 20 are shown among the variables not in the equation, the machine program excluded them from consideration, since they were the dependent variables used in subproblems one and three. Actually, no purpose was accomplished by including them in the printed output of subproblem two. They were allowed to print only because of the difficulty of programming their elimination from the printout of the subproblems to which they did not apply, and because some uses of the computer program find an advantage in having them included.
The reader should be cautioned that t,e numbers identifying the variables in the machine output are not the same as the identification symbols used in this report of the study. The computer program automatically numbers the variables in the order that they appear in the punched cards used for machine input, whereas it was deemed advisable to symbolize the variables for report purposes consistent with the symbols used in the related previous studies. The respective equivalents are indicated in the tabulation on the following page:
TABLE 8
CORRESPONDENCE BETWEEN COMPUTER IDENTIFICATION
NUMBERS AND VARIANCE SYMBOLS
Identification Symbol Identification Symbol Number in used Number in used Computer Output in Report Computer Output in Report E5 or E7 11 X14 2 X 12 X15 3 X2 13 x16 4 X3 14 X17 5 X5 15 X18 6 X6 16 X19 7 X7 17 X21 8 x8 18 X22
9 X12 19 D3 or D5
10 X13 20 R4
The third step brought variable 18 into the computation; the
fourth step, variable 7. The computation continued in this manner until all independent variables were tested for entry and all variables entered were tested for rejection. In the particular subproblem chosen for illustration, all 17 of the independent variables were eventually chosen for inclusion, and none was rejected after being entered. However, only four steps are shown, since this number of steps suffices for the purpose of demonstrating the application of the ttest for significance, as follows.
In step one, the regression coefficient of 0.03467 is more than 1.98 times its standard error of 0.00905, and as such it is considered significant, and the test proceeds to the next step. The coefficients in step two, 0.02735 and 0.01253, exceed their respective standard errors,
0.00945 and 0.00546, by more than a multiple of 1.98, so this step was also accepted. Similarly, the coefficients in step three all passed the ttest thus applied, but in step four, variable seven, which was being entered, failed to equal 1.98 times its standard error (0.02329 compared to 0.01548), and therefore the entire step was rejected. The previous step, step three, was thus accepted as final, with only the variables accepted at that point being considered significant. Furthermore, the regression equation set forth by that step was considered the most significant equation for predicting the dependent variable.
Table 7 of the illustration displays a summary of the entry
and removal of variables throughout all the different steps of the computation, and it shows the value of both multiple correlation and variance at the completion of each step, together with the change in variance caused by each entry and each removal. This table is very relevant to the first three hypotheses of this study inasmuch as it indicates the contribution of each variable to the overall variance.
Up to this point, the multiple regression techniques employed in this study are similar to those used in the separate studies of Florida, Georgia, Kentucky, and Illinois. The computer program has been redesigned to reflect more information in a more usable format, but the statistical result is identical. And the significance tests employed here are the same as the ones used previously, such that any given set of data would product identical regression equations and related constants.
Therefore, the results, up to this point, are comparable, and they have been compared in the analyses of data to the extent such comparison was deemed relevant to the current study.
However, it was felt that a refinement was needed to the above procedure before the coefficients of the regression equation would indicate with the desired degree of specificity the relationship of each included independent variable to the related dependent variable. Therefore, the current study needed a rather extensive modification to the statistical procedures used in the previous studies, in order to transform the regression equations into more meaningful form. The need for this modification and its application are described in the following section.
Removal of interdependency between independent variables
CelIa (1967) cautions that the theory of regression requires all observations of each independent variable to be completely free of any interrelationships with other independent variables. He points out that violations of this principle can result in overstatement of regression relationships, and he makes the following statement regarding computation of regression equations by usual methods (which would include the methods used in this study):
When model building is completed, the multiple correlation between the dependent variable and the independent variable will be high and the variance will be
small so the model will be suitable for predicting purposes. However, it will be of little value for other
analysis purposes because the parameters will be so
obviously unrealistic.
Since the primary purpose of deriving regression equations in this study is not for prediction purposes, but rather for illustrating relationships between variables, it is obvious that some adjustment in the
parameters produced by the above multiple regression procedures was
needed. That is not to say that these procedures should not have been
used, for quantification of the components of the regression model must
begin with the calculation of the parameters of the functional relationships between the independent variable and the data of each independent
variable. Celia (1967) refers to these as "gross" regressions because
"part of the changes in the values of the dependent variable are due to
changes in the values of one independent variable and the remainder are
due to changes in other independent variables." Under these circumstances, the measurement of the regression relationship is the largest
possible, because all the changes in the dependent variable have been
attributed to one variable. Yet variations in the dependent variable
are almost invariably caused by changes in several independent variables
acting simultaneouslythus, the term "multiple regression."
The following explanation by Celia (1967) tells why it is so
essential to transform these gross regressions to net regressions, thus
eliminating the effect of interdependency between independent variables:
In a multiple regression, the relationship between
each independent variable and the dependent variable is a net rather than a gross. The net regression measures the
variation of the dependent variable which is caused by
variations in an independent variable, with the impact of
the other independent variables measured also. Each of
these latter is measured as though all of its values were
identical so instead of multiplying a regression coefficient by a variable, the same amount is deducted from the
dependent variable for each observation. As a result,
the net regression describes the variation in the dependent variable which is due to changes in a particular independent variable. Since the net regression only
explains the variation in the dependent variables which is due to a particular independent variable, it will be less than the gross regression. In a demand analysis a
gross regression merely measures the amount of associated
variation between the variable while a net regression
attempts to measure the amount of cause and effect.
These remarks imply that the parameters of the net regression
equation indicate the relationship of each independent variable to the dependent variable more accurately than do the parameters of the unrefined regression equation. Since accuracy with regard to this relationship lies at the heart of the present study, it was felt to be essential that the gross regression coefficients be converted to net coefficients. As explained in the M.I.T. Summer Course on Operations Research (1953), this requires the calculation of a system of weights which indicate the relative importance of the independent variables. The effect of this weighting is to appreciably scale down the size of coefficients which have minor influence upon the dependent variable and to make lesser reductions in coefficients having more significant effect upon the dependent variable. Different methods for applying weightings are proposed by Frisch (1934), Wold (1953), Ferber (1962), and others. These methods for quantifying the model are not the same as the conventional least squares analysis approach, although the objectives are similar. Furthermore, the models which have been transformed by weighting are suitable for a variety of applications rather than being restricted to prediction purposes.
The weighting system is actually a second weighting, inasmuch as the gross regression coefficients themselves are weights, functioning as multipliers of the independent variables. Celia (1967) therefore describes the weighting system of a transformed regression equation by a formula similar to that shown below, and he illustrates the effect of the transformation as shown in Figure 1 on the following page.
Y = b0 + w b X + w b X +
0 1 11 22 2
42
Y
S=b Gross 4y 1 = Regression A x
"yNet x I Regression II I I I bo 0
0 X Figure 1. Gross Regression Versus Net Regression
Source: Celia (1967)
where b, b etc., are gross regression weights and w, w2, etc., are the importance weights for converting to net regression.
Importance weights used in this study for converting from gross to net regression consist of coefficients of partial correlation between the individual significant independent variables and the concerned dependent variables. In suggesting this use of partial correlations, Celia (1967) advises the reader as follows: A partial correlation is a measure of the extent to
which the variation in the dependent variable is explained
by an independent variable. When all the factors which
influence a dependent variable are included in an analysis,
the partial correlation coefficients will measure the extent to which each independent variable affects the
dependent variable.
Croxton and Cowden (1955) describe coefficients of partial correlation as measures of "the relative importance of the different independent variables in a problem in explaining variations in the dependent variable." Inasmuch as the present study is highly concerned with
discovering the relative importance of the different independent variables in molding school fiscal policy, it makes extensive use of partial correlations as a weighting system for refining the gross regression equations.
However, Cella (1967) cautions, "The calculation of importance weights is a drawnout task, even with the aid of a computer." It requires first the computations of zeroorder correlations for each posSsible pairing of variables from the gross regression equation. The zeroorder correlations are used in turn to compute a series of first order correlations, using the general formula
r r 2 r2
r12 13 23
1i2.3 = _
(1 rl3)( r23)
where one is the dependent variable, two is the first independent variable being correlated with the dependent variable, and three is the particular independent variable being held constant. The subscripts are changed to fit the numbers of the variables involved in the computation. The "order" of a partial correlation refers to the number of variables being held constant, and the symbol for partial correlation indicates this by the number of subscripts following the decimal. Thus, the above formula provides for the computation of first order correlations.
Each partial correlation used as an importance weight for transforming a gross regression to net must hold constant all but one of the independent variables. The order of the partial correlation required is therefore one less than the number of independent variables. Since some of the regression equations found to be significant in this study contained as many as seven independent variables, it was necessary to compute partials as high as the sixth order, requiring the use of the following formulas in addition to the one shown above: r r1. r2.
second order r 12.34 r 12.3 LI.3 24.3 'J(I rl4.3)(l r2k3
r r r2
14.324.3)
third order r12.345 = 12.34 15.34 25.34 ( 1 r5.34) ( r25.34)
fourth order fifth order sixth order
r123456 12.345 16.345 r26.345
12 3456 r 2 )(1 r
16.345) 26.345)
r1234567 r 12.3456 r 17.3456 r27.3456 S 3456)(1 r27.3456)
r1234567 r18.34567 r28.34567 r12.34567
./( r(1 r 2
r18.34567) r28.34567)
The first order partials are used to calculate the second order,
the second to compute the third, etc. It becomes apparent that a tremendous number of computations are required in order to obtain the needed importance weights when the number of independent variables reaches four or more. This might well have been an influential factor retarding the application of weightings to multiple regression equations in prior research.
To illustrate the use of partial correlations as weighting factors for converting gross multiple correlations to net, the significant equation for D based upon raw data, is used.
Gross
Regression D = .14608 +.02366 x + .01564 X + .00296 X
Equation: 5 11 02
Partial coefficients and their conversion to importance weights:
Partial
Coefficient
o5 to Xio = .2229 o5 to Xl] = .2523 D5 to X17 = .2133 Total .6885
Importance
Weight
.2229 = .3237
1 .6885 w2 =.6885
w .2133 =
3 .6885 3099
In converting partial coefficients to importance weights, all values are treated as positive, regardless of their actual sign. But when the weights are multiplied by gross coefficients to produce net coefficients, the signs of the coefficients are retained. This transformation appears as follows:
Gross
Regression blo = +.02366 b l = +.01564 b = +.00296 17
Importance Weight
.3237 .2664 .3099
Net
Regression
.00756 .00573 .00092
The constant term must also be transformed, using the following formula:
I  I. w '2 b; b Y x b2 X2 b X b 'X3
0 11 2 2 3 3 3
where b is the constant term of the net equation; Y, the mean of the
0
dependent variable; the b terms, the net regression coefficients computed above; and the X terms, the means of the respective independent variables. The last term of the formula illustrates the fact that the
net regression coefficient would be calculated for higher powers of a variable in exactly the same way as for linear terms. Using the above formula, the constant term for the D5 raw data net regression would be calculated as follows:
(1) (2) (3) (4) (5)
Gross Net Means of Difference Constant Regression Independent Product of in Totals
Term Coefficient Variables (2) x (3) (1) less (4) b0 = 1.12090
b 10= "00756 bll = .00573 b 7 = .00092
34.29835 22.88852
36.37048
1.12090
This completes the transformation computed estimates of net regression for tion yields the following net regression
.25935
.13116 .03352
.42403 = .69687 = b0
of parameters. Substituting the the gross parameters, the equamodel:
D5 69867 + .00756 Xlo + .00573 X11 + .00092 X17
This equation gives the relationships of the respective significant independent variables to the dependent variable, with the interdependent effects of other independent variables eliminated. Thus it can be used to more realistically analyze the relationships of socioeconomic factors to school fiscal policy. Therefore, the net regression has been derived in this study for each of the dimensions of local school fiscal policy: financial effort, elasticity of demand for education, and revenue receipts per pupil. This, together with the gross multiple correlation and its related constants have been used to investigate the last three hypotheses.
The use of weighting systems to convert gross regression models to net is not a new or exclusive statistical technique. It was a central topic at the MIT Summer Course on Operations Research (1953), and it has been discussed in statistical tests including those by Frisch (1934), Wold (1953), Ferber (1962), and Croxton and Cowden (1955). However, it was felt to be advisable to make a sample test of the regression models which were thus transformed in the present study. The test was conducted as follows, for each regression equation tested.
The gross equation was used to predict the value of the dependent variable for each of the "122 districts in the sample. Next the corresponding net equation was used to calculate its prediction of the same dependent variable for each of the districts. Then each set of predictions was correlated against the actual values of the dependent variable in order to ascertain that there was no material loss of predictive accuracy resulting from the transformation. The results of these tests are discussed in the next chapter. Alternative significance test
In the procedures described above, this study has followed the identical significance test as was used in the original studies. This has allowed the results of the current study to be compared to those of the original, but this researcher feels that the application of a ttest is in effect the rendering of a second significance test. The use of F levels as criteria for entry and removal of independent variables during the multiple regression computation serves as a basic significance test. By regulation of the F levels specified for inclusion, the degree of relationship of selected variables could be controlled, eliminating the need for a second significance procedure.
49
Futhermore, it is felt that the elimination of variables through this particular application of the ttest at a level as high as 0.05 is undesirable because of the extensive impact it has upon total variance. This is illustrated in Table 7, which summarizes the results of elasticity of demand D5 being regressed in multiple step wise regression against the 17 selected socioeconomic variables. Only three variables are accepted by the ttest as being significant, whereas all 17 of the independent variables are brought into the regression equation by the multiple correlation program. The variance associated with the three variables is only 0.1856 as compared to 0.2523 for all seventeen. Although it is convenient to reduce the number of variables by the application of a significance test beyond that of the F levels used in the multiple regression program, the accuracy of the computation appears to be much greater with the retention of a larger number of variables. The progressive effect of the eliminations is shown by the "INCREASE IN RSQ (R squared, or variance)" column of Table 7. The first variable eliminated by the ttest would have contributed more than 8 per cent as much variance than the total variance accepted as being significant. The total variance eliminated by the ttest would have contributed more than 35 per cent as much as the recognized variance.
Therefore, as an additional procedure, the 1960 regression equations for financial effort, elasticity of demand, and revenue receipts per pupil were recomputed without the benefit of the ttest. In each case, the gross equation was determined and then transformed to net. This was followed by calculating partial correlations between the independent variables with the respective dependent variables, coefficients of partial determination, importance weights, contributions toward total
50
variance, total multiple correlation, and total variance. The significance of each of these is discussed in Chapter III, and the computed values are tabulated for easy reference. The computations were made both using raw data and using standardized deviate value equivalents.
CHAPTER I II
ANALYSES AND INTERPRETATIONS OF DATA All of the 122 districts provide local support of public education through property taxes. As pointed out in Chapter I, the equality of the instructional program is strongly related to the financial support provided. For this reason, educators are vitally concerned with maintaining a school fiscal policy that is conducive to adequate financial support. The purpose of this chapter is to examine the relationship of the 17 selected socioeconomic variables to local school fiscal policy, so as to determine whether they might serve as a leverage toward better support.
To relate fiscal policy statistically, it was necessary to quantify each of the study variables. Three measures of fiscal policy were used in the original studies of Florida, Georgia, Kentucky, and Illinois: Financial effort, elasticity of demand for education, and revenue receipts per pupil. Each of these is defined in Chapter I under "Definition of terms," and discussed in Chapter II under "Sources of data." The most traditional measure is revenue receipts per pupil, for which fiscal policy is quantified by dividing total revenue receipts by total pupils in average daily attendance. However, there is an inherent limitation in this measure of fiscal policy. It corresponds too closely with the amount of financial resources availablethe ability to support education. Those districts which have higher per capita personal income tend to pay more for education. A measure of fiscal policy which would
51
be more meaningful to educators would be an index of the effort made by the district to use its resources for education, regardless of the level of resources available. As such, a second measure of fiscal policy has been used, one which tends to eliminate the effect of adequacy of financial resources. It relates financial support actually provided for education to the total available resources. Total local school revenue is divided by total disposable personal income for the district, reflecting a measure which is defined in this study as financial effort. This may be considered as an index of the district's willingness to use its resources for education.
Another measure of fiscal policy, which has proven to be quite useful is the elasticity of demand for education. It indicates the response of a school district to a change in per capita disposable income. The greater the portion of an income increment invested in education, the greater the elasticity of demand. Basically, the coefficient of elasticity indicates what percentage change in revenue per pupil accompanies each percentage change in per capita net effective buying income.
If the ratio of pupils to total population remains unchanged, then the coefficient of elasticity of demand indicates the tendency of financial effort to change, since the basic formula would be reduced to percentage change in revenue divided by percentage change in net effective buying income. For this reason, elasticity of demand is sometimes seen as a modification of "financial effort," denoting the extent of inclination for effort to change directly with change in personal income. A difficulty is presented with using the basic formula when there exists a change in revenue but none in personal income, for the computation would give infinity as an answer. For this reason a more sophisticated
formula is provided, as described under "Source of data," Chapter II, which gives essentially the same result while overcoming this difficulty.
The first step in analyzing the data relating to the above three measures of fiscal policy was to examine the patterns of financial effort and elasticity of demand to determine their consistency among the respective districts over a period of time.
Consistency of Effort and Elasticity
As might be suspected, there was considerable variation in financial effort among districts.. The highest among the 122 districts had an effort more than fifteen times as high as that of the lowest. This is shown by Table 9, which, in addition to ranking the districts by level of financial effort (E7) shows the specific effort rating of each district and the change in ranking during the previous ten years. The ranking change was computed by comparing E7 and E5 rankings. A summary of these changes show that out of 122 ranks, a majority of 69 districts experienced ranking changes of less than 15 places. Furthermore, 105 of the districts changed less than 30.places, indicating high stability of effort. High effort districts tended to remain high, and low effort districts tended to remain low. A few districts made marked changes in relative position over the ten year time span. Eight districts changed in rank by more than forty places. Table 9 identifies these districts only by code number, so it was necessary to refer to Appendix B in order to find the names of these districts, which are as follows:
State District Ranking Change
Florida Orange 55 Florida Leon 70
Georgia Clayton 74 Kentucky Carter 47 Kentucky Knox 43 Kentucky Pike 54 Illinois Jacksonville +45
A quick review of Table 9 shows that the four states tend to stratify, with Illinois tending to fill the upper ranks, Georgia the lower, and Florida and Kentucky respectively filling the intermediate ranks. The average ranks andmean financial effort ratings by state are shown below, and they further substantiate the stratification mentioned above:
Average Mean E7 Mean E5 State Rank Effort Effort
Illinois 15.2 3.422 2.0864 Florida 59.4 1.573 1.3947 Kentucky 70.4 1.3935 1.3626 Georgia 92.5 0.9400 0.8167
For each of the four states, the mean E7 effort was higher than the mean E5 effort. Similarly, the mean effort of the fourstate composite increased from 1.39060 to 1.7835 during the same period. These points indicate that there was a general tendency for the level of effort to increase over the tenyear time span.
In summary,. the analysis of rankings by financial effort tends to confirm the first hypothesis, which is restated as follows: "Most school districts follow consistent patterns of financial effort and elasticity, yet some make marked changes in relatively short periods of
TABLE 9
RANKINGS OF 1960 FINANCIAL EFFORT (E7) ANC
CHANGES IN RANK SINCE 1950
Dist. E7 Rank Chg. Dist. E7 Rank Chg. Dist. E7 Rank Chg. Dist. E7 Rank Chg. Dist. E7 Rank Chg.
412 5.226
404 4.447 426 4.430
I +8 2 1 3 0
409 4.123 4 9 418 4.118 5 +15 413 3.946 6 + 6
427 3.853 416 3.846 41o 3.779
7 +7 8 45 9 4
402 3.706 10 +22 414 3.660 11 + 8 403 3.640 12 + 9
411 3.632 13 6 401 3.545 14 8 417 3.517 15 + 2
419 3.436 16 + 7 428 3.234 17 15
424 3.058 18 +15
421 3,033 19 +12
415 3.012 20 9 422 2.970 21 +21
406 2.789 22 +15 420 2.788 23 +11 317 2.701 24 + 6
308 2.573 26 +32 408 2.572 27 3 423 2.550 28 +31
130 2,440 29 +27 425 2.437 30 +15 104 2.222 31 21
310 2.185 32 +20 115 2.143 33 7 110 2.091. 34 30
126 2.036 35 +14 106 2.011 36 7 117 2.007 37 + 4
114 1.987 38 +16 125 1.947 39 0 112 1.841 40 + 7
407 1.835 41 + 9 220 1.818 42 +25 128 1.801 43 +14
122 1.789 44 0 302 1.769 45 +27 301 1.764 46 31
105 1.762 47 +35 313 1.718 48 30 323 1.702 49 13
221 1.622 51 +40 123 1.606 52 30 324 1.598 53 +37
325 1.591 54 +11 316 1.581 55 0 118 1.566 56 8
119 1.558 57 30 103 1.550 58 +16 132 1.504 59 21
101 1.503 60 +23 311 1.491 61 +14 327 1.483 62 54
121 1.474 63 12 318 1.453 64 + 6 304 1.436 65 +13
312 1.430 66 26 309 1.423 67 +14 131 1.398 68 25
320 1.386 69 +21 I1 1.383 70 10 218 1.365 71 +35
209 1.330 72 +28 303 1.320 73 +22 127 1.293 74 +22
226 1.260 76 0 319 1.243 77 +10 108 1.227 78 +10
207 1.189 79 +40 216 1.182 80 +30 227 1.178 81 8
215 1.166 82 +30 107 1.159 83 14 116 1.150 84 +17
109" 1.134 85 +15 229 1.127 86 I 322 1.110 87 24
328 1.097 88 27 219 1.051 89 +28 222 1.047 90 28
217 1.036 91 + 3 230 1.016 92 +11 129 1.006 93 29
329 0.986 94 17 102 0.978 95 9 202 0.977 96 + 9
212 0.952 97 +17 224 0.926 98 +10 210 0.893 99 74
208 0.856 101 + 8 307 0.849 102 84 326 0.837 103 10
213 0.803 104 + 4 315 0.782 105 21 113 0.764 106 2
214 0.732 107 + 8 228 0.716 108 6 212 0.700 109 + 5
204 0.681 110 3 232 0.672 III 22 231 0.653 112 + I
203 0.639 113 + 8 321 0.624 114 43 205 0.623 115 + 7
306 0.619 116 70 201 0.611 117 3 233 0.547 118 2
225 0.436 119 40 314 0.374 120 22 120 0.346 121 55
206 0.338 122 25
405 2.639 25 +10 124 1.663 50 +18
305 1.286 75 47 223 0.879 100 +11
time."* The analysis reflected the fact that most districts did experience relative consistency in effort pattern, with an overall trend to increase gradually. Yet, as hypothesized, a few districts made marked changes in pattern. Eight districts changed their relative ranks by more than forty places, which is over a third of the full range of rankings.
A similar analysis of rankings by elasticity of demand gave very different results. Table 10 presents the elasticity values (D5), rankings, and changes in rank. Only 52 of the 122 districts changed position by as few as 30 places. Forty of the districts changed by more than 50 per cent of the full range of rankings, and six changed by more than 100 places. The inconsistency is further highlighted by the summary of means by state, which shows two states increasing while the other two are decreasing.
Average Mean D5 Mean D3 State Rank Elasticity Elasticity
Georgia 41.1 1.7169 0.6552 Florida 54.0 1.2333 0.6872 Illinois 63.2 1.0109 1.1119 Kentucky 82.4 0.6078 0.7656
The composite mean increased from 0.73836 to 1.12090. Not only was there a general reshuffling of district rankings over the tenyear period, but the states tended to reverse their relative rank positions. The mean elasticity of two states increased sharply while the coefficients of the other two states were lowered. There was a general lack of consistency, which contradicts the first hypothesis with respect to elasticity.
TABLE 10
RANKINGS OF 1960 ELASTICITIES OF DEMAND (D5) AND
CHANGES IN RANK SINCE )950
Dist. 05 Rank Ch9. Dist. 05 Rank Chg. Dist. 05 Rank Chg. Dist. 05 Rank Chg. Dist. 05 Rank Chg.
210 4.73 +104 223 3.34 2 +109 .420 2.88 3 + 24
220 2.66 4 + 64 216 2.61 5 + 62 224 2.38 6 + 34
130 2.34 7 + 67 209 2.30 8 +109 233 2,28 9 + 98
226 2.24 10 + 67 219 2.16 11 + 32 105 2.16 12 + 12
115 2.)) 13 + 80 I17 2.10 14 + 69 232 2.07 15 + 85
128 2.03 16 +103 205 1.99 17 + 42 )08 1.96 18 + 57
427 1.86 19 + 57 221 1.85 20 + 29 )23 1.85 21 + 39
228 1.83 22 + 66 212 ).81 23 + 81 207 1.77 24 + 65
1.70 26 + 12 1.70 27 + 36 1.68 28 3
1.67 29 + 62 1.67 30 + 21 1.66 31 + 64
1.56 32 15 1.56 33 + 53 1.55 34 30
1.55 35 73 1.53 36 + 70 1.42 37 6
1.40 38 24 1.37 39 2 1.37 40 35
1.36 41 + 68 1.36 42 22 1.34 43 + 53
1.27 44 26 1.27 45 6 1.26 46 10
1.24 47 + 51 1.24 48 + 62 1.23 49 + 5
1.21 51 35 1.17 52 + 17 1.17 53 + 29
1.16 54 + 18 1.13 55 52 1.08 56 + 28
1.07 57 10 1.05 58 + 8 1.05 59 14
1.03 60 + 32 1.02 61 8 1.02 62 7
1.01 63 40 1.00 64 45 0.97 65 )
0.97 66 + 19 0.93 67 5 0.92 68 12
0.87 69 + 5 0.85 70 64
0.83 71 0
0.81 72 42 0.81 73 27 0.8O 74 59
418 0.78 76 64 325 0.77 77 66
120 0.77 78 + 35
0.76 79 46 0.72 80 + 32 0.71 81 23
0.70 82 71 0.68 83 31 0.67 84 25
0.63 85 + 17 0.63 86 54 0.63 87 39
0.62 88 + 13 o.62 89 54 0.61 90 + 20
101 0.58 91 89 412 0.58 92 70 324 0.56 93 83
0.55 94 64 0.53 95 25 0.49 96 95
0.49 97 + 6 o.48 98 + 18 0.48 99 86
0.44 10) + 1M 0.43 102 58 0.38 103 + 19
310 0.37 104 62 413 0.36 105 79 408 0.35 106 + 15
0.35 107 26 0.34 108 + 10 0,34 109 44
0.27 110 16 0.24 MII 103 0.22 111 70
0.15 113 23 0.13 114 27 0.12 115 81
0.06 116 17 0.0 117 20
0.0) 118 77
321 o.14 119 62 411 0.14 120 91 314 0.43 12) 43
306 0.52 122 42
116 1.71 25 18 404 1.23 50 + 29
106 0.79 75 47
416 0.46 loo 79
.Thus, while financial effort was rising rather uniformly for a
large group of districts with very little shifting of relative positions within the group, the elasticity of demand fluctuated without any obvious pattern, causing a complete reordering of relative ranks. Brazer (1959: 18) points out that "although these (elasticity of demand) coefficients are valid for only very small changes in the independent variable, they provide a simple measure of the 'sensitivity' of the dependent variable to changes in the independent variable." In the context of the present study, this would be a sensitivity of local revenue per pupil to net effective buying income per capita. This sensitivity can change markedly from one period of time to another without a material change in effort. This is illustrated by the following example, which used the basic formula for elasticity (percentage change in revenue per pupil related to percentage change in net effective buying income per capita) in order to simplify the example.
F
P,
a. Revenue $ b. Pupils
c. Revenue per pupil $ d. Percentage change from
previous period
e. Net effective buying
income $ f. Population g. Net effective buying.
income per capita $ h. Percentage change from
previous period i. Effort (a" e) j. Elasticity (d h)
i rst eriod
1,000,000
10,000
100.00
Second
Period
$ 1,070,000
S 1o,4oo
1 02.89
2.89
100,000,000
50,000
2,000.00
1.000
$105,000,000
52,000
Th ir d
Period $ 1,135,000
11,000 $ 103.18
0.28
$112,000,000
53,500
2,019.20 $ 2,093.50
0.96 1 .019
3.01
3.68
1.013 0.076
59
There is nothing extreme about the example shown on the previous page, yet the coefficient of elasticity of demand has fluctuated wildly while effort has remained substantially constant. Although the averaging of values over a nine year period has tended to stabilize the elasticities of the districts in the composite sample, the effect demonstrated above is still present. Even using nine year averages, many districts experienced drastic changes in elasticity coefficients while their levels of effort changed very little. This researcher questions whether elasticity of demand is not overly sensitive for the purpose of evaluating the influences of socioeconomic variables upon school fiscal policy. This will be examined further when investigating the results of stepwise multiple correlations relating elasticity of demand to the 17 selected socioeconomic variables.
Relationship of (a) Financial Effort to
(b) Fiscal Response to Income Change
It has been hypothesized that high effort districts are more
responsive to change in per capita personal income than are low effort districts, such that a greater portion of increases in their personal income is invested in education. The validity of this hypothesis was investigated by correlating financial effort E the average effort for years 1959 through 1961, against elasticity of demand for education D the 1953 through 1962 average.
Pearson r was first calculated using raw data and found to have a value of 0.00516. This is obviously an extremely low correlation, but to further evaluate its significance, a ttest was applied, using the formula
t T r'2
where r is the Pearson r discussed, and N is the number of pairs of observations in the sample. This computation reflected a value of 0.0565 for t, and it was used in a test for significance as described by Crowley and Cohen (1963). "The test of significance of a correlation is a test of the null hypothesis, 'the obtained correlation in this sample is not different from a correlation of zero. Any difference can be ascribed easily to a chance variation about population correlation of zero."'
If the calculated value of t exceeds the ttable value, significance is indicated; otherwise, the null hypothesis is confirmed. In the present case, the ttable value for 120 degrees of freedom at the 0.05 level is 1.98. The calculated value, being much smaller than this, confirms the null hypothesis and leads to the conclusion that any difference can be ascribed easily to chance variation.
But have we combined the variables from the four states on comparable bases? It has been pointed out in the previous section of this chapter that there is a consistent stratification of effort levels between the four states, and Chapter II explained that raw data permit extraneous factors to influence variables in some states while not affecting those in others. Legal restrictions upon levels of taxation and fiscal dependence, for example, are among the factors most commonly found to cause such stratification. The effects of such extraneous factors had to be removed if the correlations were to be meaningful. The method chosen for placing the values of effort and elasticity for the districts of the four respective states on a comparative basis was transformation from raw values to Z values using the simple formula X M
Z value =
SD
where X is the raw value of the variable being transformed, M is the mean of the sample variable, and SD is the standard deviation of its distribution. Transformations of variables from the four states were made separately and the resultant Z values provided bases sufficiently comparable to permit the data to be combined for composite analysis.
Drawbacks in the use of standardized data were recognized. While standardization eliminated deviations caused by extraneous effects, it was likely that some of the soughtfor deviation would also be eliminated, that which was caused by the selected socioeconomic factors. Furthermore, it was necessary to proceed on the assumption that the forms of distribution for the different states were nearly identical, which is highly improbable. However, as Guilford (1965) points out, "In spite of these limitations, it is almost certain that derived scales, such as the standardscore scale, provide us with more nearly comparable values than do rawscore scales."
After converting both varaibles to standardized deviate value equivalents, the Pearson r was again calculated and found to have a higher correlation. The coefficient based on Z values was 0.2607. The ttest showed significance at the 0.01 level, with a tvalue of 2.95. But even with the higher correlation using Z values instead of raw data, only 6.20 per cent of the total variance is accounted for. This degree of support for the second hypothesis is still very weak to be considered. This researcher has therefore reached the conclusion that there is little recognizable association between level of effort and fiscal response to change in personal income.
Relationship of Socioeconomic Factors to Local School Financial Effort
At this point it might be well to recall the statement of the central problem with which this study is concerned. In Chapter I it was brought out that recent research studies concerning influences upon school fiscal policy have identified two general categories of determinants: (a) socioeconomicthose which are inherent in the society, the culture, and the economic system of the district; and (b) leadershiprelatedthose which are based upon leadership traits of influentials, decision making processes, val.ue systems of the informal power structure, typology of the power structure, and leadership of the superintendent and other educational officials. If educational leaders are to be effective in shaping school fiscal policy, they must know which of the above categories of determinants are influential and to what degree, for the strategies which would be effective in bringing about desirable change would be exceedingly different under the two alternatives.
The primary purpose of the current study was to test a selected group of variables from the first category, socioeconomic determinants, so as to investigate their effect upon school fiscal policy. If found to be influential, then educators must consider them in planning strategies for change, but if ineffective, they must look to other factors as possible determinants, such as the leadershiprelated determinants. Current research is being increasingly devoted to investigating the influence of the latter upon school fiscal policy. The results of that research should complement the findings of the current study in guiding educators to the most effective means of shaping school fiscal policy.
The investigation of possible relationships between socioeconomic variables and school fiscal policy was begun by using a stepwide multiple correlation technique relating the selected 17 socioeconomic variables to local school financial effort. Due to dependence of the investigator upon the federal census, socioeconomic data were available only for decennial years. As such, relationships between variables had to be examined on a crosssectional basis (also called placetoplace or spatial) rather than a time (or sequential) basis.
All the firstorder correlations generated by the computer program are presented in Appendix C. Their importance derives from the fact that they not only provide the basic values for determining the selection of variables for inclusion in the multiple correlation models, but they also provide the means of transforming gross regression equations to net. The use of firstorder correlations in generating importance weights is discussed in Chapter II. By listing the correlation matrices in full in Appendix C, the writer avoided the necessity of repeatedly extracting partial listings for insertion at appropriate points in the text, as was done in the previous studies of the four states. The reader will notice that a single table presents all possible firstorder correlations among the three dependent variables and 17 socioeconomic variables. However, separate tables are required for different time periods (1950 and 1960) and for different bases of data (all raw and all standardized Z values.). Relationship of 1950 socioeconomic factors to financial effort E "5
Two separate regressions were made relating the dependent factor of financial effort E to the 17 selected socioeconomic independent variables. The first regression used raw data for all variables; the
second, Z values for all variables. The results of these regressions are summarized in Tables 11 and 12, respectively.
The first line of each table lists the constant term and all coefficiants of the regression equation which were found to be significant by ttest (described in Chapter II). These coefficients are labeled as "gross regression coefficients," following the terminology used by Cella (1967). The term "gross" implies that "part of the changes in the values of the dependent variable are due to changes in the values of one independent variable and the remainder are due to changes in other independent variables." Coefficients obtained by multiple correlation are therefore overstated because of the effect of interdependency between independent variables. A detailed explanation of this effect is given in Chapter II, showing that such equations are suitable for predicting purposes but are of little value for other analysis purposes because the parameters are so unrealistic. The explanation presented there goes on to describe a method for transforming the gross regression equation to net, thereby providing coefficients which attempt to measure amount of cause and effect rather than mere association between variables. The second lines of the respective summaries of regression analysis present the coefficients and the constant term of the net regression equations.
Referring to Table 11, for example, there is a striking difference between the coefficients of the gross and the net regression equations. Each net coefficient is only a fraction of the respective gross coefficient, and the constant term of the net equation is positive compared to the negative constant term in the gross equation. Cella (1967) commented as follows regarding the effects that occur in building a gross model,
TABLE II
SUMMARY OF E5 REGRESSION ANALYSIS
BASED UPON RAW DATA
Variables
E5 X3 X7 X8 X19 Constant Gross Regression Coefficient 0.05699 0.16196 0.01355 0.08361 0.32493 Net Regression Coefficient 0.01814 0.03572 0.00342 0.02234 0.89634 Mean 1.39060 16.39739 2.00410 16.23770 8.09098
0%
Standard Deviation 0.62929 4.08254 1.23606 14.42674 2.68396 Simple Correlation with E5 0.085 0.313 0.401 0.420 Partial Correlation with E5 0.3779 0.3206 0.3669 0.3884 Coefficient of Partial Determination 0.1428 0.1028 0.1346 0.1509 Importance Weight 0.25994 0.22053 0.25237 0.26716 Contribution Toward Variance 0.0481 0.0678 0.1124 0.1768 Multiple Correlation 0.6365 Total Variance 0.4051
TABLE 12
SUMMARY OF E5 REGRESSION ANALYSIS
BASED UPON Z VALUES
Variables
E5 X2 X16 X17 Constant Gross Regression Coefficient 0.73115 0.30243 0.44452 0.00000 Net Regression Coefficient 0.31184 0.06562 0.15847 0.00000 Mean 0.00000 0.00000 0.00000 0.00000 Standard Deviation 1.00000 1.00000 1.00000 1.00000 Simple Correlation with E5 0.330 0.098 0.171 Partial Correlation with E5 0.5020 0.2554 0.4196 Coefficient of Partial Determination 0.2520 0.0653 0.1761 Importance Weight 0.42651 0.21699 0.35650 Contribution Toward Variance 0.1092 0.1290 0.0500 Multiple Correlation 0.5369 Total Variance 0.2882
which bring about the need for refinement:
Suppose, however, that the regression between a
dependent variable and one independent variable is
calculated and a high positive correlation is found
to exist. Then another independent variable is found
which also correlates highly with the dependent variable
in a positive manner and the multiple regression of the
two independent variables is calculated. When this is done, the original value of the regression coefficient
for the first independent variable may be reduced appreciably. Then a third independent variable is
located which also correlates highly with the dependent variable in a positive manner; the process is
repeated. At about this stage, however, two possibilities occur: (1) the previous pattern will be repeated, or (2) some of the previous regression
coefficients will increase and take on unrealistic
values while the last regression may become a negative.
Also, the value of the constant term of the regression
equation, which will have been reducing a little in
the previous calculations, may undergo a sharp increase in this last calculation to further balance the adjustment being generated by the negative regression.
These effects do not damage the suitability of the completed model
for predicting purposes, but they do cause the parameters to be obviously
unrealistic for other analysis purposes. Since the primary use of the
regression equation in this study is to show relationships between
variables rather than for prediction purposes, it was urgent that the
transformation be made. The gross coefficient for independent variable
X3 was 0.05699, indicating that for every unit change in X3, the dependent variable, E changed 0.05699 units. This is misleading inasmuch
as only 0.01814 units of change, the amount of the net X coefficient,
3
are caused by a unit change in X3 alone. The rest of the change in E5
is caused by other independent variables, through interdependency with X3.
The third and fourth lines of each regression summary table show
the means and standard deviations, respectively. The former are used
in calculating the constant term for the net regression model, and the
latter are required in deriving the coefficients of separate determination. The next line of the summary table lists the simple correlations of each independent variable with the dependent, and this is followed by the partial correlations for each independent variable. The latter factor determines which variable will be entered into the multiple correlation computation first. The highest partial correlation in Table 11 is shown for X,9, and this independent variable was the first to be entered into the regression model. The second highest was the X3P but it was not entered second, since partial correlations must be recomputed for the outstanding independent variables at each step of the computation. After X 9 was entered, the recomputation of partials reflected a higher value for X8 than for X so X8 was entered second. The partial correlations are also used in deriving a weighting system for transforming the gross regression equation to net.
Each coefficient of partial determination is the square of the partial correlation, which it follows in the table, and its value constitutes a ratio explaining that portion of the variability in the dependent variable which may be attributed to specific independent variable when all other independent variables are held constant. The importance weights of the independent variables, which are listed next, show what portion each partial correlation bears to the total of all correlations of significant independent variables. Chapter II explains how these are used to refine multiple correlation equations so as to eliminate the effects of interdependency between independent variables and thus obtain parameters which show more realistic relationships between variables.
The next item is "contribution toward variance," and it indicates how much each entry into the multiple correlation increased the total
variance. The last two items are multiple correlation and total variance, respectively.
It is interesting to notice from Tables 11 and 12, that the
regression using raw data und entirely different significant independent variables related to financial effort E5 than did the regression using Z values. Significants in the former, with their respective contributions toward variance, were X,9, 0.1768; X89 0.1124, X 0.0678; and X3, 0.0481; total variance, 0.4051. In the latter, significant variables were X6, 0.1290; X2, 0.1092; and XI7 0.0500; total variance of
0.2882. It is obvious that standardization of data from raw form to Z values has had a tremendous impact on the results. As has been pointed out earlier, however, Z values are more comparable from state to state than are raw data. They therefore can be expected to give a truer indication of dispersion of actual distribution with respect to the influences of the selected independent variables.
Despite the inherent limitations upon the use of standardized
values, Guilford (1965:515) pointed out, "In spite of these limitations, it is almost certain that derived scales, such as the standardscore scale, provide us with more nearly comparable values that do raw score scales." That is the reason why this researcher places more emphasis on the results obtained from regressing Z values than from using raw data.
Furthermore, Tate (1955) observed,
Standard scores have several advantages in statistical
theory and practice. They are algebraic and hence are tractable in mathematical discussion. Since a standard
score is derived by dividing a deviation from the mean by
the standard deviation, both of which are the same unit, it is an abstract quantity, i.e., a quantity independent
of the original measurement unit....
He points out that the use of standard scores simplifies many statistical procedures.
By their use an individual's performance in one test
can be compared with his performance in a second, regardless of differences in the measurement units. Since they
are algebraic, the standard scores of individuals in
several tests can be combined into a composition score.
In the present study the measurement units are not different per se, but the units which were measured existed under circumstances that were quite different, causing the need for the data from different states to be transformed to a comparable base before being analyzed as a composite.
The relationship of student hours of preparation to grades
awarded by a highgrading teacher will be different from such a relationship under a lowgrading teacher. Similarly, there will be a difference between the relationships of personal income and school financial support in separate states where tax limitations are different, or where procedures of budget allocation and control are dissimilar. There are distinct advantages in transforming such statistical data to a more comparable base before proceeding with analyses of composite relationships.
As does Guilford, Tate defends the soundness of analyses using such standardized data, provided the distributions of raw scores are normal or approximately so. Even where nonnormal he points out (1955)
...that the standardization ratio has considerable stability of meaning except in markedly nonnormal distributions.
The standard score transformation may be applied to the
majority of distributions encountered in educational
testing without introducing serious error.
Why were different independent variables more significant with
Z values than with raw data? Two significance tests are embedded in the regression program; the selection of variables by F level and the 0.05
level ttest. The transforming of both dependent and independent variables, together with the resultant changes in distributions, makes it possible for these tests to select different variables from the different forms of data. Other possible explanations are the chance that minor nonlinear relationships may exist between one or more of the included independent variables and the dependent variable, and the fact that the slope and/or level of the distributions have been changed during the transformation, as the value of the constant term has been lowered from the level obtained with raw data to a zero level when using standardized Z values.
In the analysis of E5 regressions (Table 12), the total variance of only 0.2882 leaves a balance of 0.7118 unexplained. This tends to confirm the hypothesis that there is little association between socioeconomic factors and local school financial effort, and educational leaders should look to other factors for the principal causes of variance in financial effort.
In Table 12, the summary of E5 regression analysis based on Z values, although X2 had the greatest partial correlation with E5 and therefore was entered first, it does not make the greatest contribution toward variance. However, the net regression equation shows that a unit change in X2, per capita net effective buying income, has a greater impact on E5 thandoesX16 per cent of population comprised of college educated adults, or X17, median family income, when the effect of interdependency between independent variables is eliminated.
It is interesting to notice the comparison of significant variables and their respective coefficients of separate determination, as reflected by regression analyses of the separate states and of the
composite. This comparison is summarized in Table 13. The lack of consistency is obvious. It is observed that although XI9, per cent of population made up of 65yearolds, was significant in only one state, it showed up strongly in the composite based upon raw data. However, it was eliminated in the composite using Z values. On the other hand, X2 per capita net effective buying income, was omitted from significance in the raw data composite despite its being significant in two of the four states, but was included in the composite based on Z values. X was also significant in two states, but data for this variable were unavailable in Illinois and therefore had to be eliminated from consideration in the composite analyses.
The coefficients of separate determination shown on Table 13 and similar tables later in this report were calculated by multiplying the beta coefficients by the simple correlation between the independent and the respective dependent variables. The beta coefficients were obtained by multiplying the gross regression coefficients by the ratio of the standard deviation of the independent variable to the standard deviation of the dependent variable.
Relationship of 1960 socioeconomic factors to financial effort E7
Tables 14 and 15 summarize regression analyses similar to those presented in the previous section, and they present even more forcefully the contrast between results obtained from using Z values as compared to those based upon raw data. The total variance from significant variables is only 0.2549 when using Z values, whereas variance reaches
0.7550 with raw data. If one accepts Guilford's conclusion that standardscore scales provide us with more comparable data than do rawscore scales, he will realize that by far the greater portion of the
TABLE 13
COMPARISON OF COEFFICIENTS OF SEPARATE DETERMINATION FOR
SOCIOECONOMIC VARIABLES FOUND TO BE SIGNIFICANT
IN PREDICTING FINANCIAL EFFORT E5
Coefficient of Separate Determinationa Based on Raw Data Based on Z Values
Variable Fla.u Ga.L X2 (per capita net effective buying income) O.06N X3 (%ADA to total population) X5 (state revenue receipts per pupil) X7 (% of families with $10,000 income) 0.25P X8 (nonwhite % of population) XII (rural nonfarm % of population) O.19N X16 (college educated adults % of population) Xl7 (median family income)
X19 (65 yearolds, % of population O.16N X20 (ADA % of school age population) O.IIP
Ky.u Ill.e Composite Composite
0.21N
0.57P 0.03P
0.06P
0. lOP O.12N
O. 76P
O.09N
0. 15P
a The P or N following the coefficient indicates a positive or negative simple
Correlation with dependent variable. b Source: Hopper 1965 c Source: King 1965 d Source: Adams 1965 e Source: Quick 1965
0 24N
0.03N 0.08P
TABLE 14
SUMMARY OF E7 REGRESSION ANALYSIS
BASED UPON RAW DATA
Variables
E7 X2 X3 X12 X17 X18 X19 X22 Constant
Gross Regression Coefficient Net Regression Coefficient Mean I Standard Deviation I Simple Correlation with E7 Partial Correlation with E7 Coefficient of Part. Determination Importance Wt. Contribution Toward Var.
Multiple Correlation 0 Total Variance 0
.78354 .06337
0.00099 0.00014 1618.16393 441.64314
0.636
0.3719 0.1383
0.14592
0.4042
0.10898 0.02676 20.05598
4.39468 o.186
0.6257 0.3915 0.24551
0.1678
0.02211
0.00175
84.43030
5.83733
0.327
0.2014 0.0406
0.07902
0.0105
0.00025 0.00003
4746.67212 1291.28027
0.608 0.2883
0.0831
0.11312
0.0224
.8689
.7550
1.77862 1.03862
0.23203
0.02237
2.23443 0. 73864
0.543
o.2457 0.0604 0.09641
o.o145
0.11412 0.02609 9.54016
3.73092
0.444
0.5827
0.3395
0.22864
0.1213
0.00241
0.00022 36.37048 54.77359
0.031
0.2329
0.0542
0.09138
0.0142
TABLE 15
SUMMARY OF E7 REGRESSION ANALYSIS
BASED UPON Z VALUES
Variables
E7 X3 X5 X19 X22 Constant Gross Regression Coefficient 0.34001 0.36793 0.33905 0.24525 0,00000 Net Regression Coefficient 0.08561 0.09849 0.09412 0.04977 0.00000 Mean 0.00000 0.00000 0.00000 0.00000 0.00000 Standard Deviation 1.00000 1.00000 1.00000 1.00000 1.00000 Simple Correlation with E7 0.019 0.306 0.242 0.220 Partial Correlation with E7 0.3102 0.3298 0.3420 0.2500 Coefficient of Partial Determination 0.0962 0.1088 0.1170 0.0625 Importance Weight 0.25179 0.26769 0.27760 0.20292 Contribution Toward Variance 0.0443 0.0938 0.0673 0.0495 Multiple Correlation 0.5048 Total Variance 0.2549
variance in financial effort must be explained by factors other than tbe studied socioeconomic variables.
Another idfference in the analyses of the two types of data is that the transformation of the gross regression equation to net has a greater impact upon the coefficients of the raw data model. Each is more sharply reduced than are the coefficients of the standardized data equation, most of the coefficients being decreased to about 10 per cent of their gross value compared with reductions to approximately 25 per cent for the standardized data coefficients. On the other hand, the raw data constant terms receive a similarly greater but offsetting impact. The same effect was found for the E5 euqations; in each case the constant term was changed from a negative value in the gross equation to a positive value in the net equation, thus counterbalancing the reduction in size of the coefficients. In the Z value equation there was no change
in the constant term, inasmuch as standard scores do not generate a constant term, and the transformation process uses the gross constant term as a multiplier in creating a constant term for the net equation, causing the elimination of the constant term from the net equation also.
The effect of reduction in overall deviation which was caused by standardization of data may be largely responsible for the difference in the numbers of significant variables with the two different types of data. Table 16 shows that the composite analysis of raw data produces seven significant independent variables as compared with only four with standard scores. Three of these are common to both regressions: X3, ADA as a per cent of total population; Xi9, 65yearolds as a per cent of population; and X22, percentage increase in population over the previous decade. The former two were each significant in only one of the
TABLE 16
COMPARISON OF COEFFICIENTS OF SEPARATE DETERMINATION FOR
SOCIOECONOMIC VARIABLES FOUND TO BE SIGNIFICANT
IN PREDICTING FINANCIAL EFFORT E7
Variable
X2 (per capita net effective buying income) X3 (% ADA to total population) X5 (state revenue receipts per pupil) X12 (% of 1417 yearolds attending school) X17 (median family income)
X18 (% of married couples not owning homes) X19 (65 yearolds, % of population) X22 (% population increase in last decade)
Coefficient of Separate Determinationa
Based on Raw Data Based on Z Values Fla.b Ga.c Ky.d Ill.e Composite Composite
0.26P
0.78P 0.O8P
O.36N
O.1OP
0.37P
0.32P
O.o0+P 0. 18P 0.09N 0.18P O. OO4N
O.O1P 0.11 N
o.o8P O.05P
a The P or N following the coefficient indicates a
correlation with the dependent variable. b Source: Hopper 1965 c Source: King 1965 d Source: Adams 1965 e Source: Quick 1965
positive or negative simple
separate state studies, Illinois and Florida, respectively. The latter was significant in none. On the other hand, X5P state revenue receipts per pupil, was significant in two statespositively in Georgia and negatively in Illinois. It was found to be nonsignificant in the raw data composite analysis, but proved to be significant in the standardized data composite.
In searching for variables that had a tendency to remain significant over a period of years, four were found that qualified, as indicated below:
Coefficients of'Separate Determination for Variables Found to be Significant in Both 1950 and 1960 Composite Analyses
1950 1960
Raw Z Raw Z
Data Value Data Value Variable Analysis Analysis Analysis Analysis
X02 0.24 0.26
X3 0.03 0.08 0.01
x.08 0.18
X19 0.15 0.18 0.08
Even among the few variables that were consistent enough to be
significant in both periods, there was a lack of consistency as to which regression showed them to be significant. This lack of consistency causes this researcher to further doubt that a substantial association existed between the studied socioeconomic factors and financial effort.
All of tie regression analyses discussed in this chapter thus far have incorporated ttests for significance in order to eliminate several of the variables which the multiple regression program had allowed to enter, based upon their F levels. The last section of the chapter on
procedures discussed the feasibility of gaining increased accuracy by retaining all variables which had been thus accepted, and Tables 17 and 18 are presented in order to demonstrate this effect. Table 17 shows that all 17 of the raw data independent variables have been accepted into the regression equation, and Table 18 indicates the inclusion of all Z value variables with the exception of Xi1,Pthe per cent of employed persons engaged in manufacturing. Both of these tables show an increase in variance from the inclusion of more variables. In Table 17 the increase is slight, from 0.7550 with the ttest to 0.7723 without it. The elimination of the ttest appears to have less effect where the number of significant variables by ttest are greater. This was the case for Table 17, the E7 raw data composite analysis. The impact was greater for the corresponding Z value analysis, Table 18, where there had been only four significant variables by ttest. Eliminating the ttest resulted in the number of included independent variables increasing from four to 17, and the total variance increasing from 0.2549 to
0.3663.
It is suggested that where the retention of all variables accepted by the multiple correlation program is considered undesirable, that some method of determining significance be found which is superior to the ttest, as applied here. One possibility would be the rejection of variables which produce an increase in total variance of less than 0.01. This type of significance test would be extremely simple to apply, since the summary table (see Table 7) lists the independent variables in the order that they were accepted and shows the amount of contribution which each made to total variance. One could determine at a glance the last acceptable step in the computation and could immediately identify the
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variables considered significant and the regression equation adopted as being the most significant. Furthermore, this approach would immediately inform the administrator of the amount of variance eliminated by the nonacceptance of all variables. If such a significance procedure were applied to the E7 Z value regression analysis, for example, seven variables would be rejected for contributing less than 0.01 to variance, a total loss of only 0.0202. The margin could be regulated by the amount of tolerance considered allowable, whereas the consistent application of the 0.05 level ttest was a less informed approach which failed to consider the overall effect upon accuracy.
Even with 16 independent variables included in the regression model, the standardized data analysis still shows that only about onethird of the total variance in financial effort has been accounted for, and it behooves our educational leaders to search for other causes.
Relationship of Socioeconomic Factors to Local Elasticity of Demand for Education
There always have been more demands for economic goods than the resources of society have been able to fulfill, and economists believe this situation will continue. Each demand must compete with numerous other demands for a share of the available supply; the stronger the demand, the greater will be its share. Shultz (1961) and Fabricant (1959) have shown that it is in the best economic interest of our nation for education to exert a strong demand for an adequate share of economic goods.
The primary concern of this study was the extent to which education was competing for economic goods of the local districts. This section of the study specifically examines the responsiveness of this demand
to changes in disposable personal income. Where there has been an increase in per capita buying power, what portion of the increase was the average individual willing to spend for education? This responsiveness has been called "elasticity of demand for education" (Brazer, 1959; Fabricant, 1959; Hirsch, 1959; and McLoone, 1961). Basically, this is a measure of what percentage change in local school revenue receipts per pupil accompanied each percentage change in net effective buying income per capita. The formula used in this study for calculating elasticity of demand for education gives essentially this result, although it has been sophistocated to make it more suitable for statistical analysis. The chapter on procedures gives the exact formula which was used and discusses it further.
The coefficients of elasticity of demand for education were computed for all 122 districts in the previous studies of Florida, Georgia, Kentucky, and Illinois, and average elasticities were calculated for the nineyear periods 1945 through 1954 and 1953 through 1962. The symbols used for these average elasticities are D3 and D respectively. In the present research study, these average elasticities were treated as a composite sample and were regressed against the 17 selected socioeconomic variables for these districts, first using raw data, then standardized data (Z values). The following two subsections are devoted to the results of these stepwise multiple regressions and their interpretations. Relationship of 1950 socioeconomic factors to elasticity of demand D3
Tables 19 and 20 show the results of the three regressions. Each produces only one significant variable, X2, per capita net effective buying income. The total variance associated with this variable is
0.0497 for the Z value regression, and 0.0434 using raw data. Had the
ttest not been used to reject all except one variable in each regression, the total variance would have been shown as 0.1891 and 0.1915, respectively with all 17 independent variables included. The fact that both the raw and standardized data regressions retained only one variable in the significant regression equation is a coincidence caused by the fact that a large drop in contribution toward variance occurred between X2 and the next most influential variable, X22' in both regressions. This drop created a gap wide enough that the cutoff of the ttest occurred in this gap for all three computations.
In comparing Tables 19 and 20, it is i'nteresting to notice that the forms of the regressions are markedly different. The raw data model has a constant term of 0.35062 and an extremely small coefficient for the single significant variable, a value of only 0.00036. The regression based on Z values, on the other hand, has a zero constant term and a sizable coefficient, amounting to 0.20844+. The curve of the latter regression equation would begin at a lower value and slope upward at a much Faster rate as X2 increased. For both regressions the transformation of the gross regression'to net is completely ineffective. The net equations are all identical to the gross equations. The reason for this is that the function of the transformation is to eliminate the effects of interdependency between independent variables, and there can be no interdependency for a single independent variable, so no change is effected by applying the transformation procedure.
It can be observed from Table 21 that large samples can produce entirely different significance results than do smaller subsamples of the same group of variables. Whereas variable X21 was found to be significant in Kentucky and X22 was significant in both Georgia and
TABLE 19
SUMMARY OF D3 REGRESSION ANALYSIS
BASED UPON RAW DATA
Variables
D3 X2 Constant Gross Regression Coefficient 0.00036 0.35062 Net Regression Coefficient 0.00036 0.35062 Mean 1.39060 1077.86064 Standard Deviation 0.62929 415.50853 Simple Correlation with 03 0.099 Partial Correlation with 03 0.0990 Coefficient of Partial Determination 0.0098 Importance Weight 1.0000 Contribution Toward Variance 0.0497 Multiple Correlation 0.2230 Total Variance 0.0497
TABLE 20
SUMMARY OF D REGRESSION ANALYSIS
BASE; UPON Z VALUES
Variables
D3 X2 Constant Gross Regression Coefficient 0.20844 0.00000 Net Regression Coefficient 0.20844 0.00000 Mean 0.00000 0.00000 Standard Deviation 1.00000 1.00000 Simple Correlation with D3 0.208 Partial Correlation with D3 0.2080 Coefficient of Partial Determination 0.0433 Importance Weight 1.0000 Contribution Toward Variance 0.0434 Multiple Correlation 0.2084 Total Variance 0.0434
TABLE 21
COMPARISON OF COEFFICIENTS OF SEPARATE DETERMINATION FOR
SOCIOECONOMIC VARIABLES FOUND TO BE SIGNIFICANT
IN PREDICTING ELASTICITY OF DEMAND D3
Coefficient of Separate Determinationa Based on Raw Data Based on Z Values Variable Fla.b Ga.C Ky.d IIl.e Composite Composite X2 (per capita net effective buying income) O.02P O.04P X21 (population
of district) O.36P X22 (% population increase in last decade) O.17N O.17N
The P or N following the coefficient indicates a positive or negative simple correlation with the dependent variable. b Source: Hopper 1965 c Source: King 1965
d
Source: Adams 1965 e Source: Quick 1965
Illinois, neither are significant in the composite study. And X which was found to be significant in both composite analyses, was recognized in none of the four states.
In one respect, however, all three composite regressions and all four state regressions are in agreement: socioeconomic variables account for very little of the variance in elasticity of demand for education. All the 1950 regressions thereby tend to confirm the hypothesis that there is little association between socioeconomic variables and elasticity of demand for education. Relationship of 1960 socioeconomic factors to elasticity of demand 5
The D5 regression summaries shown on Tables 22 and 23 confirm the indications of the D3 analyses that the strength of relationship between socioeconomic factors and elasticity of demand for education is slight. When using raw data the total variance is only 0.1856, and when the computation is based upon Z values, it drops to 0.1548. Both the 1950 and the 1960 regressions substantiate the hypothesis that there was little association between socioeconomic factors and elasticity of demand for education. The relationship was even weaker for elasticity than it was for effort. Why this is trus is at this point a matter of conjecture. However, referring back to the first section in this chapter, Consistency of Effort and Elasticity, an example was given to show that small marginal changes in effort can be associated with extreme fluctuations in elasticity of demand. In the earlier analyses, a comparison of consistencies of effort and elasticity showed that while financial effort was rising rather uniformly over a ten year time span, with very little shifting of relative positions within the sample, elasticity of demand for education fluctuated without any discernible pattern,
TABLE 22
SUMMARY OF D5 REGRESSION ANALYSIS
BASED UPON RAW DATA
Gross Regression Coefficient Net Regression Coefficient Mean
Standard Deviation Simple Correlation with D5 Partial Correlation with D5 Coefficient of Partial Determination Importance Weight Contribution Toward Variance Multiple Correlation Total Variance
1.12090 .79375
X14
0.02336 0.00756 34.29835
7.55683
0.330
0.2229 0.0497 0.3237 0.1089
Variables
x15
0.01564 0.00573 22.88852
13.06915
0.294 0.2523 0.0637 0.3664 0.0377
0 .4308
0.1856
Constant
0.14608
0.69687
X22
0.00296 0.00092
36.37048 54.77359
0.030
0.2133 0.0455 0.3099 0.0390
TABLE 23
SUMMARY OF D5 REGRESSION ANALYSIS
BASED UPON Z VALUES
Variables
D5 X5 X8 Constant Gross Regression Coefficient 0.26978 0.27115 0.00000 Net Regression Coefficient 0.13441 0.13606 0.00000 Mean 0.00000 0.00000 0.00000 Standard Deviation 1.00000 1.00000 1.00000 Simple Correlation with D5 0.285 0.287 Partial Correlation with D5 0.2806 0.2826 Coefficient of Partial Determination 0.0787 0.0799 Importance Weight 0.49822 0.50178 Contribution Toward Variance 0.0725 0.0822 Multiple Correlation 0.3934 Total Variance 0.1548
causing a complete reordering of relative ranks. It is believed that this tendency to fluctuate vigorously in response to changes in personal income or school revenue causes a weaker relationship to socioeconomic variables.
A comparison of Tables 22 and 23 reveals an effect which has been consistent throughout the analyses in this studya reduction in the number of significant variables when raw data are standardized, with different variables being significant for the two different forms of data. For the composite raw data analysis, three variables were found to be significant: X 14, per cent of l4or more yearold females in the labor force; X15, per cent of employed persons engaged in manufacturing; and X22, per cent increase in population over the decade. The standardized data analysis found only two variables significant: X state revenue receipts per pupil; and X8, per cent of the population that is nonwhite. Even where the ttest is eliminated, there is still a greater number of independent variables brought into the regression equation when raw data are used. This can be seen by comparing Tables 25 and 26, where the former, presenting the raw data summary, includes 17 independent variables compared to 16 for the latter. This comparison has been consistent throughout the study, for all regressions where the ttest was eliminated.
Another comparison of interest which has been rather consistent
is the number of included variables and the amount of variance. The raw data analysis on Table 22 has three independent variables compared to only two on the Z value analysis of Table 23, and the variance for the raw data regression is somewhat higher, 0.1856 compared to 0.1548. When

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RELATIONSHIP OF SELECTED SOCIOECONOMIC FACTORS TO SCHOOL FISCAL POLICY By JULIAN M. DAVIS A DISSERTATION PRESENTED TO THE GRADUATE COUNCIL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF EDUCATION UNIVERSITY OF FLORIDA April, 1967
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ACKNOWLEDGMENTS The writer wishes to express his appreciation to Dr. R. L. Johns, the chairman of his doctorial committee, for his guidance in formulating the general approach to the study, particularly with regard to relating the statistical approaches to the needs of education. To Dr. C. M. Bridges, the writer is particularly grateful for advice and new ideas regarding specific statistical techniques, for locating and adapting for the use of this study computer programs which would not otherwise have been available, and for serving as a liaison with the staff at the computing center in times of difficulty. Special thanks are extended to Dr. R. B. Kimbrough, whose suggestion and encouragement led the writer to undertake this particular study. The other members of the graduate committee, Dr. W. A. LaVire and Mr. R. B. Jennings, have also been helpful, both through suggestions concerning the research and furnishing related texts and materials. Dr. D. E. Scates and Dr. E. A. Tood attended the seminar for planning the techniques for this study, and both made suggestions which have been helpful in reaching meaningful results. For invaluable assistance in typing and editing, the writer extends sincere thanks to Mrs. J. B. Parkel 1
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TABLE OF CONTENTS Page ACKNOWLEDGMENTS ii LIST OF TABLES vi LIST OF FIGURES j x CHAPTER 1. INTRODUCTION 1 Need for the Study ] Relationship to Cooperative Research Project 2 Statement of the Problem 5 Hypotheses 6 Del i mi nat i ons 6 Definition of Terms 6 Review of Related Research 7 Organization of the Study 14 II. PROCEDURES 16 Size of Sample 16 Sources of Data 17 Socioeconomic variables 17 Financial effort 19 Elasticity of demand for education 19 Revenue receipts per pupil ..... 20 Statistical Procedures 21 Comparability of data between states 21 Consistency of effort and elasticity ....... 21 Relationship of (a) financial effort to (b) fiscal response to income change 22 Multiple regression technique 22 Significance test 24 Illustration of computer output 26 Removal of interdependency between independent variables 39 Alternative significan test 48 i i i
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TABLE OF CONTENTS (Continued) Page II. ANALYSES AND INTERPRETATIONS OF DATA 51 Consistency of Effort and Elasticity 53 Relationship of (a) Financial Effort to (b) Fiscal Response to Income Change 59 Relationship of Socioeconomic Factors to Local School Financial Effort 62 Relationship of 1950 socioeconomic factors to financial effort E^ 63 Relationship of 1 960 socioeconomic factors to financial effort E j 72 Relationship of Socioeconomic Factors to Local Elasticity of Demand for Education 82 Relationship of .1950 socioeconomic factors to elasticity of demand D^ 33 Relationship of i960 socioeconomic factors to elasticity of demand D5 88 Relationship of Socioeconomic Factors to Local School Revenue Receipts per Pupil 97 Test of equation transformations 106 Correction for sample size 107 IV. SUMMARY AND CONCLUSIONS Purpose of the Study ]]0 Selection of Sampleand Variables 110 Statistical Procedures 1]] Consistency of effort and elasticity Ill Relationship of financial effort to income responsiveness r 1]] Multiple regression techniques Ill Significance test 112 Refinement of regression equations 113 Implications of the Findings 113 Hypothesis 1 : Most school districts follow consistent patterns of financial effort and elasticity, yet some make marked changes in relatively short periods of time .... 113 Hypothesis 2 : High effort districts are more responsive to changes in per capita personal income than are low effort districts, such that they invest in education a greater portion of increases in their personal income 1 14 Hypothesis 3 : There is little association between socioeconomic factors and local school financial effort to support public school s 115 i v
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TABLE OF CONTENTS (Continued) Page Hypothesis 4: There is little association between socioeconomic factors and elasticity of demand for education 116 Hypothesis 5: Local Financial support per pupil is significantly related to personal income per capita but not to other socioeconomic variables ] ] j General Comments 1)8 Effect of significance tests 118 Effect of interdependency between independent variables ] )8 Effect of using larger sample 118 Concl us ion 119 APPENDIX A 122 APPENDIX B 124 APPENX I X C 132 BIBLIOGRAPHY 1 38 BIOGRAPHICAL SKETCH 140 v
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LIST OF TABLES Tab,e Page 1. Illustration of Computer Output When Using Multiple Correlation Program. Elasticity Regressed against I960 Socioeconomic Variables. Page 1 Heading and Constant Tables 27 2. Illustration of Compu ter Output When Using Multiple Correlation Program. Elasticity Regressed against 19c0 Socioeconomic Variables. Page 2, Correlation Matrix 28 3. Illustration of Computer Output When Using Multiple Correlation Program. Elasticity Regressed against I960 Socioeconomic Variables. Page 4, Step 1 of Multiple Correlation 30 4. Illustration of Computer Output When Using Multiple Correlation Program. Elasticity Regressed against I960 Socioeconomic Variables. Page 5, Step 2 of Multiple Correlation 31 5. Illustration of Computer Output When Using Multiple Correlation Program. Elasticity Regressed against I960 Socioeconomic Variables. Page 6 Step 3 of Multiple Correlation 32 6 Illustration of Computer Output When Using Multiple Correlation Program. Elasticity Regressed against I960 Socioeconomic Variables. Page 7, Step 4 of Multiple Correlation. 33 7. Illustration of Computer Output When Using Multiple Correlation Program. Elasticity Regressed against I960 Socioeconomic Variables. Page 8 Summary Table 34 8 Cor respondence between Computer Identification Numbers and Variance Symbols 37 9. Rankings of i 960 Financial Effort (E ) and Changes in Rank Since 1950 { 55 10. Rankings of i 960 Elasticities of Demand (Dr), and Changes in Rank Since 1950 57 11. Summary of E^ Regression Analysis Based Upon Raw Data .... 65 v i
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LIST OF TABLES (Continued) ^" a k' e Page 12. Summary of Regression Analysis Based Upon Z Values .... 66 13* Comparison of Coefficients of Separate Determination for Socioeconomic Variables Found to be Significant in Predicting Financial Effort E^ 73 14. Summary of E^ Regression Analysis Based Upon Raw Data .... 74 15. Summary of E^ Regression Analysis Based Upon Z Values .... 75 lt>. Comparison of Coefficients of Separate Determination for Socioeconomic Variables Found to be Significant in Predicting Financial Effort E^ 77 17. Summary of E Regression Analysis Without ttest, Based Upon Raw Data 80 18. Summary of E Regression Analysis Without ttest, Based Upon Z Values g] 19. Summary of D^ Regression Analysis Based Upon Raw Data .... 85 20. Summary of D^ Regression Analysis Based Upon Z Values .... 86 21. Comparison of Coefficients of Separate Determination for Socioeconomic Variables Found to be Significant in Predicting Elasticity of Demand D^ 87 22. Summary of Regression Analysis Based Upon Raw Data .... 89 23. Summary of D^ Regression Analysis Based Upon Z Values .... 90 24. Comparison of Coefficients of Separate Determination for Socioeconomic Variables Found to be Significant in Predicting Elasticity of Demand D^ 93 25. Summary of D Regression Analysis Without ttest, Based Upon Raw Data ag 26. Summary of D Regression Analysis Without ttest. Based Upon Z Values 96 27. Summary of R^ Regression Analysis 3ased Upon Raw Data .... 98 28. Summary of R^ Regression Analysis Based Upon Z Values .... 99 29. Comparison of Coefficients of Separate Determination for Socioeconomic Variables Found to be Significant in Predicting Local Revenue Receipts per Pupil R ; 102 v 1 1
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LIST OF TABLES (Continued) Table p age 30 Summary of Regression Analysis Without ttest, Based Upon Raw Data 104 31. Summary of R^ Regression Analysis Without ttest, Based Upon Z Values ] 05 32. Summary of Symbols 122 33. Raw Data for Dependent and Independent Variables, Florida, i 960 124 34. Raw Data for Dependent and Independent Variables, Georgia, i 960 125 35. Raw Data for Dependent and Independent Variables, Kentucky, i 960 126 36. Raw Data for Dependent and Independent Variables, Illinois, 1 960 127 37. Raw Data for Dependent and Independent Variables, Florida, 1950 128 38 Raw Data for Dependent and Independent Variables, Georgia, 1950 129 39. Raw Data for Dependent and Independent Variables, Kentucky, 1950 1 30 40. Raw Data for Dependent and Independent Variables, Illinois, 1 950 131 41. First Order Correlation Matrix of 1950 Variables Expressed in Raw Form' 132 42. First Order Correlation Matrix of 1 96 O Variables Expressed in Raw Form 1 33 43. First Order Correlation Matrix of 1950 Variables Expressed as Z Values 1 34 44. First Order Correlation Matrix of 1 960 Variables Expressed as Z Values ] 35 v i i i
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LIST OF ILLUSTRATIONS Fi 9 ure Page 1. Gross Regression Versus Net Regression 42 ix
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CHAPTER I INTRODUCTION Need for the Study Recent research (Schultz 1961, and Fabricant 1959) has shown that growth In the national economy is directly related to increased investment in education. Obviously it is extremely important that educators and other leaders become familiar with those factors which are associated with optimal school fiscal policy. According to Morton (1965), there need be no uncertainty about the nation's ability to finance the kind and amount of education we need. "Our economy is fabulously productive. We can pay for anything we really believe is important.... 11 Dr. Norton points out that new economic insights have been developed regarding the productivity of education. In the past, educational expenditures were looked upon as a levy upon the economy, and cuts in school budgets as "savings." Economists today see that the concept of capital formation must be broadened to include education as an addition to human capital. Johns (1961) expressed a similar opinion in even stronger terms: ...vie can make cur economy of trained people one of plenty instead of one of scarcity by adequate investment in the education of people, and the evidence is clear that we can do this without depriving the private economy of the funds needed for investment in physical capital. National progress and national survival in the future may well depend upon which of the following policies we follow: We can minimize the investment in education and provide a minimum quality and quantity of education or we can invest 1
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2 what is needed in education to maximize national progress and the chances of national survival. Furthermore, Johns and Morphet (i960) have shown that the quality of the instructional program in the schools is strongly related to the financial support of the educational program. A review of recent research concerned with influences upon school fiscal policy reveals that the determining variables fall into two general categories: (a) soc ioeconomi cthose which are inherent in the society, the culture, and the economic system of the district; and (b) 1 eadersh i prel atedthose which are based upon leadership traits of i nf 1 uent i a 1 s decision making processes, value systems of the informal power structure, typology of the power structure, and leadership of the superintendent and other educational officials. It is essential that educational administrators know the importance of each group of variables if they are to effectively plan strategies for bringing about desirable change. Relationship to C ooperative Research Proj ect 2842 This is one of several studies conducted or planned to meet the objectives of United states Office of Education Research Project Number 2842, "The Relationship of Socioeconomic Factors, Educational Leadership Patterns, and Elements of Community Power Structure to Local School Fiscal Policy." The directors of this project, Professors Roe L. Johns and Ralph B. Kimbrough, of the College of Education, University of Florida, selected the states of Florida, Georgia, Kentucky, and Illinois for an intensive threeyear study. They have brought together in one design methods for i nvest i gat i ng the interrelationships of socioeconomic factors, educational leadership, and community power structure, and the relationship of these factors to local fiscal policy.
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3 The various studies in the overall project seek to answer the following questions: (a) Have most school districts in the selected states followed relatively consistent patterns of local school fiscal policy as measured by local effort in relation to ability and elasticity of demand for education? (b) What socioeconomic factors are associated with effort in relation to ability and elasticity of demand? (c) What unusual changes in fiscal policy have occurred through time in school districts in the selected states? (d) Are such factors as social power exchanges, economic changes, and changes in educational leadership activities related to changes in local school fiscal policy? (e) What relationships do the characteristics of community power structure (e.g., monopolistic, competitive, pluralistic) have with the level of local financial effort? (f) What relationships do the characteristics of educational leadership have with observed variation in effort? (g) How are certain socioeconomic beliefs among the population, power wielders, and teachers in selected school districts related to financial effort? (h) Do economic beliefs have a closer relationship than educational beliefs to liberal or conservative fiscal policies among selected school districts? This study deals with the first three of these questions. It followsup four separate studies of socioeconomic factors associated with patterns of school fiscal policy in Florida, Georgia, Kentucky, and Illinois, respectively (Hopper, King, Adams, and Quick, each 1965). The present study deals wi th the same four states as a composite rather than separate entities. The combination should provide more suitable samples for statistical analysis. It is not suggested that findings from this composite fourstate
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4 area can be generalized for either the region or the nation, but it is felt that such findings will be of national interest and importance. Probably no set of individual states could be selected such that a study of the effects of socioeconomic factors, power structure, and leadership in decision making with respect to local school fiscal policy would produce a valid basis for generalizations with national applications. Patterns of behavior with respect to fiscal policy decisions in local districts vary widely for different states and different regions. As James, Thomas, and Dyck (1963) pointed out, "The pattern of relationship between expenditures and our measures of wealth and aspiration seems to vary significantly from state to state, not only in the level of expenditures but also in the strength of the effects of the different explanatory variables." The four states included in this study do, however, provide a variety of characteristics which might, either directly or indirectly, have some bearing upon decisions with respect to local fiscal policy. Florida is a rapidly growing state with an exclusive county unit school system. It has only 67 school districts, is the wealthiest state in the southeast, and has an emerging twoparty system. Kentucky, on the other hand, is a relatively poor state, and it has a mixed county unitindependent city school system, with a total of 206 school districts. Geographically, it is a border state, and it has a twoparty political system. Georgia is average in wealth for the southeast and is more representative of the old South. It has a mixed county un i ti ndependent city school system organization, with 197 school districts. It continues to maintain a oneparty political system. Illinois was selected from the
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5 midwest because of its citydistrict type of organization with a sufficient number of districts suitable for study. Its per capita personal income was above the national average in I960, and it has a two party political system. Statement of the Problem Since the quality of our instructional programs are dependent upon adequate financial resources, one of the primary objectives of educational administrators should be shaping the school fiscal policies of their districts. In fact, .a great amount of time and energy is already being expended for this purpose, but a major portion of this energy will be ineffective unless these administrators know what factors determine fiscal policy. Which categories of determinants are effective and to what degree? Educational leaders must know this in order to develop adequate strategies for needed change. If fiscal policy is shaped primarily by socioeconomic factors, then administrators will be limited as to how much impact they can bring upon it, for charac ter i s t i cs of the society and the economic system are slow to change. There is little that educational leaders can do within a limited number of years, for example, to markedly change the population density, the employment structure of the community, personal income levels, etc. School administrators need to know which socioeconomic factors are effective and to what degree. But if socioeconomic variables are not the major cause of variance in school fiscal policy, then educacors should look to other factors as possible deter.ni rents such as the leadershiprelated variables mentioned on page two. These factors, if effective, would lead to quite
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6 different strategies of improvement, and would likely indicate more ( openness to change. It is, therefore, urgent that school administrators know which variables influence school fiscal policy and to what degree. Hypotheses 1. Host school districts follow consistent patterns of financial effort and elasticity, yet some make marked changes in relatively short periods of time. 2. High effort districts are more responsive to change in per capita personal income than are low effort districts, such that they invest in education a greater portion of increases in their personal i ncome. 3. There is little association between socioeconomic factors and local school financial effort to support public schools. 4. There is little association between socioeconomic factors and elasticity of demand for education. 5. Local financial support per pupil is significantly related to personal income per capita but not to other socioeconomic variables. Del i mi tat i ons Only districts with populations of 20,000 or more (U. S. Eureau of the Census, 1961) from the states of Florida, Georgia, Kentucky, and Illinois, are included in the study. There are a total of 122 of these districts. Definition of Terms Soc i oeconomi c factors Character i s t i c measures of the society, the culture, and the economic system. School fisca l pol icy. Level of support of the public schools.
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7 In this study it is analyzed from three aspec tsf i nanc i a 1 effort, elasticity of demand for education, and financial support per pupil. Pup i 1 Â• Defined in terms of average daily attendance for the purpose of this study. Fincial effort Local school revenue receipts divided by net effective buying income of the school district. Local school revenue recei pts A1 1 school financial receipts from local sources, including city, county, and district revenue, whether earmarked for specific purpose (debt service, etc.) or unrestricted. Net effective buying i ncome Tota 1 income received by individuals, including salaries, wages, profits, property income, and other personal income, less all tax payments to federal, state, and local governments. This is the same factor defined by the U. S. Department of Commerce as "disposable personal income." i lg. s t i c i ty of demand for educat ion The ratio of percentage change in per pupil revenue receipts to percentage change in per capita net effective buying income. V/ hen greater than one, it is referred to as being elastic; less than one, inelastic. A formula somewhat more sophisticated than the above ratio was used in the study. However, it produces essentially the same result. It is described in Chapter II, under "Sources of data." Review of Relate d Researc h Numerous research studies have sought to identify the causes of variations in school fiscal policy, both from district to district and from one period of time to another. Yet an adequate explanation has not been found.
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8 The research approaches to this problem have varied greatly. Many studies have related financial support to personal income. Hirsch (1959), for example, found that 76 per cent of the variation in per pupil expenditure for 1900 through 1958 was explained by changes in per capita personal income, when the urbanization factor and the ratio of nigh school enrollment to total enrollment were held constant. As an alternate approach, he correlated total current expenditures against the following four variables and found that they accounted for 99.8 per cent of the variance from year to year: 1. High school enrollment as a per cent of total enrollment 2. Average daily attendance as a per cent of 5~to 19yearold population in urban areas 3. Average annual salary of instructional staff members 4. Number of principals, superintendents, and consultants per 1,000 pupils in average daily attendance Shapiro (1962) also used per capita personal income as an independent variable, in analyzing educational expenditures among different states for the years 1920, 1930, 1940, and 1950. He found it to be highly significant in explaining variations in per pupil expenditure in all areas except in the south, where no significant relationship could be found. Brazer (1959) used median family income rather than personal per capita income in analyzing the variance in educational expenditures between different urban areas. The following independent variables were used: 1 City population 2. Population growth rate
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9 3. Population density 4. Ratio of school enrollment to total population 5. Ratio of manufacturing employment to total employment 6. Median family income 7. Revenue from state and federal agencies Only population density and ratio of school enrollment to total population proved to be significant. Although it had been expected that population and manufacturing employment would be important factors, they were found to be relatively immaterial. Brazer (1959:35) recognized other factors as probably being important influences upon educational expenditures, such as cultural and ethnic background of population elements, climate and topographical features, tax and debt limits, political patterns, etc. And despite the iack of correlation in the above study, he felt educational expenditures are being increasingly influenced by the size of population, both through diseconomies of scale and because of association "with other factors, such as income and population density, which in turn account for the apparent association between per capita expenditures and city size." Norton (1965) has expressed a similar concern over the effects of city size: Many things have caused overall expenditures to rise rapidly in big cities. One of the most potent factors has been termed 'bigcity overburden. 1 It refers to the fact that the need for public services accelerates as the density of the population rises. The concentration of population increases old needs and spawns new ones. Police and fire protection, traffic control, waste removal, sanitary and health facilities, control of air and water pollution, and welfare measures increase in amount and cost. Some of these services, less needed in rural areas, have an immediate and sharp impact in the crowded city. They cannot be put off. The adequate education of children can be put offor at least this is often the short sighted decision that is made.
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10 He further pointed out that the lack of fiscal independence often places big city schools at a serious disadvantage in securing needed local revenue. Furthermore, cities often receive smaller allocations of state aid funds per pupil than do other parts of the state. There has been a growing awareness that metropolitan areas present special fiscal problems which have a strong bearing on educational fiscal policy. Margolis ( 1 96 1 ) made comprehensive analyses of such fiscal problems in several metropolitan centers; Lindman ( 1 963) formulated an approach to educational fiscal policy which related educational costs to other governmental costs; and Johns (19&3) provided statistical information relating to educational finance in certain urban areas. Lohnes (1958) investigated the relationship of educational expenditures to size of school and to rate of growth in enrollments. He found that increases in spending were greater in systems with 500 to 1,199 pupils than in smaller or larger systems and the rate of growth in expenditures correlated positively with rate of growth in enrollments. Wolfbein (1962) found that the occupational structure of the district had a strong relationship to investment in education. Three forces that were found to be particularly influential were (a) continued structural changes in the economy which bring about growth in the service sector, (b) marked increase in professional and technical employment, and (c) substantial rise in productivity, causing relative increases in employment in the service sector and relative decreases in employment in goodsproduc i ng enterprises. There appears to be an inevitable poor fit between the skills and competencies produced by education and the needs of business, industry, and other societal activities. Hanson (1962) found that one of the most
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pressing shortages was in the number of qualified teachers, a fact that has profound implications for education. He suggested that insight into the causes of teacher shortages requires an understanding of (a) factors that affect the demand for education, (b) factors that affect teacher supply, and (c) changes in these factors. Kershaw and McKean (1962) suggested the abvisability of modifyinq the single salary schedule in order to meet the competition of business and industry in critical areas. Unless education successfully competes for the available supply of key personnel, a circular process will work against the financing of our schools. Low quality of teaching discourages the public from providing an adequate supply of funds, and inadequate financing in turn leads to obtaining poorer teachers. Some researchers found that the amount of state aid revenue had a substantial effect upon expenditures per pupil. Renshaw (1960:172), for example, found a significant association between these two variables. James, Thomas, and Dyck ( 1 963 ) also studied the effects of state spending upon local support. The usual purpose of statesupported programs is the attainment of equality among school districts, both in per pupil expenditures and in sacrifice required of each taxpayer. They found that this objective was not generally being met because other objectives were leading to conflicting results. Such conflicting objectives include the shifting of revenue demands away from the property tax, and directing expenditures into specified educational activi ties. They further hypothesized that demand for education is related to (a) financial ability of the community, (b) aspirations for education among citizens, and (c) the degree of freedom of expression of preferences
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12 by members of the community. Multiple regression techniques reflected that the level of wealth was the factor most closely associated with the rate of educational expenditure. Fiscal independence bore some relationship to local expenditure levels in the different states and in the composite sample, but other governmental variables were rather inconsistently related. When wealth and other variables were held constant, expenditures by state educational agencies proved to be highly influential on local support. Miner (1963) found that total educational expenditures, including state aid, varied positively with the wealth of the state, the relative number of children, the proportion of pupils in the secondary grades, and the salary level of beginning teachers. Total expenditures were negatively related to population density, fiscal dependency of school agencies, and location in a metropolitan area. Local expenditures varied directly with ability to pay for education and with the costs of services provided. Roos (1957) analyzed all consumer expendi 'cures rather than just educational ones, and he saw nonincome factors as being of primary importance. He found that outlays for science were increasing and that greater proportions of consumer income were being spent for insurance, medical care, education, and other services. McMahon (1958), in analyzing the 1956 school expenditures in several states, found that 52 per cent of the variations between states were associated with three nonincome variables as follows: 1. Proportion of noriwhites 2. Proportion of the population consisting of school age children 3. Proportion of children not attending public schools
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13 Many educators have felt that the values and accomplishments of parents constitute perhaps the strongest influence upon the family's demand for education. Brazer and David ( 1 962 ) used educational attainment of children as the dependent variable, representing the demand for education, in attempting to prove this hypothesis. Using multiple correlation procedures, they found that approximately 40 per cent of the variance in attainment were caused by parental values and accomplishments. Gentry (1959) chose independent variables such as social climate, years of formal schooling completed by adults, and population change. These accounted for only 30 per cent of the variation in school financial effort, but he suggested other factors observed in his study which may be significant. Adams, Hopper, King, and Quick (each 1965 ) chose socioeconomic factors to explain the variability in school fiscal policy between school districts of Kentucky, Florida, Georgia, and Illinois, respectively. Each concluded that none of the following variables: effort, level of support per pupil, and elasticity of demand could be adequately explained by socioeconomic factors. They suggested, however, that other factors may be more influential. These include leadership of the superintendent, typology of the informal power structure, political organization for decision making, etc. Johns and Morphet (i 960 ) suggested that variations in support levels are caused by a combination of cultural factors and qualities of educational leadership. In line with this suggestion, recent studies have been directed toward community leadership and its related power systems as well as toward cultural elements. When Hirsch (1959) related school financial support to per capita personal income, as discussed above, he found a nationwide tendency for
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14 the two variables to increase or decrease together. The ratio of percentage change in pupil financial support to percentage change in per capita income is called elasticity of demand for education. Hirsch's study of the period 1900 through 1958 found the elasticity for the nation as a whole to be 1.09. Fabricant (1959), on the other hand, found the state to state elasticity for the United States to be only Â•73 in 1942. McLoone's (1981) study, however, agrees much more closely with that of Hirsch. He made a statetostate analysis for the years 1929 through 1958 and found the elasticity to be .99. He made a similar study for the period 1947 through 1958 and found an elasticity of 1.34, indicating increasing interest in education. James ( 1 96 1 ) studied almost identical years, 1946 through 1958, and made findings that confirmed McLoone's latter figure. Burk (1958) cautions the reader that pi acetopl ace data generally produce an elasticity coefficient which is slightly lower than one computed with time series data. This may account for some of the difference between Hirsch's coefficient and those of Fabricant, McLoone and James. Futhermore, the coefficients produced by the latter two tend to confirm each other, providing confidence in the results. Although the above research has added greatly to our knowledge of school fiscal policy determinants, it has also given evidence that further research is needed. Organization of the Stud y Chapter I includes the introduction to the study, an explanation of the relationship of this study to Cooperative Research Project 2842, the statement of the problem, hypotheses, delimitations, definition of
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15 terms, review of related research and the organization of the study. Chapter II covers the procedures followed, including the selection of the sample size, the sources of data, and the statistical procedu res Chapter III describes the analyses made, gives interpretations of the data, and brings out conclusions regarding hypotheses. Chapter IV summarizes the study and suggests implications for educat i on
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CHAPTER I I PROCEDURES Size of Sample Hopper, King, Adams, and Quick (each 1 965 ) studied the socioeconomic factors associated wi.th the patterns of school fiscal policy in Florida, Georgia, Kentucky, and Illinois, respectively. Using only chose districts with 1 960 populations of 20,000 or over in each of the four states, rather small samples were used as follows: State Number of Districts Studied Florida 32 Georg i a 33 Ken tucky 29 Illinois 28 The results of these individual state s tudies were both incon elusive and inconsistent. For example, Hopper commented as follows: The evidence presented ... on the relationship of socioeconomic variables to local school effort is quite inconclusive. Socioeconomic variables leave a large part of the variation in local effort unexplained. Furthermore, in the same state at different points in time, different socioeconomic variables were not common to the fourstate study. The evidence indicates clearly that regression equations to predict local financial effort for schools, using socioeconomic factors as independent variables, are quite unstable; that is, it is impossible to generalize through time in any given state on the relationship with any particular set of socioeconomic variables to local school effort. Nor is it possible to generalize from statetostate, on the evidence presented in this study. 16
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17 Similar difficulties were experienced with respect to elasticity of demand for education and for financial support per pupil, and these problems were common to all four studies. An evaluation of the statistical procedures used in these studies has led to the opinion that a composite study of the fourstate area may provide a more suitable sample and generate more definite evidence. Sources of Data Socioeconomic variables After reviewing previous research, a panel of doctoral students and faculty members selected 22 variables on the basis of their relevance to schoo 1 fiscal po 1 i cy and their suitability for statistical treatment. These were the 22 variables used in the studies of Florida, Georgia, and Kentucky, with the following five factors being unavailable for Illinois: federal revenue receipts per pupil, population per square mile, per cent rural nonfarm population, per cent rural farm, and per cent of 619yearolds attending school. The loss of these factors from the composite study has been considered carefully and for the following reasons judged not to materially damage the validity. None of these five factors was shown in the original studies to be significantly related to eitner financial effort or to local revenue per pupil for the year I960 in any state studies. Also only federal revenue receipts per pupil was significant with respect to elasticity. Even this relationship was very slight and negative in effect. The 17 r ema ining variables are used in this study as lis ted below. They are numbered so as to be consistent with the symbols in
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18 the previous studies, the elimination of the five listed independent variables accounting for the numbering gaps. X  Average daily attendance in public schools X 2 Per capita net effective buying income X 3 Average daily attendance as a per cent of total population State revenue receipts per pupil X^ Per cent of civilian labor force employed X 7 Per cent of families with income of $10,000 or more X 3 Per cent of population that is nonwhite CT X ] 2 Pei cer t of 1 41 7yea ro 1 ds attending public or private school s Xjj Median school years completed by 25~ormoreyearo 1 ds X ]4 Per cent of 14ormoreyearol d females in labor force X ) 5 Per cent of employed persons engaged in manufactur i ng X ] 6 Per cent of population comprised of 25 ormoreyearo! ds with four years of college education X]j Median family income X) 8 Per cenc of married couples not owning homes X 1 9 Per cent of population comprised of 65 ormoreyearol ds X 2 j Population of district X 22 Per cent increase in population over the past decade These data were available only for decennial years, being dependent upon the federal census (U. S. Bureau of the Census, 1952, 1961). They were collected for 1950 and i 960 for all districts having I 960 census populations of 20,000 or more. The decision to restrict the study to rionrural districts was based primarily on the fact that data on net effective buying income were available only for districts having
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19 populations as great as 20,000. There is, however, an additional advantage to this restriction, in that extraneous effects upon the relationships being studied might otherwise be caused by the sparcity of population in smaller districts, effects with which the original researchers chose to eliminate from consideration. Financial effort Financial effort has been defined earlier as total local school revenue receipts divided by net effective buying income. Data for the former factor were obtained from the biennial r ports of the state educational superintendents of the respective states. Data for the latter were found in Sales Management Magazine (1950, etc.). Information from both of these sources was summarized in the four independent state studies by Hopper, King, Adams, and Quick (each 1965), where the respective efiort computations were made. In order to eliminate the effects of fluctuations from year to year, three year averages were computed for each district: (a) 1949, 1950, and 1951; and (b) 1959, I960, and 1961. The results of these computations became the sources of data for the present study. To be consistent with the previous studies, E 5 and Ey are used to symbolize these respective three year averages. Elasticity of deman d for edu cation This factor was computed by relating change in per pupil local scnool revenue to change in per capita net effective buying income. The revenue information was obtained from biennial reports of the respective chief state school officers, and the data regarding buying i ncome were available from Sales M ana geme nt (1950, etc.). Brazer (1959), Fabricant (1959), and Hirsch (1959) have each suggested using a formula for computing elasticity which readily lends itself to statistical
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20 analysis. It consists of the regression coefficient of the independent variable multiplied by the ratio of the mean of the independent variable to the mean of the dependent variable, as follows: Elasticity of demand 'Â£XY (EX) (IY) N X EX 2 () 2 Y by.xX X represents the independent variable, which in this case is per capita net effective buying income, and Y represents the dependent vari able, per pupil revenue receipts. When inspecting data for the respective districts from year to year, the original researchers observed a tendency for increases in school revenue to lag increases in personal income. Furthermore, there wei e fluctuations in revenue from year to year which would cause elasticities of demand trends from year to year to be very erratic. It became obvious that to obtain meaningful coeffecients of elasticity, it would be necessary to base the computations on extended periods of time rather than on single years. Therefore, elasticities of demand for education were computed for nineyear periods, 1 945 through 1954, and 1953 thi ougli 1962, for which symbols 0^ and were chosen to represent the respective values. The same symbols are used in the current study, and the. elastici ty values computed there provide one of the primary sour ces of information for the present study. Revenue receipts per pupil Receipts per pupil were calculated for the year i960 and summarized m the separate studies by Hooper, King, Adams, and Quick. The results of their calculations are used in this study, and the symbol R^
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21 is used here to represent this quotient, as was done in the prior stud i es Statistical Procedures Compar a bility of data between s t a t e s There was considerable discussion among the judges regarding the advantages of using raw data as opposed to using standardized deviate value equivalent data in the various correlations of the current study. There appeared to be advantages and disadvantages in each approach. Even though raw data provided a much broader range of dispersion, certain extraneous factors were permitted to influence the variables in some states while those in other states were unaffected, thus distorting the result. For example, legal restrictions upon levels of property taxation or fiscal dependence of school districts might have had the effect of lowering the effort levels in some states. Standardizing the data would tend to restrict the impact of such extraneous effects, but it would also narrow the range of dispersions caused by the independent variables, thus eliminating the very effects we are seeking to discover. For this study it was decided to compare the independent and dependent variables in both forms. The multiple correlations were computed first using raw data, and then using standardized data. Consistency of effort and elasticity Financial effort E_, which is a three year average for years 1359 through 1961, was compared with E<_ a similar average for 1959 through 1961. The comparison was made by ranking E^ by district in descending older, and similarly ranking E r in descending order. For
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22 each county, the change in relative rank was calculated, and the results were summarized and interpreted in order to evaluate the consistency of effort over a period of years. In an identical manner, elasticities of demand for education a. ,d were compared in order to evaluate consistency over a time base. Relationship o _f (a) financial effo rt to (b) fiscal response to i ncome change The second hypothesis was tested by relating financial effort, as represented by E^, the average for years 1959 through 1961, to fiscal response to personal income change, as represented by elasticity of demand the 19531962 average. Pearson r was calculated to determine whether response to change in personal income varied directly with variation in effort. This correlation was thus based on a space relationship rather than a time relationship. The computation was executed both using raw data and using standardized Z values. Each result was evaluated and the two were compared. Multiple regression technique It was decided that in investigating the third through fifth hypotheses, a multiple regression analysis would be employed. More specifically, a stepwise multiple regression equations in a stepwise manner. In each step, one additional independent variable was brought into the computation for consideration. In this program che first step involved selecting the independent variable which has the highest simple correlation with the dependent
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23 variable. In the second and in each subsequent step, the independent variable selected for inclusion was the remaining independent variable having the highest partial correlation with the dependent variable. Thus, in each step, the variable being brought into the computation was the one which made the greatest reduction in error in the analysis of variance, based upon the sum of squares of deviation. The variable selected in this manner was also the one which has the highest F ratio when brought into the regression equation. In fact, the value of the F ratio was used as the criteria for bringing in additional variables. In the present study, an F value of .001 was used as the cutoff point. Variables which, if brought into the computation, would have an F value lower than this, were omitted from the correlation equation. The program also provided for the rejection of any variable which after being accepted, experienced a drop in its F ratio down to some pre selected level due to the effects of later variables being added. In this study the rejection level was established at .00001. Th*i s was found to be sufficiently low so that no variable, once having been accepted, was ever rejected. This was consistent with the practice in the studies by Hopper, King, Adams, and Quick (each 1965). The output from this program included the following information: 1. Prior to computing regression stepsa. Mean of each variable b. Standard deviation of each variable c. Correlation matrix 2. During computation of each regression stepa. Multiple correlation after the most recent addition or deletion
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2k b. Standard error of estimate of the multiple correl at ion c. Analysis of variance table, showing the foil owi ng: Degrees of freedom for both the included and the excluded groups of variables Sum of squares of deviations for each group Mean square for each group F ratio for included variables d. For each included variable: Regression coefficient Standard error F level at or below which deletion will occur e. For each variable not included: Paitial correlation with the dependent variable F level required for entry Toll erance 3. After completion of ali regression stepsSummary table identifying the variables entered and the ones removed, and giving the following information for each: Multiple correlation after inclusion or deletion Multiple correlation squared Tne increase in the squared multiple correlation caused by entry or removal The F value required for entry or removal Si qn i f i c anc e tes t Upon completion of the above computation, certain of the included variables were selected as being significant. Since the present study is a composite of the four previous studies of Florida, Georgia,
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25 Kentucky and Illinois, with the composite results to be compared to those from such original studies, it was felt that the statistical procedures should be identical, at least up to the point where comparisons were to be made. For this reason, the .05 level ttest which was previously used, was similarly applied in the current study, as follows. I First the value of t was determined. Three of the degrees of freedom provided by the 122 cases in the sample had been consumed in computing the means, the standard deviations, and the simple correlations. Consulting a ttable, the t value corresponding to the remaining 119 degrees of freedom was found to be 1.98. Each step of the multiple correlation computation was examined in order, until one was found with a coefficient that failed to equal or exceed 1.98 times its standard error. That step and all subsequent ones were discarded. The variables in the previous step were accepted as being the only ones considered sufficiently significant for consideration. Furthermore, the equation used in such previous step was accepted as the most significant regression equation for predicting the dependent variable. This was the identical significance test applied in the original studies of the four states. As an additional measure in testing significance, failure to reduce the standard error of the dependent variable was also considered grounds for elimination. Again, this was a precaution applied in the four original studies. However, when it was applied in the current study, no eliminations were effected, for all steps which were otherwise significant did cause reductions in standard error of their respective dependent variables.
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26 Illustration of computer output Inasmuch as the computerized multiple correlation program was the heart of the procedure used for investigating the hypothesized relationships, the writer felt that the machine output from this program should be illustrated in sufficient detail to clearly show the progression of the computation and the arrangement of information furnished. Therefore, the next several pages are provided as an exact reproduction of a representative portion of the computer output. Table 1 of the illustration identifies the program being used, summarizes the numbers of cases, variables, and subproblems, and gives the code number for the time period involved. Then it lists the means and standard deviations for each of the dependent and independent variables. i he reader will notice tnat 20 variables are i ncl uded, whereas each computation involves only one dependent variable and 17 independent variables, a total of only 18. The reason for this is that the machine program consolidates the regressions of three different dependent variables against the same set of independent variables into one overall problem, having three subproblems. For computation efficiency, the machine was programmed to compute simultaneously for all variables, including the three different dependent variables, those constants and relationships which could be handled jointly. I he results of these calculations are shown on the first three pages of the illustration. Pages two and three tabulate the simple correlation (Pearson r) of each variable to all other variables. This tabulation is commonly called the correlation matrix and will be referred to accordingly in this report. These simple correlations
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27 TABLE 1 ILLUSTRATION OF COMPUTER OUTPUT WHEN USING MULTIPLE CORRELATION PROGRAM ELASTICITY D 5 REGRESSED AGAINST I960 SOCIOECONOMIC VARIABLES HEADING AND CONSTANT TABLES BSL070 STEPWISE REGRESSION VERSION OF JUNE 2, 1964 UNIVERSITY OF FLORIDA COMPUTI NG CENTER PROBLEM CODE YEAR 6 NUMBER OF CASES 122 NUMBER OF ORIGINAL VARIABLES 20 NUMBER OF VARIABLES ADDED 0 TOTAL NUMBER OF VARIABLES 20 NUMBER OF SUBPROBLEMS 3 VARIABLE MEAN STANDARD DEVIATION 1 1 Â• 78354 1.06337 2 18213.22119 41724.51953 3 1618 16393 44 1 .64314 4 20.05598 4.39468 5 160.14028 41.26210 6 5.23852 2.22337 7 10.50491 5.07090 8 15.04016 1 3 24465 3 84.43030 5.83733 10 9.83524 1.34342 1 1 34.29835 7.55683 12 22.88852 13.06915 13 4.42049 3.72405 14 4746.67212 1291.28027 15 2.23443 0.73864 16 9.54016 3.73092 17 107892.30273 336400.64063 18 36.37048 54.77359 19 1 12090 0.79375 20 168.25732 132. 00801
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ILLUSTRATION OF COMPUTER OUTPUT WHEN USING MULTIPLE CORRELATION PROGRAM 28 CO < OH < o o LU o o O X t/> Â— CH O IÂ— vO < ca 2: ho LT> Â— h< 5 CD LU < 0(1 CC Q O LU O LO LT) LU QT CD LU CÂ£ LTV Q >co < CA 00 MO CO
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TABLE 2Â— CONTINUED 29 CA 00 MO CO LA Ax Ax (A c.0 CA (A O O M0 Ax o 00 00 d Â• Â— dÂ‘ CM A O CM d* A A A fx 00 CM vO (A Ax A A A A CM Ax A d* o O o CO o i CO o O 1 O O O O o O O 1 o O Ax d MO o dd A A O .t A A A A O o LA Â• Â— Â• Â— A d* CO A CA A o o A o x Â— d* 00 A^ _d" A CO CA A d* CM CA o CO Ax d Â’ Â— A CM eg O Â— A rÂ— O CM Â• Â• Â— Â• Â• Â• Â• Â• Â• Â• o 1 o O 1 o O O o o 0 1 O o O Ax MO Ax LTV o o o Â— CO o o 3" d" 00 MO
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ILLUSTRATION OF COMPUTER OUTPUT WHEN USING MULTIPLE CORRELATION PROGRAM ELASTICITY D$ REGRESSED AGAINST I960 SOCIOECONOMIC VARIABLES STEP I OF MULTIPLE CORRELATION 30 O 00 Â— vÂ£> iÂ— VO < a: 4 u. cC < 4 vO O vO CA LA < ID OÂ’ 4 CM O CA CA CA O O O 0 Â— 0 cn o o o o ~ 4 Â— O Â— o o o o o o o o o o qO c\i CA LA a LU CO I U. O h cn o j uj < O _l _l CM Â— CC z UJ Ul CC LU Â— O > < CO LU > X. cC cC _J o o o 31 J2T Uli_ LU LU Z (_> J LU S J J Z CO O o LU UJ < OZ2I>>CC cC UJ Â— LU LU LU O.Q.X J J J I LU < I  O ro q j; il u. iZD to cC < ID I 31 i < CC >Â— I < < UJ o CC Â— O to CO Â— rsvfl vO LA 4 LA CA O CO vO CM O Â— ACA O CO vD LA (T\ rx o CO LA LA CA vQ OO AN NO^CDJ00 CO CA LA CM Â— LA Â— AO Â— o 0 ^ 4 o O LA 4 LA 4 CM rs o CMO OCA CMOOOOCMO Â— Â— OLAÂ— OOOOCM < I D OÂ’ LAfAOO4Jr^ Â— CM OC Â— rs PA Â— CA PAN n o CO N Â— OCAONLAtO Â— CO CA CA Â— CA O vO A. Â— vO OvOuJLA CA CM CO A*. u"\ < Â— CA CO CO CO CA CA CA CO LA A** CO A* CO 00 00 ACA CA CA CA CO OOOOOOOOOOOOOOOOOO CC < CC < LA 4 _4 CO CA CA ACO LArx(M44cO'JDutlM CO lO Â— 04; O VO Â— r^O rv LA LA Â— 'O CO CMvO CM LA O 4 00 O LA Â— _4 _4 LA CA Â— vC Â— lAut O CA Â— O^tO o fAvQ Â— tOO Â— Â— 4* Â— Â— LA CA O O O O O Â— Â— O CM OOOOOOOOOOOOOOOOOO cC < z> Â— CM CA _jLA VO A' CO CA O CM CA Â„4 LA vO A^ CO Â— Â— CM CC o CC o cC h< 4 00 vO vD CA O VO CO 4 MD CA CC < 2.2652
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TABLE 4 ILLUSTRATION OF COMPUTER OUTPUT WHEN USING MULTIPLE CORRELATION PROGRAM ELASTICITY REGRESSED AGAiNST I960 SOCIOECONOMIC VARIABLES STEP 2 OF MULTIPLE CORRELATION 31 1 Cd o o la cn cr\ o LU CO LU cd LU vo cr\ < cn CO GO zd r lt\ o la oÂ’ Â— o t: oo CM CO LU Â• Â• rÂ— LA ac CO LA IjÂ— o o Hyz ZD Li_ oo z o Â— ly: lA vO 1o J J < cd cn u~\ Ll. CM CT\ o cd o o Q Â— O LU o o Â— LU Â• Â• o o CTl 2 Q CM Â• Â• LU O O _J ^ N CD Â’ Â— LO LO CO CM csl <; 2: O CO UO Â• Â— LU Â— UJ 4I'' O OO Â— Â— _i Li_ o o o UJ ijJ a: co LU Q O hto cr Â— o 2 z u cri to < LU LU Of OT O IU LU hCO o cd cd 00 yz LU uj al co LU 2 OÂ—l _J cd Â— o Z C3 Q_ LU to ao c_> < Â— >1 o_ Â— 1 Â— Â• Â— 1 LU cd Â— 1 Q < cd 1< =>HO < 1 co > tin <
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TABLE 5 ILLUSTRATION OF COMPUTER OUTPUT WHEN USING MULTIPLE CORRELATION PROGRAM ELASTICITY REGRESSED AGAINST I960 SOCIOECONOMIC VARIABLES STEP 3 OF MULTIPLE CORRELATION 32 o Â— ca IÂ— M3 < 03 CC 00 ca < 30 M 3 M 3 O' Â— CM O') LT\ Z 4* O < LU 21 OO LU < 3 CO 4 o un cr\ Csl _4o o 00 LU o Â• z: h< 0 0 LO Â— LU LU cd CO < cd < CO 3 LU Li_ > LU O fÂ— O cd cd z Lu CD CO LU LU cd Cd O IjJ LU CQ O Cd cd 21 LU UJ cd CO 3 Â— J .u cd Z CQ Qtu CO < Â— >Q_ Â— \Â— Â• LU Cd Â— 1 0 < I Â— < 3 ICO > 2: 00 < z o h< ZD O' 00 LU _J CQ < Cd < 00 d00 o' Â— o 00 4 CM Li_ Â• Â— vO O 21 ZD OO tLCO CO Q rÂ— h~ < ZD O' LU GO LU _J CO < cd < cd J
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ILLUSTRATION OF COMPUTER OUTPUT WHEN USING MULTIPLE CORRELATION PROGRAM ELASTICITY D 5 REGRESSED AGAINST I960 SOCIOECONOMIC VARIABLES STEP 4 OF MULTIPLE CORRELATION 33 Cd UJ IÂ— LU O hLi_ Â• ^ UJ 0 (.3 Â— 2! f< < Cd 13 LU OÂ’ _J UJ O h1 Â— O Cd O Z Cd Â— Â— 0 !Â— vO 00 0 <. CL. UJ cd < LU 13 CM rÂ— Â—1 o' CA CM CQ OO 00 LA < Z CA O Cd < < LU > 2: C/7 UJ CC 0 Â— O CD O O h< 0 Â— Â• Q co Â— Â— Â— J Ll_ 0 O O O O LU UJ cd 00 < U_ 1 1 cd IJL < 00 13 LU LU > LU Q O jÂ— h0 cd Â— C3 z cd Z u_ CD OO < UJ LU cd cd 0 UJ LU \Â— CQ 0 cd or 00 t: LU UJ cd 00 LU z 13 J Cd Â— _J 0 CQ Cl. UJ 00 03 0 < Â— >< > Â— / CM OO c_ Â— hÂ• J LU Cd _J CO < cd 1 Â— < 10 h1 : < CO > 21 LO < WChOCOCO CM Â— c*'! JCJ\ CM CO Â— CT\ CM r^ r ^iAo ooo J4 j'. 3 o 4 'oo COO' Â— Â— CM CA mO CJ7 CM O Â— CM' Â— o Â— Â•Â— 000000 Â— OOOOOO Â— Â— CA 4j.4u"icruo i^(junco44o~i LncMcj\DcONoocONO>ocM\DmLn cri n cm ^404a'\r~^cMr'' 'Â£> OOOvO CA r' Â— O0 MO (A CM 4cio CM' Â— n co a) N cm Jro 4 Â— o Â— OOOOOO Â— OOOOOO Â— OOOOOOOOOOOOOOO I I I I I I I 1 Â— cMcv'\_ 4 t_rcvÂ£>cocr\ocv'i_ ; ju'\vcr^o CO CM I^CO 4 4 M3 4 vO CM CM 00 CM 4O Â— CM 00 (A 1
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ILLUSTRATION OF COMPUTER OUTPUT WHEN USING MULTIPLE CORRELATION PROGRAM ELASTICITY D REGRESSED AGAINST I960 SOCIOECONOMIC VARIABLES 34 Q LU O Z (_) LU Z Q Â— z: LU OO Q_ LU LU Â—J Cd O CQ LU ^ < CQ 51 CÂ£ ZD U< ^ O > CM ca 4 IA vD N CO (A O (vv 4LA vQ r^. LU > o o 2: ILU cd LU ID CÂ£ J O < 2> Ql 4 ca VO co CA 0 4" CTv 00 00 CA 4lA CM CA rvO LA 4" vO 4* CA CM vO CM vO csl O'V 00 O CA 0 4" LA LA CM Â— O rÂ— 0 Â— LA Â— co CM CM 00 LA 00 4" CA Â— CA VsO OA O O Â— 4" CA CA Â— O LA CM Â— O O O O O O O O O O .O O LU LO OÂ’ C 00 Lu or a: o z CA 0 LA CM O Â— CA CTv 00 1LA O CA 00 CA LA (A vQ vO vO 4" cA 0 O O CA Â— r Â— O 0 O O O O O O 0 O O O 0 O O O O 0 O O O O O O 0 O O O 0 0 O O O O 0 O O O O O O 0 O O O CA MD vO Â— CM CA CA vQ LA CA 00 CM CM CA CM vO LA Â— 4" O CA O LA CC O O 4* CO O CM CM CM (A 444LA LA LA LA LA LA *Â”1 CM CM CM CM CM CM CM CM CM CM CM CM CM O O O O O O 0 O O C O O O O O O O O CTV CO 4* 00 CA 00 4 4* (A 00 CM CM CA O CM O 00 CM CA 0 CA 0 LA 00 O 00 CA 4* lO vO CO CA o LU LU Â—J Cd CQ < a: o < LU LU hZ IU CN CO CA LTv v.O LA 00 O 4* LO rs CM 4 (Y^ CC LU CL. CO LU 21 h=> co 2: CN (A 4U"\ vQ r^CXD CA o CM
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35 were retained in the memory of the computer and used for calculating partial correlations of each independent variable not yet brought into the multiple correlation equation. This provided a measure which enabled the machine to select the appropriate independent variable to next bring into the computation. The simple correlations, used to get he r wi eh the means listed on the first page of the illustration, were again used after completion of the machine computation of multiple correlation, in order to refine the significant multiple regression equation. This refinement is described in the next section of this chapter. Tables 3 thru 6 of the computer output illustration portray the first four steps in the multiple correlation computation. The reader will notice that the illustration covers the second subproblem of the combined computation. The three subproblems were similar; nothing would be gained by showing all three. Subproblem number two, elasticity regressed against socioeconomic variables for calendar year I960, was chosen simply because fewer steps were required to reach the significant regression equation, using the significance test described above. Step one (Table 3) identified the dependent variable as number 19, and stated the F level required for inclusion (0.001), the F level at or below which an included variable will be rejected (0. 00001), and the tolerance level (0.001). It then continued with the computation, printing as output the inf or ma tion listed above under the section 11 Multiple regression technique." Independent variable number 11 was brought into the regression equation in this step. Its partial correlation with the
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36 dependent variable was not printed, but it was computed by the machine and compared to the partial correlations for all other independent variables. In order for variable 11 to be selected for inclusion, it had to have the highest partial correlation of all the outstanding independent variables, as well as having an F level as high as .001. Of the remaining independent variables, number 12 had the highest partial correlation with the dependent variable, a value of .20572, and it was the variable selected for inclusion in step two. The reader should be aware that although variables 1 and 20 are shown among the variables not in the equation, the machine program excluded them from consideration, since they were the dependent variables used in subproblems one and three. Actually, no purpose was accomplished by including them in the printed output of subproblem two. They were allowed to print only because of the difficulty of programming their elimination from the printout of the subproblems to which they did not apply, and because some uses of the computer program find an advantage in having them included. The reader should be cautioned that the numbers identifying the variables in the machine output are not the same as the identification symbols used in this report of the study. The computer program automatically numbers the variables in the order that they appear in the punched cards used for machine input, whereas it was deemed advisable to symbolize the variables for report purposes consistent with the symbols used in the related previous studies. The respective equivalents are indicated in the tabulation on the following page:
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37 TABLE 8 CORRESPONDENCE BETWEEN COMPUTER IDENTIFICATION NUMBERS AND VARIANCE SYMBOLS 1 dent i f i cat ion Number in Computer Output Symbol used in Report 1 dent i f i cat i on Number in Computer Output Symbol used in Report 1 E s or E 7 1 1 X l4 2 X 1 12 X 1 5 3 X 2 13 X ] 6 4 X 3 14 X 1 7 5 LA X 15 X 00 6 X 6 16 X 1 9 7 X 7 17 X 21 8 X 00 18 X 22 9 X 12 19 D^ or D^ 10 X I3 20 R 4 The third step brought variable 18 into the computation; the fourth step, variable 7. The computation continued in this manner until all independent variables were tested for entry and all variables entered were tested for rejection. In the particular subproblem chosen for illustration, all 17 of the independent variables were eventually chosen for inclusion, and none was rejected after being entered. However, only four steps are shown, since this number of steps suffices for the purpose of demonstrating the application of the ttest for significance, as foil ows
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38 In step one, the regression coefficient of 0.03467 is more than 1.98 times its standard error of 0.00905, and as such it is considered significant, and the test proceeds to the next step. The coefficients in step two, 0.02735 and 0.01253, exceed their respective standard errors, 0.00945 and 0.00546, by more than a multiple of I. 98 so this step was also accepted. Similarly, the coefficients in step three all passed the ttest thus applied, but in step four, variable seven, which was being entered, failed to equal I .98 times its standard error (0.02329 compared to 0.01548), and therefore the entire step was rejected. The previous step, step three, was thus accepted as final, with only the variables accepted at that point being considered significant. Furthermore, the regression equation set forth by that step was considered the most significant equation for predicting the dependent variable. Table 7 of the illustration displays a summary of the entry and removal of variables throughout all the different steps of the computation, and it shows the value of both multiple correlation and variance at the completion of each step, together with the change in variance caused by each entry and each removal. This table is very relevant to the first three hypotheses of this study inasmuch as it indicates the contribution of each variable to the overall variance. Up to this point, the multiple regression techniques employed in this study are similar to those used in the separate studies of Florida, Georgia, Kentucky, and Illinois. The computer program has been redesigned to reflect more information in a more usable format, but the statistical result is identical. And the significance tests employed here are the same as the ones used previously, such that any given set of data would product identical regression equations and related constants.
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39 Therefore, the results, up to this point, are comparable, and they have been compared in the analyses of data to the extent such comparison was deemed relevant to the current study. However, it was felt that a refinement was needed to the above procedure before the coefficients of the regression equation wou I d indicate with the desired degree of specificity the relationship of each included independent variable to the related dependent variable. Therefore, the current study needed a rather extensive modification to the statistical procedures used in the previous studies, in order to Lransfoim the regression equations into more meaningful form. The need for this modification and its application are described in the following section. Remov al of inter depe ndency between independent v ar i ab 1 es Celia (1967) cau cions that the theory of regression requires all observations of each independent variable to be completely free of any interrelationships with other independent variables. He points out that violations of this principle can result in overstatement of regression relationships, and he makes the following statement regarding computation of regression equations by usual methods (which would include the methods used in this study): When model building is completed, the multiple correlation between the dependent variable and the independent variable will be high and the variance will be small so the model will be suitable for predicting purposes. However, it will be of little value for other analysis purposes because the parameters will be so obviously unrealistic. Since the primary purpose of deriving regression equations in this stuey is not for prediction purposes, but rather for illustrating relationships between variables, it is obvious that some adjustment in the
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40 parameters produced by the above multiple regression procedures was needed. That is not to say that these procedures should not have been used, for quantification of the components of the regression model must begin with the calculation of the parameters of the functional relationships between the independent variable and the oata of each independent variable. Celia (19&7) refers to these as "gross" regressions because "part of the changes in the values of the dependent variable are due to changes in the values of one independent variable and the remainder are due to changes in other independent variables." Under these circumstances, the measurement of the regression relationship is the largest possible, because al the changes in the dependent variable have been attributed to one variable. Yet variations in the dependent variable are almost invariably caused by changes in several independent variables acting s imu 1 taneous 1 ythus the term "multiple regression." The following explanation by Celia ( 1 96 7) tells why it is so essential to transform these gross regressions to net regressions, thus eliminating the effect of interdependency between independent variables: In a multiple regression, the relationship between each independent variable and the dependent variable is a net rather than a gross. The net regression measures the variation of the dependent variable which is caused by variations in an independent variable, with the impact of the other independent variables measured also. Each of these latter is measured as though all of its values were identical so instead of multiplying a regression coefficient by a variable, the same amount is deducted from the dependent variable for each observation. As a result, the net regression describes the variation in the dependent variable which is due to changes in a particular independent variable. Since the net regression only explains the variation in the dependent variables which is due to a particular independent variable, it will be less than the gross regression. In a demand analysis a gross regression merely measures the amount of associated variation between the variable while a net regression attempts to measure the amount of cause and effect.
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4l These remarks imply that the parameters of the net regression equation indicate the relationship of each independent variable to the dependent variable more accurately than do the parameters of the unrefined regression equation. Since accuracy with regard to this relationship lies at the heart of the present study, it was felt to be essential that the gross regression coefficients be converted to net coefficients. As explained in the M.l.T. Summer Course on Operations Research ( 1953 ), this requires the calculation of a system of weights which indicate the relative importance of the independent variables. The effect of this weighting is to appreciably scale down the size of coefficients which have minor influence upon the dependent variable and to make lesser reductions in coefficients having more significant effect upon the dependent variable. Diiferent methods for applying weightings are proposed by Frisch (1934), Wold (1953), Ferber ( 1962 ), and others. These methods for quantifying the model are not the same as the conventional least squares analysis approach, although the objectives are similar. Furthermore, the models which have been transformed by weighting are suitable for a variety of applications rather than being restricted to prediction pu rposes The weighting system is actually a second weighting, inasmuch as the gross regression coefficients themselves are weights, functioning as multipliers of tne independent variables. Celia (1967) therefore describes the weighting system of a transformed regression equation by a foimula similar to that s hown be 1 ow and he illustrates the effect of the transformation as shown in Figure 1 on the following page. W b, X, + W 2 b 2 X 2 +
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42 Source : Celia (1 967)
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43 where b^, b^, etc., are gross regression weights and w^ w^, etc., are the importance weights for converting to net regression. Importance weights used in this study for converting from gross to net regression consist of coefficients of partial correlation between the individual significant independent variables and the concerned dependent variables. In suggesting this use of partial correlations, Celia ( 1967 ) advises the reader as follows: A partial correlation is a measure of the extent to which the variation in the dependent variable is explained by an independent variable. When all the factors which influence a dependent variable are included in an analysis, the partial correlation coefficients will measure the extent to which each independent variable affects the dependent variable. Croxton and Cowden (1955) describe coefficients of partial correlation as measures of "the relative importance of the different independent variables in a problem in explaining variations in the dependent variable." Inasmuch as the present study is highly concerned with discovering the relative importance of the different independent variables in molding school fiscal policy, it makes extensive use of partial correlations as a weighting system for refining the gross regression equa t i ons However, Celia ( 1 96 7) cautions, "The calculation of importance weights is a drawnout task, even with the aid of a computer." It requires first the computations of zeroorder correlations for each possible pairing of variables from the gross regression equation. The zeroorder correlations are used in turn to compute a series of first order correlations, using the general formula
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44 r 12.3 where one is the dependent variable, two is the first independent variable being correlated with the dependent variable, and three is the particular independent variable being held constant. The subscripts are changed to fit the numbers of the variables involved in the computation. The "order" of a partial correlation refers to the number of variables being held constant, and the symbol for partial correlation indicates this by the number of subscripts following the decimal. Thus, the above formula provides for the computation of first order correlations. Each partial correlation used as an importance weight for transforming a gross regression to net must hold constant all but one of the independent variables. The order of the partial correlation required is therefore one less than the number of independent variables. Since some of the regression equations found to be significant in this study contained as many as seven independent variables, it was necessary to compute partials as high as the sixth order, requiring the use of the following formulas in addition to the one shown above: second order r 12.34 r 1 2 3 r l4. 3 r 24.3 third order r 12.345 r 1 2. 34 Â“ r 1 5 34 r 25.34
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45 fourth order Â•,2.3456 = r 2 345 ~ r l6. 3 45 r 26. 3 45 \ A r 16.345 )0 r 26. 345^ f i f th order 12.34567 = 12.3456 r i 7.3456 r 2 7 3456 \A r l 73456 ) r 2~7.3456 ) sixth order r l2. 34567 = r 2.34567 r l8. 34567 r 28 34567 r l8. 34567 ) (1 28.34567 The first order partials are used to calculate the second order, the second to compute the third, etc. It becomes apparent that a tremendous number of computations are required in order to obtain the needed importance weights when the number of independent variables reaches four or moie. This might well have been an influential factor retarding the application of weightings to multiple regression equations in prior research. To illustrate the use of partial correlations as weighting factors for converting gross multiple correlations to net, the significant equation for Dj_, based upon raw data, is used. 17 Gross Regress i on Equat i on : D 5 .14608 t .02366 X ]Q .01564 X. ] + .00296 X
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46 Partial coefficients and their conversion to importance weights: Partial Importance Coefficient Weicjht D<_ to x io = .2229 .2229 W 1 .6885 Â“ .3237 to X ,1 = Â• 2523 w = 2523 2 .6885 .3664 Dj_ to X 1 7 = .2133 w Â• 21 33 3 .6885 ~ .3099 Total .6885 In converting partial coefficients to importance weights, all values are treated as positive, regardless of their actual sign. But when the weights are multiplied by gross coefficients to produce net coefficients, the signs of the coefficients are retained. This transformation appears as follows: Gross Reqress i on 1 mportance We i qht Net Reqress i on b ]Q = +.02366 .3237 .00756 bj = +.01564 .2664 .00573 bj = +.00296 .3099 .00092 The constant term must also be transformed, using the following formu 1 a : V b  X 1 b 2 *2 I I Â—O b 3 X 3 b 3 X 3 whei e b^ is the constant term of the net equation; Y, the mean of the dependent variable; the b terms, the net regression coefficients computed above; and the X terms, the means of the respective independent variables. The last term of the formula illustrates the fact that the
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47 net regression coefficient would be calculated for higher powers of a variable in exactly the same way as for linear terms. Using the above formula, the constant term for the raw data net regression would be calculated as follows: (1) Gross Constant Term (2) Net Regress i on CoeCf i ci ent (3) Means of 1 ndepenaent Variables (4) Product of (2) x (3) (5) Di f ference in Totals (1) less (4) b Q = 1 .12090 b ]Q = .00756 34.29835 .25935 b,, = .00573 Â• 22.88852 .13116 b ) = .00092 36.37048 .03352 1 12090 .42403 = .69687 = b ft This completes the transformation of parameters. Substituting the computed estimates of net regression for the gross parameters, the equation yields the following net regression model: 0 5 = .69867 + .00756 X ]Q + .00573 X f] + .00092 X )7 This equation gives the relationships of the respective significant independent variables to the dependent variable, with the interdependent effects of other independent variables eliminated. Thus it can be used to more realistically analyze the relationships of socioeconomic factors to school fiscal policy. Therefore, the net regression has been derived in this study for each of the dimensions of local school fiscal policy: financial effort, elasticity of demand for education, and revenue receipts per pupil. This, together with the gross multiple correlation and its related constants have been used to investigate the last three hypotheses
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48 The use of weighting systems to convert gross regression models to net is not a new or exclusive statistical technique. It was a central topic at the MIT Summer Course on Operations Research (1953), and it has been discussed in statistical tests including those by Frisch (1934), Wold (1953), Ferber (1962), and Croxton and Cowden (1955). However, it was felt to be advisable to make a sample test of the i egression models which were thus transformed in the present study. The test was conducted as follows, for each regression equation tested. The gross equation was used to predict the value of the dependent variable for each of the 122 districts in the sample. Next the corresponding net equation was used to calculate its prediction of the same dependent variable for each of the districts. Then each set of predictions was correlated against the actual values of the dependent variable in order to ascertain that there was no material loss of predictive accuracy resulting from the transformation. The results of these tests are discussed in the next chapter. Alternative significance test In the procedures described above, this study has followed the identical significance test as was used in the original studies. This has allowed the results of the current study to be compared to those of the original, but this researcher feels that the application of a ttest is in effect the rendering of a second significance test. The use of F levels as criteria for entry and removal of independent variables during the mu Itiple regression computation serves as a basic significance test. By regulation of the F levels specified for inclusion, the degree of relationship of selected variables could be controlled, eliminating the need for a second significance procedure.
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49 Fu t he rmo re it is felt that the elimination of variables through this particular application of the ttest at a level as high as 0.05 is undesirable because of the extensive impact it has upon total variance. Tnis is illustrated in Table 7, which summarizes the results of elasticity of demand being regressed in multiple step wise regression against the 17 selected socioeconomic variables. Only three variables are accepted by the ttest as being significant, whereas all 17 of the independent variables are brought into the regression equation by the multiple correlation program. The variance associated with the three variables is only O.I 856 as compared to 0.2523 for all seventeen. Although it is convenient to reduce the number of variables by the application of a significance test beyond that of the F levels used in the multiple regression program, the accuracy of the computation appears to be much greater with the retention of a larger number of variables. The progressive effect of the eliminations is shown by the "INCREASE IN RSQ (R squared, or variance)" column of Table 7. The first variable eliminated by the ttest would have contributed more than 8 per cent as much variance than the total variance accepted as being significant. 1 he total variance eliminated by the ttest would have contributed more than 35 per cent as much as the recognized variance. Therefore, as an additional procedure, the 1 9&0 regression equations for financial effort, elasticity of demand, and revenue receipts per pupil were recomputed without the benefit of the ttest. In each case, the gross equation was determined and then transformed to net. This was followed by calculating partial correlations between the independent variables wi th the respective dependent variables, coefficients of partial determination, importance weights, contributions toward total
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50 variance, total multiple correlation, and total variance. The significance of each of these is discussed in Chapter III, and the computed values are tabulated for easy reference. The computations were made both using raw data and using standardized deviate value equivalents.
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CHAPTER I I I ANALYSES AND INTERPRETATIONS OF DATA All of the 122 districts provide local support of public education through property taxes. As pointed out in Chapter I, the equality of the instructional program is strongly related to the financial support provided. For this reason, educators are vitally concerned with maintaining a school fiscal policy that is conducive to adequate financial support. The purpose of this chapter is to examine the relationship of the 17 selected socioeconomic variables to local school fiscal policy, so as to determine whether they might serve as a leverage toward better support. To relate fiscal policy statistically, it was necessary to quantify each of the study variables. Three measures of fiscal policy were used in the original studies of Florida, Georgia, Kentucky, and Illinois: Financial effort, elasticity of demand for education, and revenue receipts per pupil. Each of these is defined in Chapter I under "Definition of terms," and discussed in Chapter II under "Sources of data." The most traditional measure is revenue receipts per pupil, for which fiscal policy is quantified by dividing total revenue receipts by total pupils in average daily attendance. However, there is an inherent limitation in this measure of fiscal policy. It corresponds too closely with the amou nt of financial resources available Â— the ability to suppor t education. Tnose districts which have higher per capita personal income tend to pay more for education. A measure of fiscal policy which would 51
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52 be more meaningful to educators would be an index of the effort made by the disti ict to use its resources tor education, regardless of the level of resources available. As such, a second measure of fiscal policy has been used, one which tends to eliminate the effect of adequacy of financial resources. It relates financial support actually provided for education to the total available resources. Total local school revenue is divided by total disposable personal income for the district, reflecting a measure which is defined in this study as financial effort. This may oe considered as an index of the district's willingness to use its resources for education. Another measure of fiscal policy, which has proven to be quite useful is the elasticity of demand for education. It indicates the response of a school district to a change in per capita disposable income The greater the portion of an income increment invested in education, the g, ea ter the elasticity of demand. Basically, the coefficient of elasticity indicates what percentage change in revenue per pupil accompanies each percentage change in per capita net effective buying income. If the ratio of pupils to total population remains unchanged, then tne coefficient of elasticity of demand indicates the tendency of financial effort to change, since the basic formula would be reduced to percentage change in revenue divided by percentage change in net effective buying income. For this reason, elasticity of demand is sometimes seen as a modification of "financial effort," denoting the extent of inclination for effort to change directly with change in personal income. A difficulty is presented with using the basic formula when there exists a change in revenue but none in personal income, for the computation would give infinity as an answer. For this reason a more sophisticated
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53 formula is provided, as described under "Source of data," Chapter II, which gives essentially the same result while overcoming this difficulty. The first step in analyzing the data relating to the above three measures of fiscal policy was to examine the patterns of financial effort and elasticity of demand to determine their consistency among the respective districts over a period of time. Consistency of Effort and Elasticity As might be suspected, there was considerable variation in financial effort among districts.. The highest among the 122 districts had an effort more than fifteen times as high as that of the lowest. This is shown by Table 9, which, in addition to ranking the districts by level of financial effort (E^) shows the specific effort rating of each district and the change in ranking during the previous ten years. The ranking change was computed by comparing E.^ and E,_ rankings. A summary of these changes show that out of 122 ranks, a majority of 69 districts experienced ranking changes of less than 15 places. Furthermore, 105 of the districts changed less than 30 places, indicating high stability of effort. High effort districts tended to remain high, and low effort districts tended to remain low. A few districts made marked changes in relative position over the ten year time span. Eight districts changed in rank by more than forty places. Tabie 9 identifies these districts only by code number, so it was necessary to refer to Appendix B in order to find the names of these districts, which are as follows: S t a t e District Ranki ng Change Florida Orange 55 FI or i da Leon 70
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54 Georgia C 1 ay ton 74 Kentucky Carter 47 Kentucky Knox 43 Kentucky Pike 54 Illinois Jacksonv i 1 1 e +45 A quick review of Table 9 shows that the four states tend to stratify, with Illinois tending to fill the upper ranks, Georgia the lower, and Florida and Kentucky respectively filling the intermediate ranks. The average ranks and mean financial effort ratings by state are shown below, and they further substantiate the stratification mentioned above: State Average Rank Mean E^Effort Mean Er Effort Illinois 15.2 3.422 2.0864 Florida 59.4 1.573 1.3947 Kentucky 70.4 1.3935 1 3626 Georg i a 92.5 0 9400 0 81 67 each of the four states, the mean E^ effort was higher the mean effort. Similarly, the mean effort of the fourstate composite increased from 1.39060 to 1.7835 during the same period. These points indicate that there was a general tendency for the level of effort to increase over the tenyear time span. in summary, the analysis of rankings by financial effort tends to confirm the first hypothesis, which is restated as follows: "Most school districts follow consistent patterns of financial effort and elasticity, yet some make marked changes in relatively short periods of
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RANKINGS OF I960 FINANCIAL EFFORT (E ? ) ANC CHANGES IN RANK SINCE 1950 55 5 00 vO LO CO CO CO vO (T\ CO CM Â— O CM co Â— CM CM CM LO LO LO CM CM CM CO CO CO Â— r 4 4* 4 N 4 vO Â— O CM 4 4 4 vO vO vO vO vO urv CM Â•Â— CM co co Â— Â— 4 CM CM CM vO 4 vO fO N J4 co co LA 4 O CM Â— CM CM CO Â— CO Â— CO Â— CM + + Â• Â— co o Â— 5 vO lo lo Â— Â— o cr\ cn (n CM CM CM CO CO Â— lo lo lo CM MD CO Â— O CO LO LO LO N CO Cn CO LO LO LO LO LO vO CO CM CO vO CO LO CO CO o CO CO CO co cm CO CO co CM LA vO CO CO CO CM CM Â— Â— Â— O CO CO CO Â— Â— Â— Â— Â— Â— r. o Â— CM <Â— CO CO Â— CO 3 CM Â— O Â— CO CO oÂ—oo CM Â— Â— CO Â— CM 4 4 + oÂ— CO 4 4 CO CO CO CO lo 4 CM Â— + + + LO 00 Â— CO rÂ— o OO CO CO CM CO CM O LO 4 CO CM O Â— 4 Â— Â•4 lo vO co CO vO cm Â•Â— 4 Â— Â— (O 4 4 co CO CO c>~> O Â— Â— 4 4 4 Â— Â— Â— CM co Â— Â— Â— pm co 4 4 + pOO CO co vo co LO CO CO MO CO CM CO 4" LO kO lO LO 4 o Â— 4 4 CO Â— CO Â— CM + CO O Â— CO CO CM in n LO Â— vO co CO Â— CO CO (O LO CM 0"\ oo + co Â— 4 4 co 4
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56 time." The analysis reflected the fact that most districts did experience relative consistency in effort pattern, with an overall trend to increase gradually. Yet, as hypothesized, a few districts made marked changes in pattern. Eight districts changed their relative ranks by more than forty places, which is over a third of the full range of ranki ngs A similar analysis of rankings by elasticity of demand gave very different results. fable 10 presents the elasticity values (D^) rankings, and changes in rank. Only 52 of the 122 districts changed pos i t ion by as few as 30 pi aces Forty of the districts changed by more than 50 per cent of the fu 1 1 range of rankings, and six changed by more than 100 places. The inconsistency is further h i ghl i ghted by the summary of means by state, which shows two states increasing while the other two are decreasi ng. Average Mean Mean State Rank Elasticity Elasticity Georgia 41 1 1 .7169 0.6552 Florida 54.0 1.2333 0.6872 Illinois 63.2 1 .0109 1.1119 Ken tucky 82.4 0.6078 0.7656 The composite mean increased from 0.73836 to 1.12090. Not only was there a general reshuffling of district rankings over the tenyear period, but the states tended to reverse their relative rank positions. The mean elasticity of two states increased sharply while the coefficients of the other two states were lowered. There was a general lack of consistency, which contradicts the first hypothesis with respect to elasticity.
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RANKINGS OF i960 ELASTICITIES OF DEMAND (Dg) AND CHANGES IN RANK SINCE 1950 57 3 CO U\ OA 04 43 OA is UA 43 04 o 3 43 PA o O rs 0A 04 rs 04 co rs 20 77 04 4) OA PA 3 04 3 + 1 + Â• 1 1 + i 1 i 1 1 1 1 1 1 1 l i l UA rs OA 04 PA 3 UA 43 fs CO OA O 04 O O O O o O Â— Â• Â— Â— Â— *Â“ Â— Â‘ rs UA UA 3 gf rs 3 04 UA PA 04 43 O' PA 04 3 PA PA OA PA PA OA PA 04 04 04 Â— Â— d o o O o o O O O d o O d O o O O o t O 1 O 1 d 1 O 1 o UA rs rs 04 UA 04 PA 43 4) 04 O o 04 O 4PA 04 PA 04 PA 04 PA PA PA PA rs OA PA 3 o OA o PA UA UA 43 C0 43 OA vO 43 PA JOA 04 1 Â— PA 04 Â— UA PA Â— UA 04 CO rs 00 04 1 1 1 3 1 1 1 f + 1 < + 1 + i ( 1 1 1 + + 1 1 43 rs is rs 00 O'OA rs O 00 5 04 03 PA oo 3, UA 00 vO CO rs. co 88 OA CO a OA C4 OA PA OA & UA OA 43 OA rs OA OO OA 99 001 rs PA PA PA 04 04 CO 00 45 UA PA OA OA pa 43 04 UA PA is rs. 04 PA 43 04 ~ + + 1 + + + 1 + 1 3 + 1 1 1 1 +Â• 1 + 1 1 1 t+ + + PA 3 UA 4) rs co <7A O 04 PA JÂ•JA 43 rs CO OA o i 04 04 04 04 .4A PA PA PA PA PA PA oA oo PA uf T SÂ’ J4f 3,"N o~. UA PA 04 O rs rs 43 43 rs ts 43 03 PA pA rs rs <0 43 43 UD UA UA UA UA UA 4f JPA PA PA PA Â— r ~ Â— Â— ~ Â— 1 ** rs cO 04 OA 3 04 04 04 43 rs 3o PA 43 PA UA i 04 04 o O O pa 33 04 04 04 OA 04 404 OÂ’ rs 03 fs 04 04 O OA UA PA 04 rs is OA OA 43 UA 00 04 vD vO PA vD o OA 4J PA Â— CO O 4Â• + + + 4+ + + + J. + + + + + + + + 4 + + + + c4 rs 03 OA 04 PA JUA 43 fs CO OA o rj PA ~3 c. 43 VJD O rs PA O'. vO 43 UA UA PA Â— rs pa co '43 vO PA PA PA 02 04 Â— Â— Â— o O OA d pa 04 04 04 04 04 04 04 04 04 04 04 r4 04 04 ~~ ~ OA PA 43 OA UA UA rs 04 03 UA vX> rs PA co 04 IS vO 04 OA 04 O 04 eg J04 04 04 ~ 04 04 04 04 04 04 4T
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58 .Thus, while financial effort was rising rather uniformly for a large group of districts with very little shifting of relative positions within the group, the elasticity of demand fluctuated without any obvious pattern, causing a complete reordering of relative ranks. Brazer (1959: 18) points out that "although these (elasticity of demand) coefficients are valid for only very small changes in the independent variable, they provide a simple measure of the 'sensitivity' of the dependent variable to changes in the independent variable." In the context of the present study, this would be a sensitivity of local revenue per pupil to net effective buying income per capita. This sensitivity can change markedly from one period of time to another without a material change in effort. This is illustrated by the following example, which used the basic formula for elasticity (percentage change in revenue per pupil related to percentage change in net effective buying income per capita) in order to simplify the example. First Period Second Period Third Period a. Revenue $ ; 1,000,000 $ 1 ,070,000 $ 1,135,000 b Pup i 1 s 10,000 io,4oo 11,000 c. Revenue per pupil $ i 100.00 $ 102.89 $ 103.18 d. Percentage change from previous period 2.89 0.28 e. Net effective buying income $100,000,000 $105 ,000,000 $1 12,000,000 f. Population 50,000 52,000 53,500 g. Net effective buying income per capita $ 2,000.00 $ 2,019.20 $ 2,093.50 h. Percentage change from previous period 0.96 3.68 i Effort (a 4 e) 1 .000 1 .019 1.013 j. Elasticity (d 4 n) 3.01 0.076
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59 There is nothing extreme about the example shown on the previous P a 9 e > yet the coefficient of elasticity of demand has fluctuated wildly while effort has remained substantially constant. Although the averaging of values over a nine year period has tended to stabilize the elasticities of the districts in the composite sample, the effect demonstrated above is still present. Even using nine year averages, many districts experienced drastic changes in elasticity coefficients while their levels of effort changed very little. This researcher questions whether elasticity of demand is not overly sensitive for the purpose of evaluating the influences of socioeconomic variables upon school fiscal policy. This will be examined further when investigating the results of stepwise multiple correlations relating elasticity of demand to the 17 selected socioeconomic variables. Relationship of (a) Financial Effort t o ( b) Fiscal Re sponse to Income Change It has been hypothesized that high effort districts are more responsive to change in per capita personal income than are low effort districts, such that a greater portion of increases in their personal income is invested in education. The validity of this hypothesis was investigated by correlating financial effort E^, the average effort for \ears 1359 through 1961, against elasticity of demand for education D^, the 1953 through 1962 average. Pearson r was first calculated using raw data and found to have a value of 0.00516. This is obviously an extremely low correlation, but to further evaluate its significance, a ttest was applied, using the formula t = r/T~2 /rrr x~
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60 where r is the Pearson r discussed, and N is the number of pairs of observations in the sample. This computation reflected a value of O.O565 for t, and it was used in a test for significance as described by Crowley and Cohen ( 1 9 & 3 ) "The test of significance of a correlation is a test of the null hypothesis, 'the obtained correlation in this sample is not different from a correlation of zero. Any difference can be ascribed easily to a chance variation about population correlation of zero. 1 If the calculated value of t exceeds the ttable value, significance is indicated; otherwise, the null hypothesis is confirmed. In the present case, the ttable value for 120 degrees of freedom at the 0.05 level is 1 98 The calculated value, being much smaller than this, confirms the null hypothesis and leads to the conclusion that any difference can be ascribed easily to chance variation. But have we combined the variables from the four states on comparable bases? It has been pointed out in the previous section of this chapter that there is a consistent stratification of effort levels between the four states, and Chapter II explained that raw data permit extraneous factors to influence variables in some states while not affecting those in others. Legal restrictions upon levels of taxation and fiscal dependence, for example, are among the factors most commonly found to cause such stratification. The effects of such extraneous factors had to be removed if the correlations were to be meaningful. The method chosen for placing the values of effort and elasticity for the districts of the four respective states on a comparative basis was transformation from raw values to Z values using the simple formula Z value X M SD
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61 where X is the raw value of the variable being transformed, M is the mean of the sample variable, and SO is the standard deviation of its distribution. Transformations of variables from the four states were made separately and the resultant Z values provided bases sufficiently comparable to permit the data to be combined for composite analysis. Drawbacks in the use of standardized data were recognized. While standardization eliminated deviations caused by extraneous effects, it was likely that some of the soughtfor deviation would also be eliminated, that which was caused by the selected socioeconomic factors. Furthermore, it was necessary to proceed on the assumption that the forms of distribution for the different states were nearly identical, which is highly improbable. However, as Guilford (1965) points out, "In spite of these limitations, it is almost certain that derived scales, such as the standardscore scale, provide us with more nearly comparable values than do rawscore scales." After converting both varaibles to standardized deviate value equivalents, the Pearson r was again calculated and found to have a higher correlation. The coefficient based on Z values was 0.2607. The ttest showed significance at the 0.01 level, with a tvalue of 2.95. But even with the higher correlation using Z values instead of raw data, only 6.20 per cent of the total variance is accounted for. This degree of support for the second hypothesis is still very weak to be considered. This researcher has therefore reached the conclusion that there is little recognizable association between level of effort and fiscal response to change in personal income.
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62 Relationship of Socioeconomic Factors to Loca l School Financial Effort At this point it might be well to recall the statement of the central problem with which this study is concerned. In Chapter I it was brought out that recent research studies concerning influences upon school fiscal policy have identified two general categories of determinants: (a) soc i oeconom i cthose which are inherent in the society, the culture, and the economic system of the district; and (b) leadershiprelatedthose which are based upon leadership traits of i nf 1 uen t ia 1 s decision making processes, va l.ue systems of the informal power structure typology of the power structure, and leadership of the superintendent and other educational officials. If educational leaders are to be effec tive in shaping school fiscal pol icy, they must know which of the above categories of determinants are influential and to what degree, for the strategies which would be effective in bringing about desirable change would be exceedingly different under the two alternatives. The primary purpose of the current study was to test a selected group of variables from the first category, socioeconomic determinants, so as to investigate their effect upon school fiscal policy. If found to be influential, then educators must consider them in planning strategies for change, but if ineffective, they must look to other factors as possible determinants, such as the leadershiprelated determinants. Current research is being increasingly devoted to investigating the influence of the latter upon school fiscal policy. The results of that research should complement the findings of the current study in guiding educators to the most effective means of shaping school fiscal pol icy.
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63 The investigation of possible relationships between socioeconomic variables and school fiscal policy was begun by using a stepwide multiple correlation technique relating the selected 17 socioeconomic variables to local school financial effort. Due to dependence of the investigator upon the federal census, socioeconomic data were available only for decennial years. As such, relationships between variables had to be examined on a crosssectional basis (also called p 1 acetop 1 ace or spatial) rather than a time (or sequentia 1 ) bas i s All the firstorder correlations generated by the computer program are presented in Appendix C. Their importance derives from the fact that they not only provide the basic values for determining the selection of variables for inclusion in the multiple correlation models, but they also provide the means of transforming gross regression equations to net. The use of firstorder correlations in generating importance weights is discussed in Chapter II. By listing the correlation matrices in full in Appendix C, the writer avoided the necessity of repeatedly extracting partial listings for insertion at appropriate points in the text, as was done in the previous studies of the four states. The reader will notice that a single table presents all possible firstorder correlations among the three dependent variables and 17 socioeconomic variables. However, separate tables are required for different time periods (1950 and i960) and for different bases of data (all raw and all standardized Z values.). Relationship of 1950 socioeconomic factors to financial effort E,. Two separate regressions were made relating the dependent factor of financial effort E^, to the \J selected socioeconomic independent variables. The first regression used raw data for all variables; the
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64 second, Z values for all variables. The results of these regressions are summarized in Tables 11 and 12, respectively. Ttie first line of each table lists the constant term and all coefficients of the regression equation which were found to be significant by ttest (described in Chapter II). These coefficients are labeled as "gross regression coefficients," following the terminology used by Celia (1967). The term "gross" implies that "part of the changes in the values of the dependent variable are due to changes in the values of one independent variable and the remainder are due to changes in other independent variables." Coefficients obtained by multiple correlation are therefore overstated because of the effect of interdependency between independent variables. A detailed explanation of this effect is given in Chapter II, showing that such equations are suitable for predicting purposes but are of little value for other analysis purposes because the parameters are so unrealistic. The explanation presented there goes on to describe a method for transforming the gross regression equation to net, thereby providing coefficients which attempt to measure amount of cause and effect rather than mere association between variables. The second lines of the respective summaries of regression analysis present the coefficients and the constant term of the net regression equations. Referring to Table 11, for example, there is a striking difference between the coefficients of the gross and the net regression equations. Each net coefficient is only a fraction of the respective gross coefficient, and the constant term of the net equation is positive compared to the negative constant term in the gross equation. Celia ( 1 967) commented as follows regarding the effects that occur in building a gross model,
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SUMMARY OF Er REGRESSION ANALYSIS BASED UPON RAW DATA 65 4 CO 4 c CA PA 0 vQ 4J CM ( J\ to pa 00 c Â• o O o o 1 400 yO M3 M3 pa CA CA 4 CA 00 CA pa CM O PA o oo O yO rÂ— CO CM ca CO CM CO LTV yÂ£> X o O o yO 4pa Â— cm Â• Â— o O CO CM o O O o o LA CM o 4 LTV 4 CA yO PA 4 PA ca M3 Â— M3 4 CM CM 00 rÂ— O pa CM o yO CO LA X o O CM Â•44PA Â• Â— CM Â— O 1 0 1 vO 4* o o 1 O o O yO CM O M3 PA C A Ar Â— o M3 00 LA CO rÂ— LA ClM3 PA o CM O a^ yO CO o PA Â— CM O CM yO Â— o o CM PA PA Â— CM o o O CM *Â— O O o O o CA 4 CA Cj4 CA PA LA CA 00 OA Â• Â— kO CO CM LA a^ CM CA 03 LA CA CO CO a> 4 LA 4 O o PA o O PA Â— CM o o O yO 4 o o O o o O CA yO CM LA O 03 yO CA CM CA PA yO M3 Â• Â• Â• O o C o 4J 0 c Â£ M u a) c LA 0 o 0 45 Â• Â— c o 4c 4J "O o o 0 c c o L. L_ Â•Â— o o o 0 4J 0 4J c O Â— Â• Â— M Q_ _c 3 0 o u 4J 0 CD O Â— C CO 0 Â— 4Â•Â— 10 to o Â— 0 o 0 ito Â• Â— > 0 i_ C 4o 4J 4J o 4J 03 0 Â£ V_ 0 Q. c rÂ— L_ 0 0 4J Â• Â— 0 O E o 13 CD 13 ?r~ CO OO Q. O Â— o 21 Total Variance 0.4051
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SUMMARY OF E r REGRESSION ANALYSIS BASED UPON Z VALUES 66 4 o O c o O 03 o O 4J o o CO o o c Â• Â• o o o o CM O o O LA 4Â“ o o vO i Â— LA O 00 o o CA vO vO O Â— LA o o rÂ— LA LA X 4* Â— o o Â— ^4 Â— PA O o O o o o o O O PA CsJ o o CA 4 vO o o 4Â“ PA CA O vÂ£> CM LA o o CO LA LA vO CA rÂ— O vQ o o CA LA VO CM X PA O o o O CM O CM Â— O O o Â— o 1 O O o o LA 4 o o Â— 00 o o o o LA CM rÂ— Â— o o o CM CM vO OA CA Â— o o PA O LA CM O PA o o PA LA CM 41 Â— o O 1 o 1 O 1 O 1 O O O o o o o o o o o o o o C o 41 03 C E 4J 4 a) c LA a) o a) 4J LA liJ 4J c Â— C LU 03 03 o a) _C Q Â• Â— Â— _C 4J 4 o 4J Â• Â— Â— (0 4. Â— Â• Â— 3 03 > a) 4s Â•Â— o 4Â— c 4J T3 O a) c C o 4 4 o o o Â• Â— 03 4J 03 c O Â•Â— 4J CL C 3 o 4J iJ 03 CD O Â• Â— c rO 03 4Â• Â— tÂ— CO o Â— d3 o (33 lO > d) 4 3 C 03 CO 03 L_ 4 4J o CO Q 4 o c 03 Â• Â— cn 03 o O 03 O 4J 03 L_ ~o O Â• Â— C "D ac CO L_ Â— o 03 jQ 03 03 03 *D Â•Â— 4J Â• Â— CO aC ~o rÂ— Â• Â— 44 4 CO c C CL 4> 4o 4J o 4J aj CD e 4 03 CL c L_ 0) a) +J Â• Â— 03 o E o CD X s CO CO CL O Â— O Multiple Correlation 0.5369
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67 which bring about the need for refinement: Suppose, however, that the regression between a dependent variable and one independent variable is calculated and a high positive correlation is found to exist. Then another independent variable is found which also correlates highly with the dependent variable in a positive manner and the multiple regression of the two independent variables is calculated. When this is done, the original value of the regression coefficient for the first independent variable may be reduced appreciably. Then a third independent variable is located which also correlates highly with the dependent variable in a positive manner; the process is repeated. At about this stage, however, two possibilities occur: (1) the previous pattern will be repeated, or ( 2 ) some of the previous regression coefficients will increase and take on unrealistic values while the last regression may become a negative. Also, the value of the constant term of the regression equation, which will have been reducing a little in the previous calculations, may undergo a sharp increase in this last calculation to further balance the adjustment being generated by the negative regression. These effects do not damage the suitability of the completed model for predicting purposes, but they do cause the parameters to be obviously unrealistic for other analysis purposes. Since the primary use of the regression equation in this study is to show relationships between variables rather than for prediction purposes, it was urgent that the transformation be made. The gross coefficient for independent variable X^ was 0.05699, indicating that for every unit change in X^, the dependent variable, E^, changed 0.05699 units. This is misleading inasmuch as only 0.01814 units of change, the amount of the net X^ coefficient, are caused by a unit change in X^ alone. The rest of the change in E,_ is caused by other independent variables, through i nterdependency with X^. The third and fourth lines of each regression summary table show the means and standard deviations, respectively. The former are used in calculating the constant term for the net regression model, and the
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68 latter are required in deriving the coefficients of separate determination. The next line of the summary table lists the simple correlations of each independent variable with the dependent, and this is followed by the partial correlations for each independent variable. The latter factor determines which variable will be entered into the multiple correlation computation first. The highest partial correlation in Table 11 is shown for Xj 0 and this independent variable was the first to be entered into the regression model. The second highest was the X^, but it was not entered second, since partial correlations must be recomputed for the outstanding independent variables at each step of the computation. After Xjg was entered, the recomputation of partials reflected a higher value for Xg than for X^ so Xg was entered second. The partial correlations are also used in deriving a weighting system for transforming the gross regression equation to net. Each coefficient of partial determination is the square of the partial correlation, which it follows in the table, and its value constitutes a ratio explaining that portion of the variability in the dependent variable which may be attributed to specific independent variable when all other independent variables are held constant. The importance weights of the independent variables, which are listed next, show what portion each partial correlation bears to the total of all correlations of significant independent variables. Chapter II explains how these are used to refine multiple correlation equations so as to eliminate the effects of interdependency between independent variables and thus obtain parameters which show more realistic relationships between variables. The next item is "contribution toward variance," and it indicates how much each entry into the multiple correlation increased the total
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69 variance. The last two items are multiple correlation and total variance, respect i vel y It is interesting to notice from Tables 11 and 12, that the regression using raw data und entirely different significant independent variables related to financial effort than did the regression using Z values. Significants in the former, with their respective contributions toward variance, were Xjg, 0.1768; Xg, 0.1124, X^, 0.0678; and X^, 0.0481; total variance, 0.4051. in the latter, significant variables were X ]6> 0.1290; X 2> 0.1092; and 0.0500; total variance of 0.2882. It is obvious that standardization of data from raw form to Z values has had a tremendous impact on the results. As has been pointed out earlier, however, Z values are more comparable from state to state than are raw data. They therefore can be expected to give a truer indication of dispersion of actual distribution with respect to the influences of the selected independent variables. Despite the inherent limitations upon the use of standardized values, Guilford (1965:515) pointed out, "In spite of these limitations, it is almost certain that derived scales, such as the standardscore scale, provide us with more nearly comparable values that do raw score scales." That is the reason why this researcher places more emphasis on the results obtained from regressing Z values than from using raw data. Furthermore, Tate (1955) observed, Standard scores have several advantages in statistical theory and practice. They are algebraic and hence are tractable in mathematical discussion. Since a standard score is derived by dividing a deviation from the mean by the standard deviation, both of which are the same unit, it is an abstract quantity, i.e., a quantity independent of the original measurement unit....
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70 He points out that the use of standard scores simplifies many statistical procedures. By their use an individual's performance in one test can be compared with his performance in a second, regardless of differences in the measurement units. Since they are algebraic, the standard scores of individuals in several tests can be combined into a composition score. In the present study the measurement units are not different per se, but the units which were measured existed under circumstances that were quite different, causing the need for the data from different states to be transformed to a comparable base before being analyzed as a composite. The relationship of student hours of preparation to grades awarded by a highgrading teacher will be different from such a relationship under a lewgrading teacher. Similarly, there will be a difference between the relationships of personal income and school financial support in separate states where tax limitations are different, or where procedures of budget allocation and control are dissimilar. There are distinct advantages in transforming such statistical data to a more comparable base before proceeding with analyses of composite relationships. As does Guilford, Tate defends the soundness of analyses using such standardized data, provided the distributions of raw scores are normal or approximately so. Even where nonnormal he points out (1955) ...that the standardization ratio has considerable stability of meaning except in markedly nonnormal distributions. The standard score transformation may be applied to the majority of distributions encountered in educational testing without introducing serious error. Why were different independent variables more significant with Z values than with raw data? Two significance tests are embedded in the regression program; the selection of variables by F level and the 0.05
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71 level ttest. The transforming of both dependent and independent variables, together with the resultant changes in distributions, makes it possible for these tests to select different variables from the different forms of data. Other possible explanations are the chance that minor nonlinear relationships may exist between one or more of the included independent variables and the dependent variable, and the fact that the slope and/or level of the distributions have been changed during the transformation, as the value of the constant term has been lowered from the level obtained with raw data to a zero level when using standardized Z values. In the analysis of regressions (Table 12), the total variance of only 0 2882 leaves a balance of 0.7118 unexplained. This tends to confirm the hypothesis that there is little association between socioeconomic factors and local school financial effort, and educational leaders should look to other factors for the principal causes of variance in financial effort. In Table 12, the summary of regression analysis based on Z values, although X 0 had the greatest partial correlation with E and ij therefore was entered first, it does not make the greatest contribution toward variance. However, the net regression equation shows that a un i t change in X^, per capita net effective buying income, has a greater impact on E^ than does X^, per cent of population comprised of college educated adults, or X,_, median family income, when the effect of interÂ’ 1 / dependency between independent variables is eliminated. It is interesting to notice the comparison of significant variables and their respective coefficients of separate determination, as reflected by regression analyses of the separate states and of the
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72 composite. This comparison is summarized in Table 13The lack of consistency is obvious. It is observed that although X^, per cent of population made up of 65 yearolds, was significant in only one state, it showed up strongly in the composite based upon raw data. However, it was eliminated in the composite using Z values. On the other hand, X^, per capita net effective buying income, was omitted from significance in the raw data composite despite its being significant in two of the four states, but was included in the composite based on Z values. X^j was also significant in two states, but data for this variable were unavailable in Illinois and therefore had to be eliminated from consideration in the composite analyses. The coefficients of separate determination shown on Table 13 and similar tables later in this report were calculated by multiplying the beta coefficients by the simple correlation between the independent and the respective dependent variables. The beta coefficients were obtained by multiplying the gross regression coefficients by the ratio of the standard deviation of the independent variable to the standard deviation of the dependent variable. Relationship of I960 socioeconomic factors to financial effort Tables 14 and 15 summarize regression analyses similar to those presented in the previous section, and they present even more forcefully the contrast between results obtained from using Z values as compared to those based upon raw data. The total variance from significant variables is only 0.2549 when using Z values, whereas variance reaches 0.7550 with raw data. If one accepts Guilford's conclusion that standardscore scales provide us with more comparable data than do rawscore scales, he will realize that by far the greater portion of the
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73 TABLE 13 COMPARISON OF COEFFICIENTS OF SEPARATE DETERMINATION FOR SOCIOECONOMIC VARIABLES FOUND TO BE SIGNIFICANT IN PREDICTING FINANCIAL EFFORT E $ Coefficient of Separate Determination 3 Based on Raw Data Based on Z Values Variable FI a b Ga. c Ky. d 111. Compos i te Compos i te X 2 (per capi ta net effective buying income) 0.06N 0.21N 0 .24N X 3 (% ADA to total population) 0.57P 0.03P X 5 (state revenue recei pts per pupi 1 ) X 7 (% of fam i 1 i es with $ 10,000 income) 0.25P 0 .06P 0 10P X 8 (non white % of population) 0.1 2N X ] (rural nonfarm % of popu 1 at i on) 0 19N 0.76P X 1 6 (college educated adults % of population) 0.03N X ] 7 (med i an fami 1 y i ncome) 0.09N 0.08P X 1 9 (65 yearolds, % of population 0. 16N 0 15 P X 20 (ADA % of school age population) 0. 1 IP 3 The P or N following the coefficient indicates a positive or negative simple Correlation with dependent variable. Source: Hopper 1965 Source : King 1S&5 Source: Adams 1965 Source : Quick 1965
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SUMMARY OF Ey REGRESSION ANALYSIS BASED UPON RAW DATA 74 4J CM CM c MO 03 00 00 4 r\ ro S) o c Â• Â• o rÂ— o i CM CO cn 00 4" CM 4 LA CA CM CA CM CM O o CA rÂ— CM 4 Â• Â— 4 CM o O CA CA LA CA CM O O cA O CM O O o X Â• O O vO 4 O O O o o 1 CA LA 1 CM CA vO CM 4 O C T\ r*> LA 'JO CA CA 4 vO O o 4 CM CA 00 Â— CM 4 CA jCO CA CM CM X Â— O LA 4 LA CA CM 1 Â— Â• Â• t Â• Â• Â• Â• Â• Â• O O CT\ CA o o O o O CA CA 4 Â— o ca 4 MO 4 4 LA CO CM CM 4" CO CA LA o MO 3CA CM CA CA 4 4vO CA Â• Â— X CM O CM a>. LA CM O O O Â• Â• Â• Â• Â• Â• Â• O O 1 CM o O o 1 o o o (/) LTV cA CM CM 0 CM O Â— CM CA Â• Â— Â— Â— J O o CM O CO 00 CA CA CM ..Ll O o 00 o 00 CO Â• Â— CM 0 O o vO CM MO CM o Â‘ Â— O x~ o o vO Â— O O o O O 03 4* CA CM 4* LA o CA CM (A CA Â•lJ* VO O LA CM CM O > Â— o CA O CM o (A CA CM o 4 1 Â— X O o 4CO CA CM o o O Â• Â• Â• Â• Â• Â• Â• Â• O o 4 LA o o o o o 1 1 00 1 00 MD 00 00 CA O'! MO ALA LA 00 00 MO LA jvO LA Â— LA CA O CM LA CA 00 CsJ CA 4MO X O O CA Â• Â— MO CA CM 1 O O O o O O O o CM ca 4" CA 4 CM ca CA 0^ CA CM o o (A CA vO Â— 00 LA 4 o O vO 4 CA CA 4o CM o O vO vO CA Â— Â• Â— 4X Â• Â• Â• Â• Â• Â• Â• Â• o o CO Â— o o O O o Â— 4 MO 4 4 LA CA CA CA CA 00 00 MO MO O 00 c O c 0 c 0 Â•Â— 0 Â•Â— 4J c Â• Â— 4J 0 o 4J 03 c C CD rÂ— 14 Â• Â— Â• to o 0 O E 4J in 4J Â• Â— ii 0 L_ L 3 c Â• c 0 c in c L. U 4J a > 0 u 0 L. a) 'Si a> C l_ O c 4J 0 Â• Â— 0 Â• Â— U) 0 Â•O O O 0 0 O 4J 4J a) o L. o Â“O O Â• Â— O C 3 0 0 CC CD Â— L. 4J LU rÂ— UJ O 0 JO T3 Â• Â— Â— Md) 4fO 03 0 0 Â• Â— Â• 4J *Â— L. Q. 0 in 4CÂ£ 410 Â— 1 Â— _C Â• Â— JZ 4Â— 4J L. u 0 Â• Â— L J1 (D 0 c c > Q. 4> 4J MÂ— U O 4J 4J l_ o O 4J O 03 0 0) Â£ U 0 0 CL c O Â• O CO (0 co 0 Â•M 0 5 0 5 O Q_ e 0 \D O CO z 2: LO CL CO Â— CO 21 Total Variance 0.7550
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SUMMARY OF Ey REGRESSION ANALYSIS BASED UPON Z VALUES 75 W C (0 4J (/> c O o o o o o o o o o o o o o CM CNJ X ca X LA X CA X LA r>o o CM CM r\ o o O LA CA LA LA ca o o o o CM CM CA 3* Jo o CM LA vO O jCM o o o CM CM O CM O O o o Â— O O O O o LA CM O O o O Â— O o O O vO CA LA O o CM CM CA CA O o 4" 4Â“ Â— vÂ£> CA O O o CM CA Â• Â— CM o O O O Â— O O o o o CA CA O o CA CA Lf O o 00 OO vO 00 co o o vÂ£> CA CO CA vO CA o o O CM o vO <7\ CA O o o CA CA Â— CM o o O o Â— O O o O o II II Â— Â— O O CT\ o O O A.' CM CA o LA O O CA o vQ i Â— 3" 03 O o Â— rÂ— CA LA CA O O o o CA O CM o O O O Â— o O O O o LU O O O O O O o o o o o Â— oo t o LA O c O 4J 0 c E 4J u 0 c 0 u 0 4J ALU 4J c Â• Â— c LU 0 0 o 0 C Q Â•Â— Â•Â— Â• Â— _c 4J u 4o 4J Â• Â— Â— 0 4Â— Â• Â— 2 0 > O 4Â• Â— c O 4c 4J ~o 0 o 0 c c 0 L_ 1Â— Â•Â— o 0 0 0 4J 0 4J c CJ Â•Â— Â• Â— 4J CL _c 5 0 o 4> 4J 0 cn 0 Â— Â• Â— c Q 0 1 Â— 4Â• Â— h0 if) o Â• Â— Â— 0 O 0 if) Â• Â— > 0 L 3 c u 0 t/) 0 u L_ 4J 0 0 L_ if) O LO c 0 Â— 0 cn 0 O O 0 O 4J 0 u T> O Â— C 13 0 cfL c n L. Â— 0 0 _Q 0 0 0 0 Â• Â— 4J Â•Â— CL CO cC Â“O Â— Â• Â— 4L_ u Â• Â— l/) c c CL 4J 4O 4J 4J o 4J 0 0 E L 0 CL C rÂ— u 0 0 4J Â•Â— 0 O E O =3 CD X 21 CO CO a. O Â— O 2: Total Variance 0.25^9
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76 variance in financial effort must be explained by factors other than the studied socioeconomic variables. Another idfference in the analyses of the two types of data is that the transformation of the gross regression equation to net has a greater impact upon the coefficients of the raw data model. Each is more sharply reduced than are the coefficients of the standardized data equation, most of the coefficients being decreased to about 10 per cent of their gross value compared with reductions to approx i ma tel y 25 per cent for the standardized data coefficients. On the other hand, the raw data constant terms receive a similarly greater but offsetting impact. The same effect was found for the euqations; in each case the constant term was changed from a negative value in the gross equation to a positive value in the net equation, thus counterbalancing the reduction in size of the coefficients. In the Z value equation there was no change in the constant term, inasmuch as standard scores do not generate a constant term, and the transformation process uses the gross constant term as a multiplier in creating a constant term for the net equation, causing the elimination of the constant term from the net equation also. The effect of reduction in overall deviation which was caused by standardization of data may be largely responsible for the difference in the numbers of significant variables with the two different types of data. Table 16 shows that the composite analysis of raw data produces seven significant independent variables as compared with only four with standard scores. Three of these are common to both regressions: ADA as a per cent of total population; X^, 65yearolds as a per cent of population; and X^, percentage increase in population over the previous decade. The former two were each significant in only one of the
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77 TABLE 16 COMPARISON OF COEFFICIENTS OF SEPARATE DETERMINATION FOR SOCIOECONOMIC VARIABLES FOUND TO BE SIGNIFICANT IN PREDICTING FINANCIAL EFFORT E 7 Coefficient of Separate Determination 3 Based on Raw Data Based on Z Values Variable Fla .* 3 Ga c Ky. d 1 1 1 .e Compos i te Compos i te X 2 (per capita net effective buying income) 0.26P X 3 (% ADA to total population) 0 78 P 0.08P 0.01P X 5 (state revenue receipts per pupi 1 ) 0.36N 0. 10P 0. 1 IN X ] 2 (% of 1417 yearolds attending school) 0 37P 0.04P Xj ] (med i an f ami 1 y i ncome) O CO "O X] 3 (/ 0 of marri ed couples not owning homes) 0.09N X]g (65 yearolds, % of population) 0.32P 0. 18P 0.08P X 22 (% population increase in last decade) 0 004N 0.05P The P or N following the coefficient indicates a positive or negative simple correlation with the dependent variable. Sou rce : Hopper I 965 Source: King 1965 Source : Adams 1965 Source: Quick 1965
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78 separate state studies, Illinois and Florida, respectively. The latter was significant in none. On the other hand, X^, state revenue receipts per pupil, was significant in two statespos i ti vel y in Georgia and negatively in Illinois. It was found to be nonsignificant in the raw data composite analysis, but proved to be significant in the standardized data composite. In searching for variables that had a tendency to remain significant over a period of years, four were found that qualified, as indicated below: Coefficients of Separate Determination for Variables Found to be Significant in Both 1950 and i960 Composite Analyses 1950 I960 Variable Raw Data Ana lysis Z Value Anal ys i s Raw Data Ana lysis Z Va 1 ue Anal ys i s X 2 0.24 0.26 X 3 0.03 0.08 0.01 X 1 7 0.08 0.18 X 1 9 0.15 0.18 0.08 Even among the few variables that were consistent enough to significant in both periods, there was a lack of consistency as to regression showed them to be s i gn i f i cant This lack of cons i stency causes this researcher to further doubt that a substantial association existed between the studied socioeconomic factors and financial effort. All of the regression analyses discussed in this chapter thus far have incorporated ttests for significance in order to eliminate several of the variables which the multiple regression program had allowed to enter, based upon their F levels. The last section of the chapter on
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79 procedures discussed the feasibility of gaining increased accuracy by retaining all variables which had been thus accepted, and Tables 17 and 1 8 are presented in order to demonstrate this effect. Table 17 shows that all 17 of the raw data independent variables have been accepted into the regression equation, and Table 18 indicates the inclusion of all Z value variables with the exception of Xj the per cent of employed persons engaged in manufacturing. Both of these tables show an increase in variance from the inclusion of more variables. In Table 17 the increase is slight, from 0.7550 with the ttest to 0.7723 without it. The elimination of the ttest appears to have less effect where the number of significant variables by ttest are greater. This was the case for Table 17, the raw data composite analysis. The impact was greater for the corresponding Z value analysis, Table 18, where there had been only four significant variables by ttest. Eliminating the ttest resulted in the number of included independent variables increasing from four to 17, and the total variance increasing from 0.2.549 to 0.3663. It is suggested that where the retention of all variables accepted by the multiple correlation program is considered undesirable, that some method of determining significance be found which is superior to the ttest, as applied here. One possibility would be the rejection of variables wh i ch produce an increase in total variance of less than 0.01. This type of significance test would be extremely simple to apply, since the summary table (see Table 7) 1 ists the independent variables in the order that they were accepted and shows the amount of contribution which each made to total variance. One could determine at a glance the last acceptable step in the computation and could immediately identify the
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80 I $ 8 7 ? 1 I s s Â— 1 JÂ£ o 8 x\ IX O Â— o o o ? ? $ ox ? ? ? i R 5 ox 1 t Â— o 3 O o o o o X o o rsi O o o o d s 3 AX
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81
PAGE 91
82 variables considered significant and the regression equation adopted as being the most significant. Furthermore, this approach would immediately inform the administrator of the amount of variance eliminated by the nonacceptance of all variables. If such a significance procedure were applied to the Z value regression analysis, for example, seven variables would be rejected for contributing less than 0.01 to variance, a total loss of only 0.0202. The margin could be regulated by the amount of tolerance considered allowable, whereas the consistent application of the 0.05 level ttest was a less informed approach which failed to consider the overall effect upon accuracy. Even with 16 independent variables included in the regression model, the standardized data analysis still shows that only about onethird of the total variance in financial effort has been accounted for, and it behooves our educational leaders to search for other causes. Relationship of Socioeconomic Factors to Local Elasticity of Demand for Education There always have been more demands for economic goods than the resources of society have been able to fulfill, and economists believe this situation will continue. Each demand must compete with numerous other demands for a share of the available supply; the stronger the demand, the greater will be its share. Shultz (1961) and Fabricant (1959) have shown that it is in the best economic interest of our nation for education to exert a strong demand for an adequate share of economic goods The primary concern of this study was the extent to which education was competing for economic goods of the local districts. This section of the study specifically examines the responsiveness of this demand
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83 to changes in disposable personal income. Where there has been an increase in per capita buying power, what portion of the increase was the average individual willing to spend for education? This responsiveness has been called "elasticity of demand for education" (Brazer, 1959; Fabricant, 1959; Hirsch, 1959; and McLoone, 1961). Basically, this is a measure of what percentage change in local school revenue receipts per pupil accompanied each percentage change in net effective buying income per capita. The formula used in this study for calculating elasticity of demand for education gives essentially this result, although it has been sophi stocated to make it more suitable for statistical analysis. The chapter on procedures gives the exact formula which was used and discusses it further. The coefficients of elasticity of demand for education were computed for all 122 districts in the previous studies of Florida, Georgia, Kentucky, and Illinois, and average elasticities were calculated for the nineyear periods 1945 through 1954 and 1953 through 1962. The symbols used for these average elasticities are and D^, respectively. In the present research study, these average elasticities were treated as a composite sample and v/ere regressed against the 17 selected socioeconomic variables for these districts, first using raw data, then standardized data (Z values). The following two subsections are devoted to the results of these stepwise multiple regressions and their interpretations. Relationship of 1950 socioeconomic factors to elasticity of demand D ., Tables '9 and 20 show the results of the three regressions. Each produces only one significant variable, X^, per capita net effective buying income. The total variance associated with this variable is 0.0497 for the Z value regression, and 0.0434 using raw data. Had the
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84 ttest not been used to reject all except one variable in each regression, the total variance would have been shown as 0.1 89 1 and 0.1915, respectively with all 17 independent variables included. The fact that both the raw and standardized data regressions retained only one variable in the significant regression equation is a coincidence caused by the fact that a large drop in contribution toward variance occurred between X 2 and the next most influential variable, X^, in both regressions. This drop created a gap wide enough that the cutoff of the ttest occurred in this gap for all three computations. In comparing Tables 19 and 20, it is interesting co notice that the forms of the regressions are markedly different. The raw data model has a constant term of 0.35062 and an extremely small coefficient for the single significant variable, a value of only 0.00036. The regression based on Z values, on the other hand, has a zero constant term and a sizable coefficient, amounting to 0.20844. The curve of the latter regression equation would begin at a lower value and slope upward at a much faster rate as X Â£ increased. For both regressions the transformation of the gross regression to net is completely ineffective. I he net equations are all identical to the gross equations. The reason for this is that the function of the transformation is to eliminate the effects of interdependency between independent variables, and there can be no interdependency for a single independent variable, so no change is effected by applying the transformation procedure. It can be observed from Table 21 that large samples can produce entirely different significance results than do smaller subsamples of the same group of variables. Whereas variable X^j was found to be significant in Kentucky and X 22 was significant in both Georgia and
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85 TABLE 19 SUMMARY OF D 3 REGRESSION ANALYSIS BASED UPON RAW DATA Variables D 3 X 2 Constant Gross Regression Coefficient 0.00036 0.35062 Net Regression Coefficient 0.00036 0.35062 Mean 1.39060 1077.86064 Standard Deviation 0.62929 415.50853 Simple Correlation with D^ 0.099 Partial Correlation with Dj 0 .0990 Coefficient of Partial Determination 0.0098 Importance Weight 1.0000 Contribution Toward Variance 0.0497 Multiple Correlation 0.2230 Total Variance 0.0497
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86 TABLE 20 SUMMARY OF D3 REGRESSION ANALYSIS BASED UPON Z VALUES Variables D3 X2 Constant Gross Regression Coefficient Net Regression Coefficient Mean Standard Deviation Simple Correlation with D3 Partial Correlation with D3 Coefficient of Partial Determination Importance Weight Contribution Toward Variance Multiple Correlation 0 20844 0.00000 0.20844 0.00000 0.00000 0.00000 1.00000 1 .00000 0.208 0.2080 0.0433 1 .0000 0.0434 0.2034 Total Variance 0.0434
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87 TABLE 21 COMPARISON OF COEFFICIENTS OF SEPARATE DETERMINATION FOR SOCIOECONOMIC VARIABLES FOUND TO BE SIGNIFICANT IN PREDICTING ELASTICITY OF DEMAND D 3 Coefficient of Separate Determination 3 Based on Raw Data Based on Z Values Variable FI a b Ga. c Ky 8 1 1 1 e Compos i te Compos i te X 2 (per capita net effective buying income) 0.02P 0 .04P X 21 (population of district) O. 36 P X 22 (% population increase in last decade) 0.1 7N 0.1 7N The P or N following the coefficient indicates a positive or negative simple correlation with the dependent variable. Source: Hopper 1965 Source: King 1965 Source: Adams 1965 Source: Quick 1965
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83 Illinois, neither are significant in the composite study. And which was found to be significant in both composite analyses, was recognized in none of the four states. In one respect, however, all three composite regressions and all four state regressions are in agreement: socioeconomic variables account for very little of the variance in elasticity of demand for education. All the 1950 regressions thereby tend to confirm the hypothesis that there is little association between socioeconomic variables and elasticity of demand for education. Relationship of I960 socioeconomic factors to elasticity of demand D ^. The regression summaries shown on Tables 22 and 23 confirm the indications of the analyses that the strength of relationship between socioeconomic factors and elasticity of demand for education is slight. When using raw data the total variance is only 0.1856, and when the computation is based upon Z values, it drops to 0.1548. Both the 1950 and the 1 960 regressions substantiate the hypothesis that there was little association between socioeconomic factors and elasticity of demand for education. The relationship was even weaker for elasticity than it was for effort. Why this is trus is at this point a matter of conjecture. However, referring back to the first section in this chapter, Consistency of Effort and Elasticity, an example was given to show that small marginal changes in effort can be associated with extreme fluctuations in elasticity of demand. In the earlier analyses, a comparison of consistencies of effort and elasticity showed that while financial effort was rising rather uniformly over a ten year time span, with very little shifting of relative positions within the sample, elasticity of demand for education fluctuated without any discernible pattern,
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89 CO CO >_l < z < < fÂ— z < 0 Q CNl CO CM CO < LU CC UJ a: _J CD 2! CO LU O < Ql Ol. ZD LTV Q Q LU Li_ CO O < CQ >CL < Â£ ID CO 4* 00 c O 00 03 vO vQ 4J 4 CA 1/1 rÂ— NO c Â• Â• 0 O O 0 1 NO CNJ 00 CA ca CA 4 LA PA LA CTv O CNJ CNJ 0 O CA 0 PA LA 0'\ CA CNJ 0 0 PA 4 0 PA X 0 0 PA O CM O PA O 0 0 'X) 4 O O O O O 00 LA i/I 0 rÂ— d CO CNJ LA Q NO r\ LA rÂ— PA 4r\ 0 la LTV LA CO CA 4 CM PA vÂ£> Â— Â— O CO NO cr\ LA 0 vO PA L. X O O 00 0 CM (M O PA 0 03 D> O O CM PA O O O O 0 CM NO LA PA m LA PA CO c r> f\ cr\ 3* 00 00 NO O CM crv PA 00 CNl 0 cn LA PA CM 4 CM 0 X O 0 CM lA PA CM O PA Â— O 0 4 O O 0 O 0 CA O in LA Q 4~J C C O 0 0 0 0 42 Â•Â— c 0 4c 4J Â“O O O 0 c c 0 L_ L 0 0 0 Â•Â— 0 4J 0 4J C CD Â•Â— Â• Â— 4> CL _c i 0 0 4J 4J 0 cn O Â• Â— C 0 0 Â— 4Â• Â— 10 CD J) 0 Â• Â— 0 ) 0 0 l0 lO Â• Â— > 0 u c L_ c 0 1/1 0 Ll_ 4J 0 0 0 u C0 Q L. 0 c 0 C_> Â• Â— CO 0 0 CD 0 0 Â£ L> 0 CL c Â— 4J L_ 0 0 4J 0 0 E 0 0 O CD z 2 : CO CO CL O Â— 0 3C t
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90 TABLE 23 SUMMARY OF Dr REGRESSION ANALYSIS BASED UPON Z VALUES Variables 5 X vn f X 8 Constant Gross Regression Coefficient 0.26978 0 27 H 5 0.00000 Net Regression Coefficient 0. 1 3441 0. 1 3606 0.00000 Mean 0.00000 0.00000 0.00000 Standard Deviation 1.00000 1 .00000 1.00000 Simple Correlation with D5 0.285 0.287 Partial Correlation with D^ 0.2806 0.2826 Coefficient of Partial Determination 0.0787 0.0799 Importance Weight 0.49822 0.501 78 Contribution Toward Variance G. 0725 0.0822 Multiple Correlation Total Variance 0.3934 0.1548
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91 causing a complete reordering of relative ranks. It is believed that this tendency to fluctuate vigorously in response to changes in personal income or school revenue causes a weaker relationship to socioeconomic var i abl es. A comparison of Tables 22 and 23 reveals an effect which has been consistent throughout the analyses in this studya reduction in the number of significant variables when raw data are standardized, with different variables being significant for the two different forms of data. For the composite raw data analysis, three variables were found to be significant: X,^, P er cent f 14or more yearold females in the labor force; X^, per cent of employed persons engaged in manufacturing; and 22 > P er cent increase in population over the decade. The standardized data analysis found only two variables significant: X^, state revenue receipts per pupil; and X^, per cent of the population that is nonwhite. Even where the ttest is eliminated, there is still a greater number of independent variables brought into the regression equation when raw data are used. This can be seen by comparing Tables 25 and 26, where the former, presenting the raw data summary, includes >7 independent variables compared to 16 for the latter. This comparison has been consistent throughout the study, for all regressions where the ttest was eliminated. Another comparison of interest which has been rather consistent is the number of included variables and the amount of variance. The raw data analysis on Table 22 has three independent variables compared to only two on the Z value analysis of Table 23, and the variance for the raw data regression is somewhat higher, 0.1356 compared to 0.15^8. When
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92 the ttest is eliminated, however, the numbers of included variables are relatively more even, 17 to 16. Similarly, the total variances are more even, 0.2523 and 0 2666 respectively. Table 24 shows a lack of consistency in selection of significant variables between states as well as between composite computations. Of the seven significant variables in the individual states, there is only one agreement between states. Both Georgia and Illinois recognize X^, per capita net effective buying income,,as significant. However, neither composite computation finds this factor as significantly influential. As shown by Tables 25 and 26, it contributes only 0.0003 to total variance in the composite raw data analysis, and 0.0089 in the composite Z value analysis. This researcher finds this lack of consistency very disturbing. One would expect a variable which is consistently influential in the individual states to be similarly influential in a composite analysis, particularly where the relative effects of dispersions are retained in the composite by combining Z values rather than raw data. Further remarks on this phenomenon are made in the final chapter. It is suggested that a comparison of Tables 23 and 26, the composite Z value summaries with and without the ttest, clearly reveals the superiority of retaining more variables than the 0.05 level ttest would permit. First of all, the total variance when retaining all variables entered by the multiple correlation program was 72 per cent greater than when the ttest was used. The ttest had eliminated all except two independent variables. All of the variance is real and should be considered. The writer acknowl edges the practicality of eliminating variables which produce negligible effect on the relationships being studied, but the elimination procedure should provide a cutoff established
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93 TABLE 24 COMPARISON OF COEFFICIENTS OF SEPARATE DETERMINATION FOR SOCIOECONOMIC VARIABLES FOUND TO BE SIGNIFICANT IN PREDICTING ELASTICITY OF DEMAND D 5 Coef f i c i ent of Separate Determination 3 Based on Raw Data Based on Z Values Variable Fla .* 3 Ga. c Kyd 1 1 1 e Compos i te Compos i te XÂ£ (per capita net effective buying income) 0. 1 1 P 0.21 P X 4 (federal revenue recei pts per pupi 1 ) X 5 (state revenue recei pts per pupi 1 ) 0. 1 9N 0.24N 0.08N X 3 (non white % of popul ation) 0. 1 4N 0.08N X ]4 (% of 14ormore yearold females in labor force) 0.07P X 1 5 (% of employed persons in manufacturing) 0.34P 0.08P X 22 (% population increase in last decade) 0. 1 IP 0.01 P 3 The P or N following the coefficient indicates a positive or negative simple correlation with the dependent variable. b Source: Hopper 1965 C Source: King 1 965 d Source: Adams 1 965 Source: Quick 1965
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94 by informed judgment, either through preprogramming or posteriori personal judgment. The multiple correlation program provides information to facilitate either of these approaches, as summarized by Table 26. The contribution which each variable makes toward variance is given, as well as the total variance for all variables, and the comparison of these respective values provi des a very practical way of establishing a cutoff to the elimination procedure. For example, restricitng the eliminations to those variables which contribute less than 0.0050 to var i ance woul d eliminate nine variables and a total of only 0.0176 from variance, or 6.6 per cent of the gross variance accounted for. It might be advantageous to also set a maximum percentage or total variance for which elimination would be permitted. With this limitation established at 50 per cent, the cutoff for the composite Z value regression (Table 26) would eliminate seven variables, causing a total reduction in variance of 0.0089, or only 3.34 per cent of gross variance from all variables. A procedure with these limitations would assure that violence would not be done to statistical accuracy in reducing the recognized variables to a workable number. For the purposes of the present study, however, there is no particular hardship in retaining all variables entered by the correlation program, and it is felt advisable to do so in order to demonstrate the effect of each variable. Fortunately, however, there is no doubt of the conclusion to be drawn from the various regressions involving elasticity of demand, regardless of the use of significance tests or whether the data were expressed in raw form or standardized. All regressions showed a weak
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95
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96
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97 relationship between elasticity and socioeconomic variables, indicating that educational leaders should look elsewhere for the causes of change in elasticity of demand for education. Relationship of Socioeco n omic Factors to Local School Revenue Receipts per Pupil It is generally accepted that a higher quality of education will normally be concomittant with a higher expenduture of funds per pupil. Not only does this appear to be an obvious commonsense conclusion, but Johns and Morphet (i960) have supported it through experimental research. It should not be surprising that one of the most popular approaches to improving education has been the investigation of how financial support per pupil could be improved. Several of the studies mentioned in Chapter I attempted to account for variations in per pupil expenditure, and this part of the current study follows a similar approach. Local school revenue receipts per pupil for I960 (essentially the same thing as local school expenditures per pupil) have been regressed against I960 socioeconomic factors for the selected 122 school districts, and the results are presented in Tables 27 and 28. These regression summaries show that the bulk of the variance in local school revenue receipts per pupil is associated with net effective buying income per capita, and to this extent they tend to confirm the hypothesis concerning revenue receipts per pupil. However, they deny it in another respect. Whereas it was hypothesized that net effective buying income per capita was the only socioeconomic factor significantly related to financial support per pupil, several other significant variables were found, although their combined total impact was small.
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SUMMARY OF R 4 REGRESSION ANALYSIS BASED UPON RAW DATA 98 C Â— Â— Â— O 0 O O CO 4* <0 jvO LA 4LA CM CM O Â• Â• Â• O 0 O CO CO CM CA LA Â— 0 O Â— 0 Â• Â• Â• O 0 0 LA Â— CO 0 00 Â— vO CM Â— O Â— 0 Â• Â• Â• O O 0 LA rÂ— CT\ CO rÂ— OO LA 4C T> Â— O O O Â• Â• Â• O O O vO LA CO 4* CM CA LA LA CM CA CA co co a4" 4 vO a^ LA co vO 4* 4* 0 LA 4* Â• Â— O vO 00 LA CM CM a^ O O 00* vO 5 0 O O O 0 CM Â— CO 0 r\ CO LA 0 CM 0 CO CM vO co Â— Â— c 4J c 0 L_ 0 Â• Â— 0 c 4J Q0 4J 0 c 0 Â— 4C Â• 0 0 O O 4J 0 O LO Â“O Â— O 4* 4" Â• Â— Â•Â— c D cC cn Â— L_ 4J cÂ£ rÂ— cn O E 0 .O ~o 40 40 0 0 0 Â•Â— L_ 4J Â• Â— Â•ji 4CÂ£ 4Â“O Â•, Â— sz n 40 \Â— L. 0 IS) 0 0 c c > CL 4J 4J 4J 44J O 4J 0 O 4J O 0 0 0 e Â• Â— 4 Â• Â— 0 0 CL c 0 L. O 0 O 0 4J O 5 0 5 O O E 0 1 Â— O Z 2 : LO to Q_ (_) Â— 0 Multiple Correl at ion 0 9 1 10 Total Variance 0.8299
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SUMMARY OF R 4 REGRESSION ANALYSIS BASED UPON Z VALUES 99 44 0 O C 0 O 03 0 O 4 0 O CO 0 O c Â• Â• 0 0 O 0 LT\ O 0 LA LA O O 0 LA PA Â— CM O 0 cn PA CA LA vO ca CM O O 0 O CM cO rÂ— rÂ— O O 0 CM jÂ• Â— 0 X Â• Â• Â• Â• Â• Â• Â• Â• Â• O O O O O 0 O 0 CA O 0 4Â“ 4" O 0 iA 4PA a0 LA O 0 AOO CA CO CA 4" O O 0 PA CA 0 PA O X O O 0 LA O 0 O O O O O Â— O O 0 O O CM PA O 0 O Â— PA O 0 CA 0 LA LA vO LA LA O 0 4" 4vQ OO vO LA PA O 0 vO LA CM PA Â— X CM O O 0 LA PA Â• Â— 1 Â— O Â• Â• Â• Â• Â• Â• Â• Â• Â• O O O Â• Â— O O O O O Â‘ O O 0 vO 00 LA CM O 0 LA CA O t 4" O 0 ~4 CO vO O 0 PA CM < Â— PA LA O 0 O cn O PA 0 LA O LA O 0 PA V0 CM CO 4X PA O O 0 4CM Â• Â— 0 Â• Â• Â• Â• Â• Â• Â• Â• O 1 O 1 O 0 1 O 1 O O 0 vO 4" O 0 Pv vO O 0 4 O vO CA vO Â— O 0 CA CO CM cn CM pa PA O 0 PA > Â— Â• Â— X Â— O O 0 vO 4* CM Â— O 0 1 O 1 O Â— O 1 0 O 0 O O 0 4* CO CA O 0 CM PA Â— CA LA O 0 PA V0 CO PA > Â— ^0 O 0 vO 4CA < Â— OO CM PA 0 O 0 LA CM CM LA X Â• O 0 O 0 O O O O 0 0 4 0 LA 4* 0 'X> CÂ£ 0 OO Â— O C 4 c 0 U 0 Â•Â— 03 C Â— 44 Q. 0 44 03 c~ 03 Â— <4C Â• 1/) 0 Â— 03 0 0 4 > CO 4> Â— 41 a) L> Â• Â— :s C Â• c 0) c CO C 1L. 44 44 0 0 L_ 0) CO 0) C L_ 0 C 03 03 Â— 03 cn Â— CD Â— 0 0 O 03 C O 44 r> 44 Â“O Â— Â— 14 0 ) 4 Â— 03 03 03 03 1_ 4 > L_ CL 03 CO 4CC 4T3 Â— Â— _C Â• _C *4Â— 03 L_ U 03 L1/1 0) 03 c C > O. 44 4 44 U_ J4 O 3 4 L_ O O 4Â—* O 03 03 03 E Â— LÂ• Â— 03 13 CL C O rÂ— O LO 03 O 0 ) 4 Q Â— 5 <0 Â£ O Q E O H D 0 C3 2 : CO LD CL O Â— O 2 : Total Variance 0.7489
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100 A summary of the significant variables and their respective contributions to variance is shown below for both the raw data and Z value analyses : Raw Data Z Values (per capi ta net effective buying income) 71.71% 58.19% (per cent ADA to total population) 1.29 X^ (state revenue recei pts per pupi 1 ) 4.07 X, (per cent of families with $10,000 income) 1.53 Xg (nonwhite per cent of population) 1 .10 Xjg (median school years completed by adults) 1.10 Xjg (college educated adults, per cent of population) 0.97 1 .65 X (median family income) 0.93 Xjg (per cent of population 65 or more years old) 5.64 7.67 The 71.71 per cent of variance contributed by per capita net effective buying income in the raw data analysis is similar to the 75 per cent of variance in per pupil expenditures which Hirsch (1959) found to be accounted for by per capita income f 1 uctutat i ons The current Z value analysis, however, indicated only 58.19 per cent of the variance as attributable to personal disposable income per capita. This is much smaller than either Hirsch's findings or the raw data indication,
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101 reflecting the possibility that reduction in range from standardization of data may have resulted in an excessive reduction in the resultant var i ance. The next most influential factor, both in the raw data and Z value analyses, was X^, the per cent of population comprised of 65 ormore yearolds. This was surprising, inasmuch as was significant in only one of the four states originally studied, as indicated by Table 29. However, the fact that it was significant only in Florida does not mean that it completely lacked association in the other three states. It merely means that the amount of association fell below the point where the ttest for significance happened to cut off. The fact that the previous studies failed to present any information about the relationships of those variables which were nonsignificant makes it difficult to investigate the contributory influences from the separate states in bringing about the significance in the composite. The only other variable which is significant for both analyses, raw data and Z value, is X^, the per cent of total population consisting of adults (25ormore yearolds) with at least four years of college education. Table 29 shows a coefficient of separate determination of 0.14 for the Z value composite analysis and 0.08 in the raw data analysis. In no case did any of the related research studied find this factor to be influential. However, a similar factor, median school years completed by adults (X^), has been recognized in several studies, and the Z value analysis of this study indicates that it contributed 1.10 per cent of the total variance. It would appear, then, that the effect of education has a slight tendency to be circular: the higher the level of education
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102 TABLE 29 COMPARISON OF COEFFICIENTS OF SEPARATE DETERMINATION FOR SOCIOECONOMIC VARIABLES FOUND TO BE SIGNIFICANT IN PRED I C I TNG LOCAL REVENUE RECEIPTS PER PUPIL R 4 Coefficient of Separate Determination 3 Based on Raw Data Based on Z Values Variables FI a b Ga c Ky d 1 1 1 e Compos i te Compos i te XÂ£ (per cap i ta net effective buying income) 0.5CP 0.49P 0.43P 0.45P 0.28P X 3 (% ADA to total population) 0.1 7N 0.26N 0. 1 IN X 5 (state revenue recei pts per pupi 1 ) 0.25N 0.22N X 7 (% of fami 1 i es with $ 10,000 income) 0.29P C. 14P X 8 (nonwh i te % of popu 1 a t i on) 0. 04N X 1 0 (rural nonfarm % of population) 0.43N X 1 3 (median school years completed by adults) 0. 1 IP X]Â£ (college educated adults % of population) 0.08P 0. 14P X ] 7 (median family income) 0.08P X )9 ( 65 yearolds, % of population) 0.22P 0. 1 1 P 0.03P X 2 I (population of d i str i ct) 0 15 P 0 01 P ^22 (% population increase in last decade) 0.003N 3 The P or N following the coefficient indicates a positive or negative simple correlation with the dependent variable. Source: c Source: d Hopper 1965 King 1965 Adams 1965 Quick 1965 e Source: Source:
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103 for previous generations, the more the financial support for each pupil in the current generation. State revenue receipts per pupil (X^) was significant only in Illinois in the previous studies, but the standardized data composite analysis finds that this factor contributes 4.07 per cent of the total variance. The net regression equation, as shown on Table 28, shows that for every unit increase in state revenue receipts per pupil, there is a corresponding decrease in local school revenue receipts of 0.05564 units, when the effects of interdependency tetween independent variables are eleiminated. It is expected that the strongly negative relationship in Illinois has carried over into the composite analysis, but one cannot be sure of the extent to which this caused the relationship in the composite, without knowing the relationships in the other states. And no information was given in the previous studies regarding strength of relationship except where significance was indicated by the 0.05 level ttest. The revenue receipts form the state governments in this fourstate area were associated with a decline in local revenue receipts. In addition to the equalization function of foundation programs, inducement provisions often stimulate increases in the levels of local revenues. This secondary effect was not being realized in I960 for the composite a rean Information regarding direction and strength of relationships for all variables which were brought into the multiple regression computations, whether significant by ttest or not, are included on Tables 30 and 31, composite raw and Z value analyses, respectively. It was surprising to find that the inclusion of nonsignificant variables added
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104 < X EE
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105 g g Â— JT ~T O Â— O oo "Â•> O r> IS Â” 3 Â§ 2 g = 3 S 3 I S & I Â— u i t 8 Â£ 5
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106 only about 2 per cent to the total variance associated with significant variables alone. For the analyses of effort and elasticity, the increase caused by adding nonsignificant variables was much higher. in Table 30 the effect of the refinement of the gross regression equation to net is more noticeable than in the other transformations, particularly because of the large change in the constant term. Whereas the gross constant term was 36.35916, the net constant is 118.1 8586 after the transformation. The coefficients also underwent tremendous change in magnitude during the transformation. A comparison of the first two lines of the tables shows that most of the net coefficients are less than one twentieth as large as the cor respond i ng net coefficients, and some are less than a hundredth as large. It is obvious that the elimination of interdependency between independent variables reveals an entirely different relationship between the dependent variable and the respective independent variables. A review of the final lines in both Tables 30 and 31 impresses one with the lopsided strength of one variable. Certainly the financial support of each pupil related most strongly with the amount of funds each person has available, but other factors are also significant. In the standardized data analysis, Table 31 for example, other selected socioeconomic factors contribute 1 8 1 5 per cent of the variance, and 23.66 per cent is unexplained. So educational leaders must consider other factors than just the disposable income per capita, if they are to fruitfully plan strategies for increasing the support of our schools. Test of equation transformations Each of the several regression equations developed by multiple regression procedures has been transformed to a more refined equation,
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107 which we have called "net" regression equations, since they eliminate the effects of independency between independent variables. The net equations show with more specificity the relationships between variables, but the refined models would be of little use if the transformation had materially impaired their accuracy of prediction. Therefore, a sample test was conducted to compare the predictive accuracy of three of the net regression equations with that of their corresponding gross equations. For each equation tested, predicted values of the dependent variable were computed, first using the gross model, and then using the net. Each set of predictions was then correlated against the actual values of the dependent variable. The results of the test show as follows that there has been negligible change in predictive accuracy. Regress i on Equation Coef f i c i ent Predicted vs of Correlation Actual Values Variable Deri ved with tTable test? Reference Gross Equat i on Net Equa t i on Lf> LU yes 1 1 0.4453 0.4633 5 yes 22 0.4666 0.4659 D no 25 0 2844 0.2822 Correction for size of sample The tables in this report have shown no corrections to the computed values of multiple correlation and total variance simply because they are too small to be material to the results of the study. Ezekiel and Fox (1959:301) offer the following formula for making such corrections. 0 \ 1 23 Â• .kj
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108 where R is the coefficient of multiple correlation, n is the number of cases, and m represents the number of independent variables included in the multiple regression equation. This correction formula was applied to the I960 multiple correlations for each of the three dependent variables, both for raw data and for standardized Z scores. The amounts of correction are illustrated below: Reqression Analysis Multiple Correlation Total Variance Var Form of Data Table Refer Uncorrected Corrected Uncorrected Cor rected E 7 Raw 14 0 .'8689 0.8615 0.7550 0.7422 E 7 Std 15 0.5048 0.4858 0.2549 0.2360 5 Raw 22 0.4308 0.4146 0.1856 0.1719 5 Std. 23 0.3934 0 3844 0.1548 0.1478 R 4 Raw 27 0.9H0 0.9070 0.8299 0.8266 R 4 Std. 28 0.8654 0.8578 0.7489 0.7360 Each value is reduced very slightly by this correction for sample size, but not enough to have any effect upon the conclusions drawn. The direction of the correction in each case is toward a weaker relationship between the selected socioeconomic factors and the respective measures of school fiscal policy, thus tending to reinforce the conclusions that other types of variables should be investigated. A variety of statistical and analytical approaches has been used in this chapter to investigate the five hypotheses. They started with the same data and techniques which were used in the original studies of Florida, Georgia, Kentucky, and Illinois, but then branched out into the use of transformed data, alternate tests of significance, and techniques
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109 for refining regression equations. Different approaches did not always lead to the same results, but no one set of results can be considered exclusively right or wrong. An attempt was made to evaluate the advantages and disadvantages of each and to synthesize these evaluations into conclusions concerning the hypotheses. These conclusions are summarized in the following chapter.
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CHAPTER IV SUMMARY AND CONCLUSIONS Purpose of the Study The purpose of this study was to examine the relationship of selected socioeconomic factors to local patterns of school fiscal policy in Florida, Georgia, Kentucky,' and Illinois. Historically many educational leaders have felt that factors such as these were among the chief determinants of school financial support. More recently, however, another category of determinants has been suspected1 eadersh i prel ated variables, such as decision making processes, typology and value systems of the informal power structure, traits of i nf 1 uent i al s leadership of the superintendents and other educational officials, etc. Which category is effective and to what degree? The present study was designed to help answer that question. It has concentrated on examining the influences of the first group of variables, selected socioeconomic factors. Sel ec ti on of Sample and Variables This study replicates in part the procedures used in the original studies of Florida, Georgia, Kentucky, and Illinois by Hopper, King, Adams, and Quick, which related a similar group of selected socioeconomic factors to three different measures of local school fiscal policy. Data were col 1 ected for 1950 and I960, for all districts having I960 populations of 20,000 or more. The measures of school fiscal policy were:
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Measure Descr i pt i on Local school financial effort Elasticity of demand for educat i on Local school revenue receipts per pupi 1 Total local school revenue receipts divided by net effective buying income. Symbol E is used for the 1949 through 1951 average; Ep 1959 through 1 96 1 Basically this is the percentage change in local school revenue per pupil divided by the percentage change in net effective buying income per capita. The exact formula is given in Chapter II. D symbolizes the 1945 through 1954 average; D 1953 through 19*52. Total local school revenue divided by number of pupils in average daily attendance. Statistical Procedures Consistency of effort and elasticity Rankings of the districts by effort were compared to E^ rankings, and changes in rank over the ten year period were analyzed to evaluate consistency. Elasticities and were similarly ranked and analyzed. R e 1 a t i onsh i p of fi nanc i al effort t o income responsiveness Pearson r's were calculated for financial effort E^ regressed against elasticity of demand D to determine the extent to which response to change in personal income per capita varied with change in effort. A ttest was used to evaluate the significance of relationship. The computation was first performed using raw data, then using standardized Z values. Multiple regression techniques Each of the three measures of school fiscal policy was correlated against the 17 selected socioeconomic variables. Each correlation was
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112 performed twice, using a different arrangement of data each time: (1) all raw, (2) all expressed as standardized Z values. Each arrangement had advantages and disadvantages with respect to retainage of dispersions and elimination of extraneous factors which might affect some states but not others. These were discussed in Chapter II. Using the techniques of stepwise multiple regression the independent variable was selected at each step which had the highest partial correlation with the dependent variable. This caused the greatest possible error reduction in the analysis of variance based upon sum of squares of deviation. Successive steps continued to enter new variables as long as any independent variable remained which had an F level as high as 0.001. At the completion of all steps, a summary table was printed showing the contribution of each variable toward total variance, sequence of entry of variables, F level required for entry, total multiple correlation, and total variance. S i gn i f i ca nee test Following a procedure used in the original studies, a ttest was used to determine significance. Step by step through the multiple regression, the coefficient of each included variable was compared with its standard error, until one variable failed to equal the involved correlation's tvalue multiplied by such standard error. The previous step of the computation was then accepted as final, all variables not included there being considered nonsignificant. Because the application of this test appeared in some cases to eliminate unreasonable amounts of variance, summary analyses were made both with and without the use of the ttest, and results were compared.
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113 Refinement of regression e< ; at ions Each multiple correlation step provided a regression equation to show the relationship of the dependent variable to each independent variable at that time. Each coefficient is expected to show the number of unit variations in the dependent variable which result from one unit of variation in the related independent variable. Celia (1967) points out that equations resulting from multiple correlation fail to do this, since each coefficient reflects not only the var i ance, assoc i ated with the independent variable itself but also additional variance indirectly attributable to other independent variables interacting with the independent variable. Because of the inclusion of this indirect element, Celia ( 1 967 ) refers to such unrefined regression equations as gross equations, and the coefficients as gross coefficients. He and others (Frisch, 193^; Woid, 1953; Ferber, 1 962) have suggested methods of transforming gross equations to net, by using a system of weightings. The method suggested by Celia was used in this study to refine each of the regression equations produced. It required the computation of partial correlations for all independent variables, which were used as bases ror computing weightings. The details of this method were presented in Chapter II. Imp! i c at ions of the Findings Hypothes is 1 ; Mos t sc hool dis tri cts fol l ow consistent patterns of fi nancia l effort and elasticity, yet some make marked changes in rel at i ve ly short periods of time Effort. Â— The hypothesis was supported with respect to financial effort. There was a strong tendency for internal consistency, with high effort districts tending to remain high and low effort districts disposed
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to remain low. However, a few districts made marked changes in rank. These were the districts in which educators should have the greatest interest, for they demonstrate that change in fiscal policy not only can but has been made. Perhaps these districts can provide us with clues as to what factors are effective in overcoming the inertia which prevents desirable change. Elasticity The hypothesis was refuted. Forty of the 122 districts changed by more than 50 per cent of the full range of rankings, and six changed by more than 100 levels of rank. Not only was there a general reshuffling of relative positions, but the state means were scrambled, almost reversing their initial order. The contrast between the consistency of effort and the inconsistency of elasticity was striking. The latter was obviously much more sensitive to changes in personal income and educational revenues than was the former. An illustration given in Chapter II demonstrates how this sensitivity can be associated with a wildly fluctuating coefficient of elasticity and yet effort remaining stable. Blazer (1959) pointed out that elasticity is a measure of sensitivity of change in revenue per pupil to change in disposable income per capita, and it is valid only for very small changes in the latter. This researcher questions whether the elasticity coefficient is not too sensitive for evaluating relationships of socioeconomic variables over a time span of ten years. Hypothesis 2: High effort districts are more responsive to changes in per capita personal income than are low effort distri c ts, such that they invest in education a greater portion of increases in their personal i ncome There was no recognizable association between level of effort and fiscal response to income change. The hypothesis was emphatically denied.
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115 Using raw data, a simple correlation of effort E^ to elasticity yielded a correlation of only 0 005 1 6. Even using standardized data, the simple correlation was only 0.2601, a variance of less than 7 per cent being accounted for. The above remarks regarding the oversensitivity of the elasticity coefficient are again applicable here. Hypothesis 3: There is litt le association between socioeconomic factors aTid local school financial effort to support public schools The marked stratification of effort levels between states has been pointed out in Chapter II, particularly by Table 9, which shows the Illinois districts filling the top ranks of effort, and Georgia, the lowest. When the effect of this stratification was eliminated by the transformation of data to standardized Z values, it had a strong impact on the correlation of socioeconomic variables against financial effort. Using 1 960 variables, for example, the raw data correlation accounted for 75.50 per cent of the total variance in effort, whereas the correlation based on Z values accounted for only 25.49 P er cent. The conclusion regarding the third hypothesis obviously hinges strongly upon the relative merits of using the two different forms of data. Tnis researchei accepts Guilford's conclusion (1965) that standardscore scales provide us with more comparable data than do raw score scales, so more emphasis is placed on the results using Z values. The fact that the standardized data regression finds only 25.49 per cent of the total variance in effort accounted for by variation in the selected socioeconomic variables is a confirmation of the third hypothesis. For 1950 variables, the result was similar, with 28.82 per cent accounted for. This contrasts with the 1950 raw data reflection of 40.51 per cent.
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116 Four variables were significant in I960 using standardized Z values, seven using raw data. Three of these were common: X^> ADA as a percentage of total population; X, Q) per cent of population comprised of i y 65 ormore yearolds; and X^, per cent increase in population over the last decade. The zero order correlations of these factors with financial effort E j are positive in each case, both for raw data and standardized Z values. There is little educational administrators can do to change such factors as these. It is fortunate that they account for only a small portion of the total variation in school financial effort. There is a strong implication that educators should investigate the effectiveness of other types of variables as determinants of school fiscal policy, and it is suggested that leadership related variables offer a fertile possibility. Hypothesis 4: There is little association between socioeconomic factors and elasticity of demand for education No material amount of stratification between states was observed under the analysis for consistency of elasticity, and no material difference exists in the results of multiple regressions using raw and standardized data. The 1950 analyses account for 4.97 and 4.34 per cent of total variance, respectively. The 1 960 analyses account of 1543 and 18.56 per cent. In all cases, a weak. rel at i onsh i p between variables was found, confirming the fourth hypothesis. Furthermore, the variables found to be significant by raw data analysis were different from those found significant in the Z value analysis. No variable found as significant in the I960 analysis was also significant in 1950. These findings emphasize the inconsistency of elasticity of demand, which this researcher feels if the result of its over sensitivity for the purposes of this study. Similar inconsistency was found in the previous studies. In Florida, no significant factor was found in either of the two decennial years.
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117 Hypothesis 5: Local financial support per pupil is significantly related to personal income per capita but not to other socioeconomic variables. Both the raw data and standardized Z value analyses confirmed the first part of this hypothesis, for in both cases, per capita net effective buying income accounted for the bulk of the total variance accounted for. Only two ocher variables contributed os much as 2 per cent to the total variance. X^, state revenue receipts per pupil, which was significant only in Illinois of the original studies, had a negative influence upon local revenue receipts per pupil, contributing 4.07 of the total variance in the Z value analysis. was significant only in Georgia, but the strong effect there carried over into both composite analyses, contributing 564 per cent of total variance in the raw data analysis, 7.67 in the standardized data. Both were positive influences upon financial support per pupil, caused by a high proportion of 65 yearolds in the population, particularly in Florida. Although the existence of significant variables other than personal income per capita contradicts hypothesis 5, their effect is so small and so pertinent to isolated special situations that the hypothesis is felt to be substantially confirmed. But even with personal income per capita providing the principal influence upon school support, there is still room for considerable impact from other types of factors. The Z value analysis leaves 25.11 per cent of the total variance unexplained, and even the raw data regression fails to account for 17.01 per cent. The investigation of other categories of determinants is still war rantedcategor ies such as 1 eader sh i prel a ted variables previously discussed.
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118 General comments Effect of significance tests. This study has shown at several points that the use of the 0.05 significance test caused intolerable errors. The multiple correlation accounted for up to 72 per cent more total variance than was acknowledged with the use of the ttest. More preferable methods of eliminating the lesser influential variables were recommended in the body of the report. The extent to which the accuracy of the original studies was affected by the use of the ttest cannot be determined without recomputing the multiple correlations. Because of this, uncertainty the findings of these studies are open to serious quest i on i ng. Effect of interdependency between independent var i ab 1 es Twentyone summary analyses of regressions were included in this report, and each of them presents a refinement of the regression model generated by the multiple regression program. The principal use of the regression equation in this study is to show the relationship between the dependent variables and the respective independent variables. The unrefined equation fails to do this, since each coefficient shows not only the direct effect of its own variable but includes also an element of indirect effect caused by other independent variables acting through interdependence with that variable. In eliminating the indirect element, the refinement changes drastically the sizes of the coefficients. The unrefined, or "gross," equations are very misleading. Ihis researcher wonders what results might have been obtained in the original studies if the gross regression equation had been transformed to net equation. Effect of using larger sample The larger sample in this study as compared to the smaller samples used in the original studies of Florida, Georgia, Kentucky, and Illinois generated surprising results on several
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1 19 occasions. Variables were found to be significant in the composite where they had not been significant in any of the smaller sample studies. On the other hand, variables which had been strongly significant in two or three of the individual states were nonsignificant in the composite. The results from the current composite study contrast sharply with those of the four separate studies. This emphasizes the need for the present study, which has provided a wider variety of influences and a more adequate sample size. Cone! us ion Because the quality of instruction is strongly related to the financial support of education, educational leaders must find a way of increasing that support. They must be aware of every resource available to them in bringing about this change. Already, school administrators spend great amounts of time and energy trying to shape the school fiscal policies of their districts. But until they know which factors are influential and to what degree, a large part of their energy will be wasted. This study has examined the traditional category of socioeconomic determinants in a composite fourstate area, and it has found a weak relationship between them and local school financial effortthe willingness of the people to support education, regardless of fiscal ability. The major portion of the variance in effort could not be explained by the studied socioeconomic factors. An even weaker relationship was evidenced between these factors and elasticity of demand for educa t ionthe responsiveness of the people toward the needs of education when the average personal income changes. If this responsiveness is not brought about by socioeconomic factors, surely we need to find out what does bring it about.
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120 The third area where the relationship of socioeconomic variables was examined was in their relationship to local school revenue per pupil. As expected, the disposable income per capita was found to be strongly related, but no other socioeconomic factor was influential. Furthermore, the standardized data analysis showed more than onefourth (25.11 per cent) of the total variance unexplained. This leaves a wide area in which educational leaders need guidance as they attempt to plan strategies for improvement. The extreme variance in the effort exerted by the different districts in the composite sample attests to the fact that some people become far more willing to pay for superior education than do others. The effort level in some districts was over fifteen times as high as that in others. What caused this drastic difference in attitude? We have not been able to adequately answer this question by examining the relationship of socioeconomic variables to school fiscal policy. It is suggested that leadershiprelated variables, such as those described by Presthus (1964), Kimbrough (1964), and others, offer a fertile field of additional possibilities. Statistical studies of the relationship of these variables to school fiscal policy are strongly recommended.
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APPENDICES
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APPENDIX A TABLE 32 SUMMARY OF SYMBOLS Dependent Variables Financial effort for 1959 through 1 96 1 Â£ Financial effort for 1 949 through 1951 D Elasticity of demand for education 1 9^+5 through 1 95^+ Elasticity of demand for education 1953 through 1962 R^ Local revenue receipts per pupil in I960 Independent Variables '12 Average daily attendance in public schools Per capita net effective buying income (in dollars) Average daily attendance as a per cent of total population State revenue receipts per pupil (in dollars) Per cent of civilian labor force employment Per cent of families with income of $10,000 or more Per cent of population that is nonwhite Per cent of 1417 yearolds attending public or private schools Median school years completed by 25ormore yearolds X ^ Per cent of 14ormore yearold females in labor force Xj,Per cent of employed persons engaged in manufacturing XjÂ£ Per cent of population comprised of 25ormore yearolds with 4 years of college education X j y Median family income (in dollars) 122
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123 TABLE 32 (Continued) X X X X 18 19 21 22 Per cent of married couple^ not owning homes Per cent of population comprised of 65 ormore yearolds Population of the district (persons) Per cent increase in population over the past decade
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RAW DATA FOR DEPENDENT AND INDEPENDENT VARIABLES FLORIDA, I960 124 CA PA CA CM CA CO CM CM LA CM CM LA CA 0 CA PA CM O CM PA CA CM PA 3 3 Â— rs cm r3 eo CM ca fA. Ao oc CA S LA O CA PA 3* PA CA LA O CM CA CO CA CA LA Ui lO O 04 Â“ Â— 3 vA O A p. (A CA CO OO CA CO PA (A LA 00 lO Â— LA O LO LA LA CA CM 3 ALA ACA "S\ PA CM o S' (A o o S 00 CA pa pa CM PA LA PM Â— lO LA Â— LA Â— r. lO Â— CM O CM LA 00 3 aÂ— PA o LA LA PA Â— Â— r~^ la vO A^ 3* 3 CA Â— 1 Â— Â— PA 00 lO 3 CA CM O CA S PA CM cm PA CA S O 04 CM 3 Â— CO CA lC o ACM 0 lO M3 CM 3 tM O CA N LA PA 3 LA 3 vO AX oÂ’ LA LA CO o oÂ’ wA CA LA A PA CC d CM LA CM CM O LA PA CA CM O Â— CM 3 O CO CA CO 300 f'. cm A^ S PA O CA LA Â— 00 CM PA LA CO O CM O 0 O PM Â— LA CM CA CO Â— vO X N ~ 04 CM 3* ~ CM Â— PM CM CM CM CM CM CM CM CM ~ Â— O CO LA s O LA O CO LA O vO PA 3 CM O Â— CM 3 S CA vO CA CA = CM 00 M3 3 3 = 3CA o PA Â— 00 AvO CM OO vO CM Â— OO LA VO CA LA PA 3 CA Â— CM vO vO 3 3 o" sÂ’ CA LA u\ LA ~ PA 3 3 C4 PA 3 A CA (PI 3 3 Â— 3 PA 3 3* PA 3 3 vO LA PA ACA CA o 3 oPA CA CO CA vO vO 3 PA LA Â— CM PA O LA 00 r cm PA O PA lO CA rA LA sÂ’ CM LA PA PA CM PA CA 3 PM 3* 3' r*3 PA PA 3 LA LA PA LA PA PA LA la O ACO O CM 3 LA O PA (A PA O CM rsLA 3 3 00 Â— CA CA AvO CA CA O 3 PA ><_ CA LA 3 o PA = PA CM 3 0C CA Â— CA d Â— O 3 Â‘A vO A* 3 ~ 'A CM CM Â— CA 3Ol lA PA Â— CA O CM CM CM CM Â— Â— CM Â— *Â“ CM CO a! O LA LA LA CA O O 3 O O' LA CM Â— CM CM Â— L> 3 ca LA LA 04 O 779 207 co o 1 Â— cc LA O 1 CA O 3 3 O 3 3 CO PA L.A CA 3 CM CC LA 3 3 PA LA l0 3 LA 3 CM CA O CM CA CA LA A00 CA LA Â— 00 PA 00 CA co lO co LA s 1 LA CA cm CM O Â— 00 CA PA PA CA PA \0 t 4) /! X _T CM Â— Â‘ _* o vLA PA CA O 5 o PA CA S CM O aCA CM CM OO CO P^ 3 3 vO O CM vÂ£> LA 3 O 3 CM PA vO PA O LA LA 3CM o o s o. L.A o PA CO* 3 3 CA CO Â— O LA PA vO CM Â— Â— LA O vO d LA 3 Â— CM CO O CO 00 oo r> 00 o 3 oo LA LA O r'. CM r. CM CO CO 3 pa vO P>. fM 0 PA LA CM vO CÂ£ o o 3 CA 00 d CM oÂ’ CA S o 3 LA rpa cm 3 CM LA CM P~ PA PA lA CA CA Â— CA LA CA 00 3 0 co O PA 3 d 06 CO PA OO CM d d 3 r^. CA Â— 3 3 CM ALA CA 3 LA CO LA 3o O CA A^ CA o CA LA CO pa Â— r*O ACA PA 3 3 PA 71 10 Â•3 a3 lO cm LA LA LA ro 3 PA CM LA vO LA LA PA O PA 3 lA PA 3 Â— 3 vO O Â— ~Q O o O d CM o O o Â— CO O Â— CM CM 0 Â— O Â— ~ *Â“ ~ PN Â— CM V Â— CL VO 45 O > LU o lA CO o LA CM CM 04 O CA LA 227 3 PA Â— PA Â— CA CO 3 O CA CO 3 5 ACA PA 3 0 rLA 0 Â— 0 lO O LA CO vO 3 LA 3 LA PA 3Â’ CA vO CO O lO d \0 rÂ— vjO PA CA O CM O CO lO Q O 3 O 3 CO 3 CA O rA LA o CM CM Â— Â— O Â— CM Â— CM Â— O Â— Â— ~ Â— *Â“ CM Â— o o 104 LA o 108 CA O Â— CM PA 3 LA lO 00 119 120 121 122 123 3 LA PM 126 127 CM CA O CM PA Â— CM PA PA Q O _c u o> V Districts <0 3 Â•C o o < > 40 Brevard Broward Col umb i a Dade Duval Escamb i a Gadsden Highlands Hill sborou Indian Riv Jackson Lake Lee Leon Manatee 5 X Monroe Okaloosa Orange Â•j 40 4) m E 8 (0 4) Cl Qn 4) c CL 3 'o a Putman St. Johns St. Lucie Santa Ros. Sarasota Semi nol e Volusi a
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RAW DATA FOR DEPENDENT AND INDEPENDENT VARIABLES GEORGIA, I960 125 CA A O 3 O 00 LA ON CO 3 0 CO CO sO 3 O LA PM ON UN A A X 3 rA CM 7 CM 1 7 ON A 3 CM O 3 o LA A 00Â’ sO 3* O A O 00" 3 3* 3 A CO UN A 3 'O ON 3 CM vO ON CO O ON ON Â— A O sO O CA LA A ON O sO LA sO LA A LA Â•3. O CM sO LA sO O O X sO 3 O ON CM LA 3 3 lA ON 3 O 3 A A sO O A 3 sO 3 ON CN ON O sO CO 3 A UN sO A 3 A 3 3 3 oÂ’ LA fM go" CO CM 3 SO* 3 00 CO Â£ ~ CM 3* A CM fM LA A. sO A A CO 3 3 A A A A A LA A 3 A o CA O LA O A fM CO rM 00 ON ON ON ON A A ON rÂ— O A A sO A ON LA sO GO* Pm 3* 3 LA sO 00 LA O 3 sO X GO vO sO CM fM O O A fM 3 LA OO LA 3 sO sO O A A 3 O PM A A 3 xÂ“ A A CM CM CM CM CM CM CM CM CM fM CM 3 Ai CM CM CL A N A a CO rA O 3 LA ON LA UN 00 ON LA LA LA ON 5 CM A SO 3 LA 3 & 3 S0 O 020 A 00 O sO d 3 S 00 LA LA ON O ON 00 3 A 3 A O 00 lA LA sO A LA ON A T s A sO A A LA On s LA LA A A A 3Â’ LA CM* CA 3* 3 A 3 LA sO LA fM IA sO* 3 3 LA 3 3" 3 A UN 3 3 3 A 3 3 3 ON LA A ON LA O CM A sO A Al PM Al fM A A A SO A 3 UN 00 A 00 00 X CM CA A ^ CM CM 3 CM CM ON A CM A LA A *Â“ CM la CO sO cm 00 CM 3 LA A sO A O CO ON ON 3 0O A LA A 3 3 LA O SO UN A 3 X ON O CA 3 CM 3 CM 3 S 3* CM A A SO nr O CM CM vO A 3 CO nr CO a A 3 3 CM 3 A LA UN 3 O LA CM 3 LA Al A ON 3 A CO LA 3 A sO 3 A 3 ON 3 A X Co' CM CA CA CA sO CA O A LA A P~ O cm 3 Â£ LA A CM 3 Â• A 3 ON A O 3 O 3 LA A CM 3 3 3 CM LA A A LA A 3 A A 3 A K A CM Al LA PM CA ON 3 LA O CM LA ON CM LA sO ON A A P*. sO 3 UN sO X ON GO sO* CO CO o pm O C O 00 CM ON 0 ON ON 0 CM vO A CM Ps SO ON LA sO LA Al ON CO ON LA A. A sO A 3 P*. LA O UN UN 00 X 3* pm Â£ goÂ’ GO CA TO LA 'X LA 00 CO CO s a LA CO LA CO ON 00 d S> co" 00 d 5 A CO A CO a 00 d 00 d CO CO 00 00 CO CO CO 00 sO Â•O A ON r~~ A SO A Al 3 3 3 A CO fM 3 A LA sO A sO CO 00 3 UN X ON A CA rA sO* (A i Â£ 3* A 3* IA O 3 3Â’ CM 3 CO 3 3 A fA Pi CO A C CM 3* A A A A A A ON LA Â— A CO A CO 3 A CM 00 A CO CM O sO A A LA A ON ON A 00 PM 00 LA CM LA CA 3* o A Â— oÂ’ 3 LA 3* 3 3* CM ON 7 ON LA ON 00* LA A 3 3 CA ON ^ SO O ON A sO 3 rv. A LA A ON CM sO 00 O A 00 A sO A A A ON 3 CM 3 LA LA CM A 3* 3 UN A 3 CM CM 3 3Â’ sO* sÂ£> LA 3Â’ A A 3 3Â’ sO ON m CO CO Pm LA CM O LA CM fM ON O O A sO sO O LA O rM co O 3 LA A sO A 00 CO ON A 3 LA Â— sO LA O LA UN ON CO 3 A sO 00 x^ ON LA CM LA ON O CM 3 sO lA ON A CO 3 ON sO ON a d CM O A s O A SO CO 0 ON 3 LA sO sO sO sO CO Â— 3 UN A sO OO A & O ON ON LA LA 3 A GO ON O LA o o io A sO ON ON LA LA LA O O LA CM ON O O ON Jm ON A sO A 3 A LA 3 3 O UN 3 ON O sO O UN A CM CM CM CM CA IM 3 A CM CM Â— 3 A CM O CM 3 CM CM Â£ nr CM ON O CM CO Al A d A A O A A N A 5 A CM vO LA sO GO LA O 00 ON ON M Â— CM CO o O LA O sO CM sO LA is 5 O CM 00 3 CM CO ON CO A ON SO LA O O CM rM 3 3 A UN ON 00 O Co 3 SO 00 3 LA LA 00 A A A A CO SO 00 3 O A 3 sO 3 4) ~ C 2 a SI o e 3 o CA LA 3 LA LA 3 A 3 r" = O CM LA LA LA 3 A sO sO CO OO ON ON sO* ON LA A A 3* A sO sO o CM sO 3 0 ON ON CM sO O PM A PM ON A O LA Â— fM UN pA CO 0 Â£ LA LA cO sO CM 3 CM O CA fM 35 ON CM sO 3 Â— ON LA 3 LA A A A LA ON sO O 00 LO CO A sO sO A CO 3 ON A O ON CO ON A ON 3 A 3 A A sO sO LA sO 3 00 3 3 A sO O CO UN CM 3 ON A CM LA A PM Â— CO O ON A sO CM A A <0 1 (Ml c W Â— fM 3Â’ O O O A d A O Â•O O 1 A A AAl sO sO LA OO Al A ON sO sO 1 S sO PM sO A A PM CJ Q <0 > 3 CA 00 3 A A GO LA A CO A ON 00 CA ON O Pm a A sO O A O CO sO O CO ON 3 O SO sO UN O o O o o o O Â— O O O O O Â“ O O d Â— ~ Â•n T3 O CM o CA O 3 o LA O vO O CM o CM CO ON O O CM CM O CM CM CM 3 LA M s O CM CO CM ON CM CM IN J CM CM A 3 A A LA CM 226 227 50 A A O A A A Ml A A A A Q c_> >CO LJ >X) O c 3 Q 1 &> C L. L. u O 0 C V 5 ON 4) c 0 C C a L. U Â£ 5 n 0 4) o O x O 3 a> U o> V c c tn U 3 3 X Â•O 3 u. Q It co O CO 3 co 3 <0 u Q u <0 o V Â•? 3 Â— O O O 3 0 O CB X O Q V Q O a 3 Q CC < 0 'X "i 0 X a 3 1 3 0 z OC O 5 X 3
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RAW DATA FOR DEPENDENT AND INDEPENDENT VARIABLES KENTUCKY, I960 126 cm fN X 68.6 0.5 13.9 cn r~ji i m o cn no O cn cm cn Â— cm i in pn oo p. 4 oo Â— cn cm 0.9 26. 1 5.8 co o pn pn nO o cn co CC O 00 no cn cn CO CM JCO* Â— lO cn Â— nO .4 nO* m m rn CM* oo" O m i Â— ON CO ON p* p^ cn nC o cm cm m 4 CM vO vO OO OO o o CO CM CM CM m CM 4 Â— Â— CM CM CM f Â— nO P^ CM Â— CM m rn CO CM CM CM vO oo cn CO O Pn Â— CM Â— CM 4 Â•r O ON vO p cn co o .4 cn cn 4 nO O 4 ON 00 O Pn cm 4 mm O CM CM Â— o CM co m p UN nO O Â— Â— m nO O' Pn m ON m m oo o rn nO co NO NO Pn C cn Â— CM 4 \D >< cm pn cm O' Â— CM o cm cn nO in o in oo in 4 O'. UN fM. p m Pn cn cn vO m Â— Pn ON UN X 4 m cm cm in cn in cn cn cn cn Â— pn cn cn m in cm cn O cn .4 oc oo in CM CM O rn cn cm ON ON CM CM CM Â— NO 4 ON CM CM Pn CO Pn Â— 00 O NO 4 X m ON Â— CM cm JÂ‘ C 0 Â‘ m Â— cm Â— NO* cn Â— cn m CO Â— CM pn 4 Â— co vO Pn Â— CM Â— ON vO nO cn cn m cm cn m IN ON CO cn cn Â— co p' O 4 co o oo IN CO CO cn Â— nO Â— CM 4 CM Â— cn X 00 CM oo cn !M VO cn co cm in on Â— Â— m Â— Â— CM Â— 4 rn Pn 4 rM 4 CM Â— Â— co cm in CM Â— O On m i Â— Pn nO nO 00 CC 4 4 ON CM Â— CM CM rn Pn 0 Â— 0 CM Â— CM CM Â— NO CM CM ON 00 O' Â— Â— CM p*. co cn cn o 4 CM CM Â— CM 3 CO CM CM CM 4 ON Pn nO CO* Â— CM X 4 Â— co 4 UN pn m pn pn O nO in o cn Pn ra O' Â— Â— N CO N 0 Â— 0 vO CM o o Â— Â— Â• 4 oo o o o 4 m in Â— O O vO Pn ON CM CM 4 Â— o o m cn 4 co NO Â— 1 CM Â— nO Â— O UN fN. Â— ON PN o 4 oo co 4 vO kz o > UJ 4 cn o lO nQ CM no no cn cn oo Â— Â— Â— o On cn cn 4 pcm O CM Â— in Â— o co ON cn CM Â— Â— CO 4 CM Â— r Â— co pm p^ Â— o O Â— Â— cn co o m m pn 4 cn nO 4 4 co cm cm cn nO O CM OO Â— O ON Â— pn m Â— pn rn ON PN CO m 00 4 Pn vO ON 00 O ON Â•*> a o Â— c Â— cm m o o o rn n pn m ON O Â— Â— CM CM m cn cn cm cn 4 CM CM CM m m rn m NO Pn CM CM CM cn PN PN O 0 ON CM CM m m
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RAW DATA FOR DEPENDENT AND INDEPENDENT VARIABLES ILLINOIS, I960 127 Â— CM CA CA LA Pm 00 Pm ** **a . pp PA CM vO CA CA LA Â— CA CA Pm NO Â— d IA CM Â— O lOOÂ— lO Pp O CA LA CM d X CM Â— Â— d ad CA CO CA d Â— CA O CO CA CA CM CA CA (A Pm CM LA CM CM CM CA d CM vO d pp d CM LA dfPCO Â— CA CM dPAPA d PA Â— PA d 0 Â— 00 CA P O d O co co 0 O CM Â— Â— d PJ LA CM Pp Â— CO O 0 X vO Â— Â— pa d d OOO d d d CM Pm vO d CA CA CO ca CM M N IA CM CA CA CA d PA COOCA LAPpPp Â— rp d la pa co X CT\ vO LA CA LA Pm CA CO P^ d CA Pm CA O LA VO CA vO CO 00 00 Â— vO LA O CA CM vO pp CO Â— LA 00 CO Â— VO LA cm d d d d CO LA _d CA Â— vO vO Pm vO CA 00 Â— Â— LA d* vÂ£> PA IPÂ— LA r* CA co d CA LA CM JPA d d Â— CA O PA d LA CA CM d d A 1 PP* d CA CA d d pa d d pa d pa pa O pp pa CO PA Â— PA PA Pp CM lO vO vO LA O CA CA r^. Pm d CO vO O Â— Â— Â— LA CA Pm O vO pa co rpcouA 00 pp rp d LA pp vO CO O vO CM O LA PM vO O A CO CO PA CJ O Â— ~ Â— O O Â— O Â— Â— O O O O Â— OOO Â— CMÂ— Â— Â— ~ c > c A1 ton Aurora tas Aurora Wes O 0 ** c L Ol til c Â— T3 Â— *0 & Â— O 0 41 Â— JZ qd ca 0 <0 Â— c 0 C J O OOO Dixon East St. L Edwordsvi 1 Elgin Freeport Galesburg Jacksonvi 1 Kankakee Mat toon Mol i ne Peoria Qu i ncy Rockford Rock Islai Spr i ngf i e Urbana Col 1 i nsvi Gran i te C Marion
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RAW DATA FOR DEPENDENT AND INDEPENDENT VARIABLES FLORIDA 1950 128 04 O'. ON 0 ON ON UN UN NO ON 00 0 0 CO 3 0 3 co 3 ON ON 0 ON O UN CM X 3 vO O d 3O CO 3 O UN UN 3 CO ON 04 d ON ON ON ON nO ON 04 = = d 3 3 3 04 Â— O' CM X 01 O ON CO UN ON nO Eo ON nO 0 p' UN 3 NO ON NO & CO 04 CO UN 3 NO O 3 ON 3 O 3 O 3 ON O UN !* 00 O' UN ON ON UN 0 UN ON 00 eg nO ON UN ON 3 04 ON ON UN Co 00 CN ON 0 CO 3 O' UN 04 UN CO rt CO CO ON CM ><* UN 04 3ON ON CO OO ON UN 33Â’ 0 ON 3 nO* ON ON ON 3 04 = 3 nO ON ON 04 UN ON CO ON f' 04 3 3* 04 UN 04 ** 04 04 ON ON ON 04 CO CO 04 ON 3 NO ON ON 4^N O 04 00 3 04 r' O' ON CO 3 X d Â— r>. UN UN CO O CO CO p' ON UN ON CO 3* 3 O UN UN ON p' ON UN ON ON 04 3 vO ON UN NO ON CO O' ON ON ON 3 O' 3 CM 3 UN r^. 300 ON vO ON UN NO UN vO UN 0 nO NO* r 1 00* NO P' X O on CO ON 04 3 O 0 04 0 CO O 0 04 NO O 3 UN CO ON 04 ON o~ CO CO 3 O 00 ON NO ON ON p' ON O ON X*3 UN 3 CO O NO 00 ON O 3 CO O O' UN 0 NT. ON UN O ON 3 UN ON vO CC O O 0 co O ON 3 O CM ON ON UN NO X 0 O ON 04 UN ON O ON 0 3 ON 04 ON CO nO ON 04 ON CO ON O O 04 ON 00 N X d 330 3ON 0 tÂ’ 04 3* 3 3* UN ON 04 ON 04 UN l/N UN ON vO OON O3 ON Â— NO __ 3 ON O Â— 04 00 O' NO ON ON 04 UN co X i' rr UN d z rP ON ON ON UN CO UN co* ON NO* O' ON 04 ON rN. 04 UN nO O' UN CO ON UN 04 NO O OO ON ON O Â— r' 3 3 3 UN CO O. O* 0 X O' on nO O ON ON ON ON ON ON 3* ON CO 04 UN ON ON 04 ON ON ON ON 04 ON 04 ON 00 <*N ON ON ON 04 ON CO ON 3 04 04 ON ON ON ON Â— CO ON ON ON O 01 04 04 ON ON CO ON ON UN O' ON NO 3 nO NO ON O' ON OO 3 ON O vO CN4 3 vO X O ON ON d OO Z ON ON nO* ON ON CO* nO* ON ON ON ON 3 O ON O = 04 CO ON ON CO 04 UN 04 ON O NO NO O O "O ON 3 OO 04 UN OO nO 3 UN UN CO 3 x <3 CO ON OO ON O' O' 04 CO CO 00 CO CO co CO Pi CO CO CO 3 O ON ON 3 ON 04 04 vO 3 d 3* O OO p' T o*. ON UN 3O ON 0 3CO 3 as CO NO UN ON nO O' O' ON O co ru ON vO ON 3 04 04 CO NO 0 O UN ON CO ao 0 3 O O' vO ON NO O' CM CM d 00 NO d O 3r' UN ON 3 CO r'O' ON ON NO UN 3 ON d UN ON 04 ON UN UN Â„ UN 3, O Â— ON ON 04 vO O ~ O CO 00 ON co 04 0 NO CO co UN NO 3 UN Â— ON CO ON NO 0 04 04 O' 3 O O O 3 Â— O c _T _* _* _T _* Â— Â— Â— Â— Â— Â— Â— Â— Â— 0 nO vO O UN ON NO CN4 Â— O ON vO UN Pi ON Pi NO 04 O o ON O ON UN NO UN O 00 UN Co 3 3 UN 3 CN LCN ON UN 04 O 00 X vO O UN 00 ON CM ON 04 p~ 04 NO 3 ON NO O' 04 3 NO ON O NO 3ON ON 300 00 04 (M 04 04 3 UN O aON ON ON $N ON ON ON UN CO 3 O O 3 04 O ON 3 04 O' ON 3 CO ON O ON 3 X UN ON Â— Â— vO ON O CO NO Â— i/i d O O O O O O O O Â— O O O O d O C 0) "O Q C TO OJ Q. u un O O ON CO CO co 3 ON UN O 3 rv 04 O ON 0 CO 04 0 ON UN ON Pi 3 3 r>. ON ON ON UN O 00 ON Â— cc r P' UN ON UN 3 00 co ON 3 3 ON 3 OO O' CO ON w 04 ON UN UN 3 O' '0 CO O' UN ON .257 Â•377 NO CM UN UN 3 Q > ~ 0 04 O 0 04 ~ ~ 0 O Â— Â— ~ Â— ~ 1/1 ~o O t UN NO 00 0 ON O O 04 3 UN vO O' CO On O >4 04 04 04 PN 04 3 UN 04 vO 04 p' 00 04 ON O CM ON CM ON 0 0 X r lets <0 3 0 L. ra Â•0 ra ra  ra Â•i C O O i/l O C ra 0 0 X > oe c ra c O 0) O c 0 ra O ra b O <7> O ra ra CO O ra C 1 X 0 > Lucie /I O ra os O ra V d c ra 1/1 0 ra < ra co u CD O iD 0 0 O ra 0 > O O 0 in "ra 0 "o' X "x X! C n Â—> ra 1) ra Â•J O C ra X ra X c O X ra 0 ra i_ 0 ra a 41 ra a. c CL. O a. 3 3a U) C U ra ra 1/1 u> i ra u> *0 >
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RAW DATA FOR OEPENOENT AND INDEPENDENT VARIABLES GEORGIA 1950 129 m Â£ d Â£ LA 4 28.4 3. 1 28.7 vO CO 00 Â— vO PA cn PA PA Â— vO nO AIA PA LA Â— AvO LA Â— PA CM PA vO rÂ— LA CO PA CO Â— LA 8.7 33.0 21.8 28.5 23.1 18.0 CM X vo cn 0 O pa 4 cn 4 4 N M co LA PA AJ cn lo LA 4 V LA AJ Â— Â— 0 0 Â— O lO LA AJ PA N PA N Â— O O A ^ CO vO AJ lO OJ Â— O PA PA jAJ 4 AJ M AJ Â• Â— LA AÂ— 4 PA Â— CO AJ 4 PA LA 4 LO 5 PA 0 PA LA CX> A4 0 PM O LA Â— JA PM CM 4 LA CO lO PM CM cn 0 0 PM PM Â— Â“S3 PM O PM NO 00 4 PM PA Â— cn O cO LA A* l/\ LA PA nO 4 LO 4 4 IA la 00 PA 00 4 nÂ— la la cn cn Â— vÂ£> CM cn la ncn 0 cn CO X N (O vO LA LA O p 4 lA sO LA vO CO LA CO PA CO vO LA LA 4 p^ la Â— LO CM cn pa rA cn 0 cn X r Â£ Â— ia cn pa Â— CM Â— LA AJ LA vO 00 Â— AJ rA IA GO vO PA O AJ Â— AJ go O lO AJ cn vO _T CM 4 AJ LA AJ AJ CM PA Â— Â— PA LA PA PA Â— CO PM 4 PM PM f" lS 4 LA sO PM cm Â— PA Â— 0 4 CO CO AJ PA CO N CD O 4 LA vO 4 LA PA O 4 LA NO tA Â— PA vO nO cn pa cn nO X PA CM CM O Â— CM O lG cn pm Â— Â— AJ LA 00 Â— cm vO PA LA fA LO NO 4 PA LA la o PM LA N (N vfl Â— CM O AJ PA O 0 O m 34 AJ AJ AJ O CO AJ 4 Â— cn 4 pa 0 cn CM CO 0 CO nO CO PM AJ AJ AJ Â— Â— rco cn PA vO AÂ— Â— Â— 4 O CO CM PM sO 4 PA Â— AJ rpa la LA O A 4 PA PA PM CM vO CO O O LA PA no cn Â— PM Â— LA 4 r O AJ nO Â— vO O Â— Â— AJ 4 coÂ’ ia cn 00 Â— vO O CO 4 PA LA Â— AJ Â— Â— PA ALA cn lC  x' r~Â— aj AJ 0 O pa co 4 LA AJ CO lO 0 pa cn la ia 4 000 vO d s 3 4 CO d 0 co cn pa LA O AJ U*. ia CO 000 PA LA cn Â— O Â— Â— CM PA AJ PA vO cc cn vo avO lO Â— 00 OOO r O pa 0 npa 1 CO IA OOO PM PM PA CO 4 PA LA CM cn oÂ’ Â— 0 LO Â— O A CO CO CM LO LA Â— do vO LA C\ 4 PM 00 O Â— Â— O CO CM CO CO nO ia cn ia OOO Â— Â— 0 no no cn vO cn LA odd s' O Â— O Cl O Â— AJ PA OOO AJ AJ CM 4 O AJ LA vO O O AJ AJ a co m 000 aj rJ aj 0 Â— CM PA 4 LA CM PM PM CM PM CM vC n ffl CM CM CM cn 0 Â— CM PA 4 PM PM PM CM CM PM LA vO A~ PM PM CM PM AJ CM co cn 0 PM CM PA CM PM CM PA IA PA CM CM CM >Â• Districts c Â— 0 l 0 00 Â— 0 Â— JO Â— 3 co ca co V 3 co Â— IT) Â£ 8 L tJ ID ID O O e S D * 0 x 0 * ID V <0 C X Â— (_><_> 0 ID C *s L. O > 0 30 Â•J O fl) Â— >. O Â— UID ID D Q L. Â•*O X Â— 0 O OOO 0 0 X OOO O >Â• L. L 3 O *< .c o ID W > 8 8 S O O U. >u ID O *> c c 8 ; t x < 3 cn *Â• c ** Â— <0 O c Â— c Â— c cn 4) O 0 cn ID 0 ID L. O 3 <3 10 0 'D 3 X _J X. O Â§ i J JC *j i 0 Â•*V Â— Â— z ae yPO Â— u 4) 0 U0 4 *> Â•> 5 !*
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RAW DATA FOR DEPENDENT AND INDEPENDENT VARIABLES KENTUCKY, 1950 130 X^ d 3 CTl o in UN cn n; CM d 3 d d OI Â— 27.7 12.6 1 .0 Â— oo r^ d CM 3 Â• rs i 2.7 25.7 15.7 01 01 0 Â— d CM 2.6 1.2 2.8 in 3 Â— d CM 3 m co d m 1 CM cm X vO Â— Â— vO Â— d Â— 3Oi d 3ui d Â— CM OI d cm cm v O Â— Â— oi m d d d CM CM d CM 3 o Â— d o in in d 3 n in ci in m cm O 35 CM 3 M3 co 0 01 00 CO CM d Â— OI 3 CM d d m 00 3 3 CM lO CM Â— 01 ai 0 O CM vO d 00 d Â— d 0 Â— 0 d CO O pm m 0 cm d nm r*M m 3 d d Â— CO* d Â— ai X Â— Â— d O P^ 01 0 oi co 01 vO ON 3 3 Â— in oo Oi in cm ao ooÂ’ d d oÂ’ 3Â’ d 3 OI d 01 N CO m cm m co 01 3 3 m CO d 01 ai co 3 O 00 d 3 Pm d pC oi CO X Pm pm pm 3 sÂ£> m 1 Â— CM G1 3 v d Â— d n Pm 3 O pm 3 Oi oi Â— ui CO 3 3 3 ui m pm ai d mi Â— co 0 Â— m m m 3 3 ai 3 cO m fM aO Pm m 3 in 01 3 m fM. X CO d 3 4. Â— Oi d 'O 01 00 0 co ao CM UN Â— I'm vO Â— Â— 301 d m Â— CM co 01 Â— 3 ai 3 Â— d  3 CM CO d Pm 3 Â— do Â— d CM 3 o Â— Â— in o 3 d d O in 3 pm oÂ’ Â— 0 OI CM OI O CM Â— CM CC C Â— d oÂ’ d cm d d Â— Â— m 3 3 OOO 3 CO O Â— in CO CM 3 UN OO Â— ~ N CO ui o un in o o d cm Â— CM CM CM 3 O CM CM d 0 00 d 01 ooÂ’ Â— O r^ 3 3 Pm Â— 3* d Â— d d m Â— 3 ai Â— Â— 00 d Â— O CM CM Â— fM. 00 d d CM CO oi 3 Â’ 3 X 4 CO co im d pm Â— CM CM in in cm d CM CM d Â— CM OI OI OI 3 CO O CM d C 13 d Â— vOO d d Â— cm in 0 3* O Â— d in cm 3* Â— Â’ 3* Â— d d cm ai n. O d 0 3 O CO 00 OI CM CM d rÂ— Pm 3 Â— Â— O 3 3 ui 3 Â— d d X 00 VO CO co ci CO 0 3 3 00 rco cm oi 3 CO co 3 C0 d o oi f" d O 'O a ai n d O OI 00 ai 00 01 CO d CO CO CM cm co I'm co CO 0 00 d co* ri ^ 0 ai co ao CM X~ 3 O CTl CM 3 3 00 00 co CM 3 Â— 3 Â— d ao pm 3 3 o oi 3 ^ m 3 Â— Â— Â— 3 CO CO O in Â— cm i J S m d ai O d (M IM CO 00 Odd 0 ai co co vo O Â— Â— ui CM d 3 co co rM 0 ao m 3 prM. 3 3 3 CM m 0 3 co CO X J UJ Â— CM Â— CM Â— 3 d O d CM cm Â— in o m rd O CM Â— ni r Â— co iO 0 m pm m 01 pm 01 cm m (BON d in Â— 0 CM d d CM vO O d m m d Â— 0 co CM d pm X J vO C" O CM Â— o oo o Â— o Â— Oi Â— r' o CM CM pm cm o d CM Â— 0 01 d ooÂ—Â’ Â— d pÂ— d CM r*M ci Â— 00 co Â— 0 0 CM CM 3 Ci 01 OOO ui cm d d o X 00 3 CTl Â— Id O p^ Â— in ui 3 Â— 3 in pm o cm d in in 3 co CO 3 CM 3 0 cm n* ui 3 Â’ 3 m 3 m d 3 d O Ui 3 VO 3 rn 0 O Cl rM d 3 ai cm d m LTV X (0 1*10 00 o co 01Â—0 d 3 m n N 1*1 o o co in o d mom 00 m m 01 3 o d Pm oi pm 3 3 o d 3 d oi in 3 d in 3 CM 3 CM 3 CM iO 3 m cm r* pm cm in vO d m 0 3 3 ui O O Â— Â— Â— 3 Nm cm 0 3 iO co vO fÂ“M O d d d m 0 ai vO 3 d Â— Â— m d in m m 01 3 33 m 0 ai 3 UI Pm pM 3 d d X o d oo <71 >o o 3 vO O 3 co o oi CM d CO Oi O cm d 3 o CM CM CM Â— Â— CM O 3 3 0 0 CM O CM OI CM d ai cm 0 oi d 0 Â— CM O 3 ai m ri CM 01 iO Â— 0 3 m 00 Â— CO co 3 CM Â— CM ai ai d 3 d CM Â— Â— 3 0 3 dm Â— oi CM CM Â— CM CM O PM 3 ai ao Â— x~ ui co ci d m m CO Â— M Â— in d d .3 o CM^ 3 O d CO cm Â— o CM CM OI CM 3 in pm 3 d 3 o in m cm r3 300 3 0 0 Â— m cm 3 3 00 0 vo ai 3 co d co m 3 d d mod CM O CM m fm cm Â— dm ui m d m Pm s c o X V a. v X 1 Â— 3 Ui 3 S s Â— m Â— co 3 d Oi O pm 00 O Â— cm in d 00 CM 3 co cm O OI Â— 3 CM 3 O co oo Â— co o vo in oo in in o pm m 01 3 OI CM co 0 cm d d d d 01 3 ai cm_ d 3 m Â— d 0 d vO CO Â— co 3 ai cm m 3 fM O v0 CM 3 vO d 1 Â— m I'M CM* 3* 0 3 Oi m 3 Â— co m O 3 co 3 5 Â£ d Â— Â— >1 d Q 5 o 5 oÂ’ Â— o 00 3 vo lO 3 4 o oÂ’ o in d O CM CO pm d d o morn 3 Â— o* d o i i OI CM O cm in 3 OOO CM f 3 O d Â— Â— O d CM N O vO CO 00 OOO 3 Â— 3 0 d 3 Â— O Â— Â— m ai 3 01 Â— Â— Â’ Â’ 0 ? 3 Â— Â’ d 0) x c i Â• a ft! Q 10 UN l. LU 0 d ai ai 7 0 0 CM Â— CO O d 3 3 pm p* O cm 3 CTl d r 0 3 0 Â— d O 3 ui cm Â— cm p3 m ai mo O 01 Â— co 01 CM 3 ^0 (m m 01 O m in 00 Â— ai 01 0 Â— m 0 Â— rM cm m cm 3 ai O 3 Â— c (B > S) Â— UI OI u C X ft) Â— > >x o B ft) Â— d 3 m d d d a. see c Â— n ft) X Â— ft) U L. V. 10 IB O X X \0 N (O d d d 4) c Â— 0 Â— c > Â— ft) in X uÂ— a. m3 0 ft) 0 X 3 ai 0 Â— d d d C O C 01 0 C ui Â— X c > 0 ft) 0 c X O X CM d 3 CM CM CM d d d c U ft) C ft) X IB X CB O Ol3 m <_) X ft) O IB 3X0. m 3 pm CM CM CM d d d CTl ft) 3 C 4) >. Â— U ft) X Â•X 3 ft) Â— Â£ a. a. 00 ai CM CM d d c 1) ft) 0 15 c* (B Â— Â— J 3 O 0. CO
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TABLE bO RAW DATA FOR DEPENDENT AND INDEPENDENT VARIABLES ILLINOIS, 1950 131 CM Â— CM CM 4 A O CO CM vO O 00 vo CM CA CA CO CM Â— OO vO CM CM CA O vO O LA 0 LA LA O CM CA CA CM vO vO CM 4 CA L0 vO vO CA LA lO cm CA r^ LA CM CA rM. LA CM vO CM CM 4 4 vo r. co la 4 CA CO LA r^. lO O CA LA LA CA 00 4 r> 0 co CM Â— CM CA P^ vO 4 vO CM ca vO Â— CM CO Â— CO 4 CM Â— 4 CM CA 0 la r* CM CM Â— CA i Â— 4 CA 4 00 CM Â— CM vO CA 4 0 0 CA LA vO 4 O 4 r 4 CO LO LA CA CO LA CM Â— vo vO Â— Â•Â’A CA CO vO CM X cn O O Â— 1 Â— voÂ’ r^. Â— O Â— A' O Â— CM Â— LA CA O O CA cm CA CA O N (A vo CM CO O CA CA cm r>A 4 la CA LA ACA CM O O CO Â— r>. P* cm vO CA 4 O O PA O X vO vO 'O 44OO CA LA 00 LA CO LA Ar4 LA LA LA LA VO LA vO vO LA CO N vO LA rX ca I. r (T\ fA 0 4 4 la Â— CM vO 'O 0 LA CA 4 N (A CA 00 O r"rco 00 LA lO CM LA 4 4 O CA CA O CA 4 O CO (A CM CA 0 0 CO CM (A <Â— *Â— CA CA O pa 4 0 4 CM CM CM CA Â— 4 vO 00 lO Â— CM CA vO O Â— M3 4 LA O CA LA P' 4 CM CA CA 4 LA LA 4 4 la vO vC 4r. Â— CA Â— OO Â— 4 la vo r>* la CA vO OO Â£> IT Â£ LA CA CM 4 VO CA CA CA CO LA lO LA OOO ca 00 Â— CM A* O A* Â— CA CO O 00 CM co co N LA vO CA vO LA (A N vO 4 CA LA vO cm r '' CA LA 00 la 4 CM CO 4 VO ca LA CA LA CA CM 00 CA 4 LA rv. P^ 00 4 4 O CM r'CM 4 vO CA 4 CO ca cm cm Â— O LA O c 4) t/1 T3 0) C Â— CA CA 0 CA ca 4 CA 0 N CO 4 4 0 1 Â— vO Â— CM LA O LA O LA \Q Â— CM LA r^LA Â— vO CM vO CM Â— CM O LA 3 Â£ ,0 LA Â— O Â— O CA 4 4 4 CA 0 LA r^. 00 0 Â— Â— CM 0 Â— 0 Â— J. 0 Â— Â— Â— Â— Â— Â— O Â— 0 Â— 0 Â— Â— O OOO [I c a ! T5 X C (t no Â— I a v LA UJ 4 LA \0 0 CA _4vfl N OA CA CM CA p^ cm Â— CO LO VO 4 CM O CM CA CO 4 00 CM 4 4 00 vO ca CA vO 4 ca Â— CA LA 0 p*** M O O CA 4 LA LA O vO (A 4 Â— CM N LA vO 4 CM CA 00 vO ALA 1 Â— O vO CA CM LA CA 1 Â— CM CA CA CO O f'4 O CM CM CA 11 a> x Q > CM Â— Â— CA Â— Â— Â— Â— CM CM CM CM CM CM CM Â— CM CM Â— Â— Â— Â— fA CM CA u> L. L3 O jQ C CL c/l 0)1) cn c Â— 0 Â— 1 c Â— 0 Â— O
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FIRST ORDER CORRELATION MATRIX OF 1950 VARIABLES EXPRESSED IN RAW FORM 132
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FIRST ORDER CORRELATION MATRIX OF I960 VARIABLES EXPRESSED IN RAW FORM 133 000
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FIRST ORDER CORRELATION MATRIX OF 1950 VARIABLES EXPRESSED AS Z VALUES 134
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FIRST ORDER CORRELATION MATRIX OF I960 VARIABLES EXPRESSED AS Z VALUES 135
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BIBLIOGRAPHY Adams, Perry R. 1 965 "Socioeconomic Factors Associated with Patterns of School Fiscal Policy in Kentucky," unpublished Ed. D. dissertation, Department of Educational Administration, University of Florida. Brazer, Harvey E. 1959. "City Expenditures in the United States." Â’occasional Paper 66, National Bureau of Economic Research, Inc. Brazer, Harvey E. and David, Martin. 1962. "Social and Economic Determinants of the Demand for Education." E conomics 01 Hi gher Education. (Edited by Selma J. Muskin.) U. S. Department of Health, Education, and Welfare, Office of Education, 0E50027. Washington, D. C.: Government Printing Office, 2142. Burk, Marguerite C. 1958. "Some Analyses of IncomeFood relationships." Journal of t he American Statistical Association, 53 (December 1958), 905 927Celia, Francis R. 1 96 7 Managerial Economics unpublished manuscript, University of Oklahoma, Norman, Oklahoma. Crowley, Frances J. and Cohen, Martin. 1963. Statistics New York: Collier Books. Croxton, R. and Cowden, D. 1955Applied General Statistics Englewood Cliffs: PrenticeHall, Inc., 535Ezekiel, Mordecai and Fox, Karl A. 1959. Methods of Cor re 1 aljor^nd Regressio n Analysi s, New York: John Wiley and Sons, Inc. Fabricent, Sol Oman. 1959Prerequisites for Economic Growth Conference Board Studies in Business Economics, No. 66 New York: National Industrial Conference Board. Ferber, R. and Verbeorn, P. 1962. Research Methods in Business and Economics. New York: The MacMi Ilian Company, 388. Frisch, Ragnar. 1934. Statistical Confluence Analysis by Means of Compl etc. Reg ression Systems Un i vers i tetets Okonomiske Institutt, Oslo, Norway, 83115. Gentry, Gilbert. 1959. "The relationship of Certain Cultural Factors to Â’initiative in the Local Support of Education in Florida," unpublished Ed. D. dissertation, Department of Educational Administration, University of Florida. 136
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137 Guilford, J. P. 1965. Fundamental Statistics in Psych ology and Education. New York: McGrawHill Book Company. Hanson, W. Lee. 1962. "Educational Plans and Teacher Supply." ComparaÂ’ tive Education Review 6:13641, October 1962 Hirsch, Werner Z. 1959. Analysis of the Rising Costs of P.ubj_ic Education. Study Paper No. 4. Study of Employment, Growth and Price Levels for Consideration by the Joint Economic Committee, EightySixth Congress of the United States, First Session, Washington, D. C.: Superintendent of Documents, Government Printing Office, November 1959, 143. Hopper, Harold H. 1965* "Socioeconomic Factors Associated with Patterns Â’of School Fiscal Policy in Florida," unpublished Ed. D. dissertation, Department of Educational Administration, University of Florida. James, H. Thomas, Thomas, J. Alan and Dyck, Harold. J. 1963. Wealt h, Expenditure, and DecisionMaking for Education U. S. Department of Health, Education, and Welfare, Office of Education, Cooperative Research Project No. 1241. Stanford, California: School of Education, Stanford University. James, H. Thomas. 1 96 1 School Revenue Systems in Five State s. Stanford California: School of Education, Stanford Un i vers i ty Roe L. 1963. "Educational Finance in a Metropolitan Taxing District." LongRange Planning in School Finance Based on Proceedings of the Sixth National School Finance Conference. Washington, D. C.: Special Committee on Educational Finance, National Education Association, 13844. Roe L. 1961. "The Economic of Education." Faculty lecture, University of Florida, April 1961. Roe L. and Morphet, Edgar L. I960. Financing th e Publ j_c_SchooLs. Englewood Cliffs: Pr i nt i ceHa 1 1 Inc. Kershaw, Joseph A. and McKean, Roland N. 1962. Teacher Shortages and Salary Schedules New York: McGrawHi 1 1 Book Company. Kimbrough, Ralph B. 1964. Political Power and Educati onal Decision^ Maki na Chicago: Rand McNally and Company. King, Charles R. 1965. "Socioeconomic Factors Associated with Patterns of School Fiscal Policy in Georgia," unpublished Ed. D.. dissertation, Department of Educational Administration, Univeisity of Florida. Johns Johns Johns
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138 L i ndman Erick L. 1963. "School Support and Municipal Government Costs. L ongRange Planning in School Finance Based on Proceedings of the Sixth National School Finance Conference. Washington, D. C.: Special Committee on Educational Finance, National Education Association, 13844. I I Lohnes, Paul R. 1958. New England Finances Publi c Education. Cambridge: New England School Development Council. Margolis, Julius. 1961. "Metropolitan Finance Problems: Territories, Functions, and Growth." Public Fina nces: Needs, Sources and Utilization. Report of the National Bureau of Economic Research, New YorkÂ” Princeton, N. J.: Princeton University Press, 229"70. McLoone, Eugene P. 1961. Effects of Tax Elas ticity prL^jmancial Support of Education Doctorial dissertation. Urbana: University of Illinois. McMahon, Walter W 1958. "TheÂ’ Determi nants of Public Expenditure: An Econometric Analysis of the Demand for Public Education, unpublished paper. Urbana: Department of Economics, University of Illinois. Miner, Jerry. 1963. "Social and Economic Factors in Spending for Public Education." The Economics and Politics of Public Educa tion_. No. 11. Syracuse University Press. MIT Summer Gourse on Operations Research 1953Camb ^ d 9 : Technology Press, Massachusetts Institute of Technology, 91 92 Norton, John K. 1965"The Score on School Finance." P.T.A. Magazine ., 59:46, May 1965Presthus, Robert. 1964. Men at the Top New York: Oxford University Press Quick Walter J. 1965. "Socioeconomic Factors Associated with Patterns of School Fiscal Policy in Illinois," unpublished Ed. D. dissertation, Department of Educational Administration, University of Florida. Renshaw, Edward F. I960. "A Note on the Expenditure Effect of Aid to Education," LXV I Journal of Political Econ omy., April 19b0. Rcos Charles F. 1957Dynamics o f Economic Growth: Th e American Econ_2 omy. 19571975 Econometric Institute. 250 Park Avenue, New York Schultz, Theodore W. 1961. "Education and Economic Growth. ^Â£Â£1 Forces Influencing Amer ican Education Sixtieth Yearbook National Society for the Study of Education. Chicago: University of Chicago Press. Shapiro, Sherman. 1962. "Some Socioeconomic Determinants of Expenditures for Education: Southern and Other States Compared, 6 Comparative Education Review, October 1962.
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139 Sales Management 1950, etc. "Survey of Buying Power." May 10, 1950, etc. New York. Tate, Merle W. 1955Statistics in Education New York: The Macmillan Company. U. S. Bureau of the Census. 1961. "General Population Characteristics, Florida." U. S. Census of Population: I960 Final Report PC (1) 1 1 B Wash i ngton D. C.: Government Printing Office. U. S. Bureau of the Census. I 96 I. "General Social and Economic Characteristics, Florida." U. S. Census of Population: I960 Final Report PC (1) 11C. Washington, D. C.: Government Printing Off ice. Wold, Herman. 1953. Demand Ana lys is New York: John Wiley and Sons, 4648. Wolfbein, Seymour L 1962. "The Need for Professional Personnel." Economics of Higher Education (Edited by Selma J. Mushkin.) U. S Department of Health, Education and Welfare, Office of Education, 0E50027. Washington, D. C.: Government Printing Office, 4346.
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BIOGRAPHICAL SKETCH Julian Monroe Davis was born September 15, >922, at Macon, Georgia. In June, 1940, he was graduated from Lanier High School. He then studied electrical engineering at Georgia Institute of Technology until April, 1943, at which time he entered the United States Army and served as commander of a field radio company in the Far East. In September, 1946, he returned to his studies at Georgia Institute of Technology and in June, 1947, received the depree of Bachelor of Science with major in Electrical Engineering. From then until October 1956 he served as an application engineer with Westinghouse Electric Corporation, assisting central station customers in Atlanta, Georgia, with power distribution problems, and electrical contractors in Nashville, Tennessee, with applications involving distribution systems for buildings. This period of service was interrupted, however, from December, 1952 to May, 1955, when he worked with two Certified Public Accounting firms: Cambell Napier, Atlanta, Georgia, and H. E. Fourcher, Jr., Macon, Georgia, as an accountant. During this time, he passed the required examination to obtain certification as a certified public accountant. From October, 1956 until July 1958, he was Assistant to the Director of the Engineering Experiment Station at the University of Florida, at which time he became the Director of Finance and Accounting of the University. His interest in administrative problems while in that 140
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141 job led to parttime graduate study, and eventually into a fulltime doctoral program in Educational Administration at the University of Florida. Julian Monroe Davis is married to the former Marion Frances Grove and is the father of four girls. He i s a member of Phi Delta Kappa Professional Education Fraternity, Phi Eta Sigma, Eta Kappa Nu, Tau Beta Pi, and Phi Kappa Phi.
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This dissertation was prepared under the direction of the chairman of the candidate's supervisory committee and has been approved by all members of that committee. It was submitted to the Dean of the College of Education and to the Graduate Council and was approved as partial fulfillment of the requirements for the degree of Doctor of Educat i on. April 22 1 967 Dean, College of Education Dean, Graduate School
