AN ANALYSiS OF SELECTED ASPECTS OF THE PUBLIC SCHWL FINANCE SYSTEM IN MICHIGAN Thais {or the Degree of Ph. D. MICHIGAN STATE UNWERSiTY Jeung Rhee 1961 W4 Lillie WWW/ii I 850 2670 This is to certify that the L j;- .: jhe'sii Entitled. "‘”Zh”in5t§?is‘o€ Selected ASpects - of-the.Pubiic School Finance System in Michigan r.—... - _.. ._ 9.. . ._ ‘ _ ».. . , _,. .. .. v . no. «9 '- presented by Jeung Rhee has been accepted towards fulfillment of the requirements for _Eh.D.._ degree in Mn Dr. Donald J. Leu '} \ ( «_ ').I’ 1,111,: - ._,“‘ (K— F‘\ e #4" e L. Major profeésor Date August 3, I961 0-169 LIBRARY Michigan State University PLACE IN RETURN BOX to remove this checkout from your record. TO AVOID FINES return on or before date due. DATE DUE DATE DUE DATE DUE ll Eli“: 5 PM ' 2'" v in J MSU Is An Affirmative Action/Equal Opportunity Institution cMMuns-od “ii _._: a.” ABSTRACT AN ANALYSIS OF SELECTED ASPECTS OF THE PUBLIC SCHOOL FINANCE SYSTEM IN MICHIGAN by Jeung Rhee I. The Purpose This study proposed to examine quantitatively selected aspects of the state public school finance system in Michigan. More specifically, the main purposes of the study were: 1. To analyze quantitatively the differences in each of the selected financial and educational factors among selected groups (types) of K-12 school districts classified in terms of financial need, ability, and effort. 2. To identify the general relationships between each of the selected financial and educational factors and each of the three variables of financial need, ability, and effort. II. Methodologyp 1. The basic data of this study were derived from the Annual Reports for 1959-60 and the answers to the Special Questionnaires sent to the State Department of Public In- struction from the 535 K—12 school districts in Michigan. Jeung Rhee 2. (a) Twenty-two groups (types) of school districts comprising 520 K-lZ school districts were selected. (b) Five financial factors and five educational factors were chosen for the purpose of statistical analysis. (c) The statistical method deemed appropriate for examining the differences of the selected factors among the 22 different types of school districts was the analysis of‘ variance. (d) The Spearman rank correlation coefficient tech- nique was employed in order to identify the general re- lationships between the differences of each of the selected factors and each of the three variables of financial need, ability, and effort. III. Results 1. All null hypotheses of no significant differences among group means of each of the selected factors were re- jected by the F tests at the .05 level of significance; that is, the differences of each of the ten selected factors did, in fact, differ significantly. 2. The tests of the significance of differences among group means of each of the selected factors by use of the "t" at the .01 level of significance revealed that: (a) The least number of significant differences re: existed the tote total nu existed . the totaj receipts. differenc tnan that the .10 a ( in each 0 was eithe U relatiOns? and eduCa‘ (c a lh‘JQISe .‘ Iv ' Conc‘ \: The n ClusiOns . Jeung Rhee existed in educational factor 2, that is, the proportion of the total number of teachers holding certificates to the total number of the teaching staff. (b) The greatest number of significant differences existed in financial factor 5, that is, the proportion of the total amount of general fund property taxes to the total receipts. (c) Generally viewed, the total number of significant differences of the selected educational factors was much less than that of the selected financial factors. 3. The Spearman rank correlation coefficient tests at the .10 and .02 levels of significance indicated that: (a) The most contributive variable to the differences ixteach of the selected financial and educational factors was either financial need or financial ability. (b) Financial effort did not have any significant relationships with the differences of the selected financial and educational factors. (c) The directions of the relationships, positive or inverse, differed according to the factors observed. IV. Conclusions The findings of the present study led to the following con- clusions: Jeung Rhee 1. Observed in terms of the ideals of equal educational opportunity, the present Michigan State Aid Formula is far from being sufficient or adequate. 2. More effective measures of school district reorgani- zation and more positive ways of adjusting the disparity in financial ability are necessary to attain the ideals of equal educational opportunity. 3. Further investigations need to be conducted to find out if the existing policies and practices of "participation millage" requiring local effort and initiative, under the present Michigan State Aid Formula, really do provide an effective basis for the sound development of public school education in Michigan. AN ANALYSIS OF SELECTED ASPECTS OF THE PUBLIC SCHOOL FINANCE SYSTEM IN MICHIGAN By Jeung Rhee A THESIS Submitted to Michigan State University in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY College of Education 1961 ACKNOWLEDGEMENTS The writer wishes to express his sincere appreciation and gratitude to those who have contributed to the development and completion of this study, which was initiated as a university project. Special acknowledgement is due to Dr. Donald J. Leu, the chairman of the doctoral committee, who has given the writer constant encouragement, direction, and patient counsel at every step throughout the study. Grateful appreciation is extended: To other members of the doctoral committee, Dr. Fred J. Vescolani, Dr. John X. Jamrich, Dr. James W. Costar, and Dr. Wesley R. Fishel, who gave many valuable suggestions and advice. To Dr. Karl T. Hereford, Dr. Stanley E. Hecker, and Dr. James H. Stapleton for their suggestions and guidance con- cerning the theoretical framework, data treatment, IBM com- PUtation process, and statistical analysis of the study. To Dr. Elwood P. Lawrence, Dr. Donald W. Urquidi, other faculty members, his fellow graduate students, and Mrs. Jean NiCholas, who gave generously of their time and effort. To the State Superintendent of Public Instruction and his Staff. the members of the Michigan State Legislature, and ii I Hinged] the Michigan Education Association for their understanding and helpful assistance in the collection of the data and the development of the study. To the Korean Foundation and to the Board of Trustees of Michigan State University for their financial support, which made the completion of the study possible, and for granting an education fellowship and scholarships during the writer's period of study at the University. Finally, the writer is deeply indebted to his wife, Byong Seon, and his children, Jea In, Yeong, and Hong, and to Dr. and Mrs. Raymond A. Olson and Mr. and Mrs. Harry L. Kitselman, for their inspiration and understanding during the writer's stay in the United States. iii Mi Su III, CLAs In: C12 C15 TABLE OF CONTENTS CHAPTER PAGE I. INTRODUCTION. . . . . . . . . . . . . . . . . 1 Statement of the Problem. . . . . . . . . . 1 Definition of Terms Used. . . . . . . . . . 4 Procedures. . . . . . . . . . . . . . . . . 6 Delimitations of the Study. . . . . . . . . 9 Organization of the Study . . . . . . . . . 10 Summary . . . . . . . . . . . . . . . . . . 10 II. REVIEW OF THE LITERATURE. . . . . . . . . . . 12 Local Control of Education and Equal Educational Opportunity . . . . . . . . . 13 Public School Finance and the Quantity and Quality of Education. . . . . . . . . 31 Michigan State Aid Formula. . . . . . . . . 42 Summary . . . . . . . . . . . . . . . . . . 57 III. CLASSIFICATION OF THE SCHOOL DISTRICTS. . . . 62 Introduction. . . . . . . . . . . . . . . . 62 Classification by Need. . . . . . . . . . . 64 Classification by Ability . . . . . . . . . 69 Classification by Effort. . . . . . . . . . 73 smary O O O O O O O O O O O O O O O O O O 7 8 iv :1; .- .3? Ar CHAPTER PAGE IV. DESIGN OF THE STUDY . . . . . . . . . . . . . 79 Selection of the School Districts . . . . . 79 Selection of Financial and Educational Factors . . . . . . . . . . . . . . . . . 80 Analysis . . . . . . . . . . . . . . . . . 83 Summary . . . . . . . . . . . . . . . . . . 87 V. ANALYSIS OF SELECTED FINANCIAL FACTORS . . . 88 Analysis of Financial Factor 1 . . . . . . 89 Analysis of Financial Factor 2 . . . . . . 95 Analysis of Financial Factor 3 . . . . . . 100 Analysis of Financial Factor 4 . . . . . . 104 Analysis of Financial Factor 5 . . . . . . 109 Summary . . . . . . . . . . . . . . . . . . 113 VI. ANALYSIS OF SELECTED EDUCATIONAL FACTORS . . 119 Analysis of Educational Factor 1 . . . . . 119 Analysis of Educational Factor 2 . . . . . 124 Analysis of Educational Factor 3 . . . . . 129 Analysis of Educational Factor 4 . . . . . 134 Analysis of Educational Factor 5 . . . . . 139 Summary . . . . . . . . . . . . . . . . . . 144 CHAPTER PAGE VII. SUMMARY, CONCLUSIONS, AND SUGGESTIONS . . . . 150 Summary . . . . . . . . . . . . . . . . . . 150 Conclusions and Suggestions . . . . . . . 154 BIBLIOGRAPHY . . . . . . . . . . . . . . . . . . . . 156 APPENDICES . . . . . . . . . . . . . . . . . . . . . 161 vi F I a. Eu III. V, VI 1‘7 T s O ‘ ) I1?I‘ a : *0 Fe: Per ”1 Ma; TABLE II. III. IV. VI. VII. VIII. LIST OF TABLES Per Cent of Support from State and Federal Funds, 1890 . . . . . . . . . . . . . . . . Per Cent of Support from State and Federal Funds, 1956 . . . . . . . . . . . . . . . . Major Kinds of State Aid Funds for Elementary and Secondary Schools in Michigan in 1947- 48 and in 1957-58 . . . . . . . . . . . . Need Distribution of the 535 K—12 School Districts in Michigan . . . . . . . . . . . Ability Distribution of the 535 K-12 School Districts in Michigan . . . . . . . . . . . Effort Distribution of the 535 K-12 School Districts in Michigan . . . . . . . . . . . Classification of the 535 K—12 School Districts in Michigan in Terms of Need, Ability, and Effort . . . . . . . . . . . . The 22 Selected Groups of K-12 School Districts Classified in Terms of Need, Ability, and Effort . . . . . . . . . . . . vii PAGE 29 30 53 66 7O 74 77 81 TABLE IX. XI. XII. XIII. XIV. XVII. The 22 Selected Groups of School Districts Arrayed in Order of the Group Averages of Need, Ability, and Effort. . . . . Summary: Analysis of Variance of Financial Factor 1. . . . . . . . . . . . . . . Comparison of Annual Current Expenditures Per Pupil (in tables of "t"). . . . . Summary: Analysis of Variance of Financial Factor 2. . . . . . . . . . . . . . . Comparison of the Average Salaries of Teachers (in tables of "t") . . . . . Summary: Analysis of Variance of Financial Factor 3 O O O O O O O O O O O O O O 0 Comparison of the Proportion of the Capital Outlay Budget in Relation to the Total Expenditures (in tables of "t") . . . Summary: Analysis of Variance of Financial Factor 4. . . . . . . . . . . . . . . Comparison of the Proportion of the Total State Revenue Receipts in Relation to the Total Receipts (in tables of "t") viii PAGE 90 91 92 96 97 101 102 105 107 TABLE XVIII. XIX. XXII. XXIII. XXIV. PAGE Summary: Analysis of Variance of Financial Factor 5. . . . . . . . . . . . . . . . . . 110 Comparison of the Proportion of the Total General Fund Property Taxes in Relation to the Total Receipts (in tables of "t"). . 111 The Groups Having the Largest Difference in Each of the Five Financial Factors. . . . . 116 Tests of the Significance of Rank Corre- lation Coefficient on Each of the Selected Financial Factors and Each of the Three Variables of Need, Ability, and Effort. . . . . . . . . . . . . . . . . 117 Summary: Analysis of Variance of Educational Factor 1. . . . . . . . . . . . . . . . . . 121 Comparison of the Proportion of the Teachers Holding M. A. Degrees or Above to the Total Teaching Staff (in tables "t"). . . . . . . 122 Summary: Analysis of Variance of Educational Factor 2. . . . . . . . . . . . . . . . . . 125 Comparison of the Proportion of Teachers Holding Certificates to the Total Number of Teaching Staff (in tables of "t"). . . . 127 ix {HES TABLE PAGE XXVI. Summary: Analysis of Variance of Educational Factor 3. . . . . . . . . . . . . . . . . . 130 XXVII. Comparison of the Proportion of the Secondary Teachers Teaching in Subjects Outside of Certified Major and Minors to the Total Number of Secondary Teaching Staff (in tables of "t"). . . . . . . . . . . . . 132 XXVIII; Summary: Analysis of Variance of Educational Factor 4. . . . . . . . . . . . . . . . . . 135 XXIX; Comparison of the Proportion of Teachers Receiving Over $7,000 Annual Salary to the Total Number of Teaching Staff (in tables of "t"). . . . . . . . . . . . . 136 XXX. Summary: Analysis of Variance of Educational Factor 5. . . . . . . . . . . . . . . . . . 140 XXXI. Comparison of the Pupil-Teacher Ratio (in tables of "t"). . . . . . . . . . . . . 141 XXXII- The Groups Having the Largest Difference in Each of the Five Educational Factors . . 146 XXXIII; Tests of the Significance of Rank Correlation ' Coefficient on Each of the Selected Educa— tional Factors and Each of the Three Varia- bles of Need, Ability, and Effort . . . . . 148 LIST OF FIGURES FIGURE PAGE 1. A Theoretical Frame of Reference for Classifying the School Districts in Terms of Need, Ability, and Effort . . . . 65 2. Need (Membership) Distribution (535 K-12 School Districts in Michigan . . . . . . . 67 3. Ability (SEV per Pupil) Distribution (535 K-12 School Districts in Michigan . . . . 71 4. Effort (Tax Rate) Distribution (535 K-12 School Districts in Michigan) . . . . . . 75 xi I. APPENDIX A Table A-I A-II A-III A-IV IT—VI LIST OF APPENDICES Page RELATED DATA . . . . . . . . . . . . 161 Group Averages of the Membership of the 22 Types of School Districts. . . . . . . . . . . . . 162 Group Averages of the State Receipts of the 22 Types of School Districts. . . . . . . . 163 Group Averages of the Total General Fund Property Tax Receipts of the 22 Types of School Districts . . . 164 Group Averages of the Total Receipts of the 22 Types of School Districts. . . . . . . . 165 Group Averages of the Total Current (Operating) Expenditures of the 22 Types of School Districts . . . 166 Group Averages of Total Capital Outlay Expenditures of the 22 Types of School Districts. . . . . 167 xii Table Page A—VII Group Averages of the Total Expen- ditures of the 22 Types of School Districts . . . . . . . . . 168 A-VIII Group Averages of Total Amount of Salaries of Teachers of the 22 Types of School Districts. . . . . 169 A-IX Group Averages of the Number of Teachers of the 22 Types of School Districts . . . . . . . . . 170 A-X Group Averages of the Number of Teachers Holding M. A. or Above Degrees of the 22 Types of School Districts. . . . . . . . 171 A-XI Group Averages of the Number of Teachers Holding Certification of the 22 Types of School Districts. . . . . . . . . . . . . 172 4A-XII Group Averages of the Total Number of Secondary Teachers Teaching in Subjects Outside of Certified Areas of the 22 Types of School Districts. . . . . . . . . . . . . 173 xiii Table Page A-XIII Group Averages of the Number of Teachers Receiving Over $7,000 Annual Salary in the 22 Groups . . . . . 174 II. APPENDIX B THE SPECIAL QUESTIONNAIRES . . . . . . 175 Part I General Information . . . . . . . . . 176 Part II Elementary School Information . . . . 182 Part III Secondary School Information . . . . . 184 xiv CHAPTE R I I NT RODUCTI ON I. Statement 9f_the Problem In the United States, there are two concepts that have been considered to be the bases that formulate the educa- tional policies and school finance systems among states: namely, the concept of "local control of education" and the concept of "equal educational opportunity." With the two concepts, there have been evolved the diversity of educa-' tional systems and policies and the variety of financial practices among states. Thus, the state aid formulas vary widely among states.‘ ' In Michigan, the state aid funds are distributed in ac— cordance with the assumptions held concerning the relation— ships among the variables of financial need, ability, and effort among school districts.1 In fact, the policies and practices of (1) the "gross allowance" on the basis of membership, (2) the "participation millage" on the basis of local effort, and (3) the "deductible millage" on the basis of ability, are the main elements that, along with other 1The State of Michigan, Sections 8, 10, 11, 15, and 35 of the State Aid Act of 1959-60. (Act Number 312 of the Public Acts of 1957, as amended.) measures, characterize the present system of financing Michigan public schools. These policies and practices can be called the reflections of the concepts of equal edu— cational opportunity and local control of education. The results of the Michigan public school finance system are, therefore, supposedly expected to be in accordance with the concept of local control of education and the ideals of equal educational opportunity. However, the actual results have been the object of much concern to the people of Michigan. It has often been pointed out that the Michigan public school financial system is still far from being adequate, and a number of new pro- posals have been suggested each year by different groups with different interests and purposes. In this connection, one of the continual endeavors of paramount importance should be the critical examination and true understanding of the financial and educational differences existing among school districts. With these considerations in mind, the present study purports to examine quantitatively selected aspects of the State public school financial system in Michigan. More specifically, the study seeks: 1. To identify and to classify all twelfth grade school districts in Michigan, in terms of financial need, ability, and effort.2 2. To analyze quantitatively the differences in each of the selected financial and educational factors among selected types of K—12 school districts classified in terms of financial need, ability, and effort. 3. To identify the general relationships, in terms of Low, Medium, and High concepts,3 between each of the three variables of financial need, ability, and effort and the differences in each of the selected financial and educational factors among different types of school districts. 4. Insofar as the evidence warrants, to suggest a set of frames of reference for further investi- gations that would be useful in improving the present financial planning in Michigan, in the light of the results of the analyses. See: The Definitions of Terms used. As to the criteria of Low, Medium, and High, see: Chap- ter III, Classification of the School Districts. II. Definition g£_Terms Used Public schools. Public schools, as used in this study, refer to the Michigan public elementary and secondary schools in school districts which maintain grades of kinder- garten through twelfth. Those schools which are fully sub- sidized from federal or state funds, and whose programs are under federal or state supervision, are excluded. School district. A school district is a quasi-municipal corporation created by the Michigan state legislature for the purpose of operating and maintaining public schools having grades of kindergarten through twelfth, and whose boundaries are not necessarily related to those of other local units of government. Type (2; category) 2f_school district. Type or cate- gory of school district as used in this study is defined as 4References: (a) Michigan State Aid Act 1959-60 pp, 91;, (b) Don Orth Tatroe, unpublished Doctoral dissertation, "A Critical Examination of the State Aid Formula for Support of Michigan Public Schools," Michigan State University, 1958, pp. 6-7. (c) Merton James Turck, Jr., unpublished Doctoral dissertation, "A Study of the Relationships Among the Factors of Financial Need, Effort, and Ability in 581 High School Districts in Michigan," Michigan State University, 1960, pp. 6-8. (d) Stanley E. Hecker, Your Michigan School Costs, Michigan State University, 1960 (34pp.). the representative characteristics common to a group of school districts classified in terms of the three criteria-- Low, Medium, and High--in each of the three variables of financial need, ability, and effort. Public school finance system. The revenue and dis- bursement system utilized by the state to support its ele- mentary and secondary schools. State aid Q£_SChOOl support. The distribution of the money collected by the state on a state-wide basis to local school districts in accordance with a statutory formula. Financial need. The total resident membership, ex- pressed in number of pupils of a school district. Financial ability. The State Equalized Valuation (SEV) expressed in dollars of a school district divided by the total resident membership including resident pupils attend- ing any public schools. Financial effort. The total tax rate (allocated and voted), which includes taxes for Operation, Building and Sites, and Debt Retirement, expressed in mills levied in a public school district for the purpose of financing the public schools. Membegship. Membership as used in this study is de- fined as the number of pupils--registration plus receipts by the Superintendent of Public Instruction in the Michigan child accounting system--enrolled in the public school from kindergarten to twelfth grade. Pupil and school children. Pupil is defined as a child in membership in a public school, and school children are defined as children in membership in any school. spate equalized valuation. The final appraisal of the worth of the real and personal property in the school dis- trict for tax purposes by the Michigan Tax Commission. Mill. The value of a tenth of a cent or a thousandth of a dollar. The term is used as a unit of local property taxation. III. Procedures The following are the main points and the steps of the procedures of this study. Data. The basic data of this study are derived from the Annual Reports for 1959-60 and the answers to the Special 7 Questionnaires,5 sent to the State Department of Public In- struction from the 535 twelfth grade school districts in Michigan. These data furnished for this study most of the necessary information for its statistical analyses. 3 Review pf_the literature. A review of the literature on educational administration, school finance, and other re- lated topics was made. The presentation of the review of the literature in this study is rather brief, but it is in- tended to present basic points of consideration in inter- preting the original data and the results of the statistical analyses made. District g1assif1gation criteria. On the basis of the examination of the data of the 535 twelfth grade school districts, three comparative classification criteria——Low, Medium, and High—-in each of the three variables of financial need, ability, and effort are established. Classifgcation pf the school districts. The 535 school districts are classified, applying the 27 classification categories created by the combinations of the three criteria in each of the variables of financial need, ability, and effort. 5See Appendix B. 8 Selection pf the schoo1_districts. Since it is not the major purpose of this study to show the characteristics of one or two school districts particularly, the five types (categories) of school districts which have less than five school districts are excluded from further statistical analysis in this study, thus eliminating four school dis— tricts. In addition, 11 school districts, including the Detroit school system, are eliminated because of the incomplete data available at the time of the study and because of the unique size of the Detroit school districts. J Therefore, the main analysis of this study in effect deals with the 22 types of school districts, comprising the remaining 520 school districts. Selection p; financial and educational factors. After several consultations with finance experts and profesSOrs of educational administration and school finance at Michigan State University, five financial factors and five educational factors were selected from the data available. Analysis. To determine statistically the significance of the differences of financial and educational factors between and among different types of school districts in ..___.__._..-— Midhice In orde Low, Her (Ii-"113 }_l Michigan, the techniques of analysis of variance are employed. In order to observe the general relationships, in terms of Low, Medium, and High concepts, between each of the three variables and the differences in each of the selected factors, Spearman's rank correlation method is employed. Conclusion. On the basis of the results of the fore- going analyses, a summary and conclusions, and suggestions for further investigations are made. IV. Delimitations pf the Study This study is delimited in the following ways: 1. The major data of this study were derived from the Annual Reports for 1959-60 and the answers to the Special Questionnaires furnished by the 535 twelfth grade school districts in Michigan. 2. The main analyses of the study deal with the 22 different types of school districts, comprising the 520 school districts. Hence, any individual school district is not the object of this study. 3. This study treats the selected financial and educational factors. Thus, this study does not intend to be comprehensive in itself. 10 4. The analyses are basically quantitative rather than qualitative. V. Organization pf the Study This study is organized into seven chapters. Follow- ing this introductory chapter, in Chapter II, the review of the literature is presented. The chapter presents some basic discussions on the topics of "local control of edu- cation" and "equal educational opportunity," "school finance and the quantity and quality of education," and the "Michigan State Aid Formula." They are brief, but it is intended to indicate some of the major issues in American education and school finance today. The classification of the school districts is presented in Chapter III. Chapter IV presents the design of the study. The differences of financial factors among different types of school districts in Michigan are analyzed in Chapter V, and the differences of educational factors in Chapter VI. Chapters V and VI consist of the major analyses of this study. Chapter VII attempts to pre- Sent an overall summary and conclusions of the study. VI. Summary The presentation, as a whole, reflects an attempt on like part of the writer to submit the facts that might be ._._» conduci' finance planting] establis first re Standing Si‘idieS to be Du: to Share ll ' conducive to the future improvement of the public school finance system in Michigan. It is believed that any proper planning of financing public school education, to achieve established goals and the ideals of educational opportunity, first requires objective examinations and unbiased under- standings of the related facts. There have been a number of studies in this direction. Nevertheless, the search is yet to be pursued. In this connection, the present study attempts to share the contribution in meeting this demand. ‘ t “F q 5 '° 5:- '4‘». - ‘ I Afl"n§,. ‘ f‘ :““‘"cb.'.- 12 CHAPTER II REVIEW OF THE LITERATURE An effort was made to review the literature concerning the issues of: (1) local control of education and equal educational opportunity, (2) school finance and the characé teristics of education in terms of its quantity and quality, and (3) Michigan State Aid Formula. Clearly it was not pro- posed in this effort to cover extensively all the issues of educational administration and school finance. Rather, it was specifically intended to consider the said issues on the grounds that: l. The two concepts of local control of education and equal educational opportunity are the funda- mentals which set the tone and the course of all aspects of education and its system in the United States. 2. The inquiry into the level of school expenditures in relation to the quantity and quality of edu- cation would give a sound general basis for considering the quantitative differences of fi- nancial and educational factors among school districts having different needs, abilities, and efforts. 13 3. The questions posed in this study are directly related to the results of the Michigan State Aid Formula. Thus, the purpose of this review is to clarify some of the fundamental issues and principles in American educational administration and school finance systems, and to establish a background for analyzing the factual differences of finan- cial and educational factors among school districts in Michigan. I. Loca1.Control p§_Education and Equal Educat1ona1 Opportunity General yigy, Since the Federal Constitution of the United States includes no reference to education, the idea that education lies within the province of state function de- rives from the Tenth Amendment of the Constitution. This amendment was an attempt to restrict the power of the nation- al government.1 Thus, as it is usually stated, education is a state function, not a federal function. But a state's 1"The powers not delegated to the United States by the Constitution, nor prohibited by it to the States, are re— served to the States respectively, or to the people." ifhis amendment is important in that it distinguishes be— tween.the delegated powers of the national government and ‘the reserved powers of the state government. See: Alfred De Grazia, The American Way pf Government (New York: John ‘Wiley'and.Sons, Inc., 1957), p. 76. 14 constitution commonly charges its legislature with the duty of setting up an adequate system of public education. The conclusion from this is that public education is a function . . . . 2 . . of state legislative respon51b111ty. Public school f1- nance systems are operated within this frame of reference. While, in legal terms, each state (state legislature) has always possessed the supreme authority concerning edu- cation, none has developed a wholly state-administered school system.3 For instance: It is uniformly held that there is no inherent power in school districts to levy taxes. That is to say, school taxes are state and not local in nature. This result follows logically from the concept that education is a state and not a local function. How- ever, as a matter of general practice in the United States, the power to levy taxes is delegated to the districts u2der legislative and constitutional re- strictions. 2Robert R. Hamilton and Paul R. Mort, The Law and Pub- lic Education (second edition; Brooklyn: The Foundation Press, Inc., 1959), p. 16. 3For purposes of determining their general powers and obligations, school districts are unquestionably quasi- corporations, but for purposes of constitutional or stat- utory interpretation, they are not infrequently held to be municipal corporations which enables the localities to regulate and administer their own local concerns. As for this point, see: Newton Edwards, The Courts and the Pub- lic Schools, The Legal Basis p§_School Organization and Administration, Revised edition (Chicago: The University of Chicago Press, 1955), pp. 54-5. 4 . - Hamilton and Mort, pp, Clt., pp. 166-7. 15 Thus, decentralization in American education and school finance systems exists between the federal and the state governments, and between the state and school districts. It must be noted here, however, that the centralist's argu- ments are not defunct; and, one of the ever-present issues in American educational administration and school finance has been the matter of centralization versus decentraliza- tion. This issue of centralization versus decentralization in educational administration is closely related to the is- sue of attaining the ideals of equal educational opportunity. The importance of these two issues lies in the fact that the two ideals, "local control of education" and "equal educa- tional opportunity," are often conflicting. As Burke point- ed out, a state, in attempting to promote both equality of educational opportunity and freedom in education through decentralization must recognize that these two ideals are conflicting.5 As this writer observes, one of the real struggles the American people have been experiencing in sup- porting public school education has been for the values placed 'upon the concept of decentralization in education and school finance system. It has been said by many that provincialism ¥ 5Arvid J. Burke, Financing Public Schools 1p_the United States, Revised edition (New YOrk: Harper and Brothers, Publishers, 1957), p. 565. cation to rev tive s; 1::- unique 1330?. l: fliCti: 16 or localism inheritedvdththe idea of decentralization is responsible for many of the existing inequalities in edu— cation. To make the problem clearer, it seems appropriate ‘to review some of the related issues in general administra- tive system and school finance. A_theoretica1 frame pf_reference. The United States is unique among the nations of the world in the emphasis placed upon local control of education. While education is a state function, in every state the financing of the schools is a joint enterprise of the central state government and the local school districts. Local initiative and participation are encouraged. In other countries much more authority is wielded by central ministries and bureaus. National in— terests and centralization of authority in other countries range downward from Russian totalitarian practices. Yet even in democratic England the national ministry of educa- tion possesses immense power over the borough and county school systems, and considerable authority over private schools. The American concept of school administration does not seem to carry much weight in other countries. In this connection, a fresh way of looking at the matter seems to be a theoretical approach to the administrative system in the context of technological development and social change. 17 It has been advocated by many political scientists that as a society becomes more and more industrialized the ad- ministrative structure tends to be more centralized, with a tendency toward dispersal in its structure as well as in its function within each level of administration. This general tendency was suggested by Riggs' model, for instance.6 Theoretically, defining any administrative system as those activities of any organization having to do with its allo- cation of goods and services,7 it can reasonably be concluded that in an agrarian society administrative systems tend to be more decentralized and concentrated, and that in an in- dustrialized society, the administration tends to be more centralized and dispersed. This theoretical model has been evidently true in most of the administrative systems in the 6 . . . Fred W. Riggs, "Agraria and Industr1a--Toward a Typo- logy of Comparative Administration," in William J. Siffin (ed.), Toward the Comparative Study pf_Pub1ic Administration (Bloomington, Indiana: Indiana University Press, 1959), pp.86-7. By dispersal, here, the writer refers to, for in- stance, the functional fragmentation or specialization of government of each level, as seen in innumerable special- purpose, goal-oriented agencies ofboth the "line" and "aux— iliary" types. This functional specialization of admini- stration would naturally have its structural effects. However, the problems here have to do not with geographic coordination. Therefore, the term dispersal must not be confused with the concept of decentralization. By the same token, the term concentration must not be mixed with the idea of centralization. See: e.g., ibid., p. 45. 7Ibid., p. 26. 18 United States. In an educational system, however, even after the development of a highly industrialized civilization, the change has been very slow. Educational administration in the United States went through a long period of struggle, and never took a centralized pattern, even though it has been securing from the federal government and the state the aid or services requisite for its survival in a complex indus- trial economy. In the main, modern American educational administration can still be characterized as being decentral- ized and dispersed, following the Riggs‘ model. It seems almost clear that this situation in American education has been mainly because of the ideological belief the American people have been holding, the belief which has been held throughout the tremendous technological development and social change. The American belief placed in. the decen- tralized pattern of the educational system has well stood the test of time and experience. In this connection, Ogburn observes: The various parts of modern culture are not chang- ing at the same rate, some parts are changing much more rapidly than others; and since there is a correlation and interdependence of parts, a rapid change in one part of our culture requires readjustments through other changes in the various correlated parts of cul- ture. . . . The extent of this lag will vary according to the nature of the cultural material, but may exist 19 for a considerable number of years. Toynbee also observes that: The pace of the material elements in culture such as technology is more rapid than that of non-material (spiritual) elements. If Riggs' theoretical model of an administrative system in the context of technological development and social change is an acceptable one, and if the observations by Ogburn and Toynbee are right, it might well be said, theo- retically at least, that the American administrative system of education is still in a transitional stage, subject to change toward centralization. It seems that although most of the cultural factors and trends have been evident for a considerable period, there has been limited educational response to many of them. This point of view is supported by the findings of research as to the adaptability of education: School change is distressingly slow. Although the rate differs under varying conditions, apparently it takes some 50 years from the identification of a need to the development of adequate means for meeting it by some societies. A second 50 year span is required for 8 W. F. Ogburn, Soci§1_Change (New York: B. W. Huebsch, Inc., 1922), pp. 200-1. 9A. J. Toynbee, A_Study p§_History (Oxford University Press, 1954), III, pp. 106-345. Toynbee's main theme is that technical or material elements are more rapidly adapt- ed than ideological (spiritual) factors. 20 general diffusion of the new practice. Some societies apparently never make the specific adaptation.lo As far as we can reasonably predict at present, it is unlikely that centralism will be prevalent in American edu- cation in the near future. If decentralization should con- tinue indefinitely, however, some of the potent theories that have been propounded by many in the field of social sciences will have to be re-examined at least in part. If any change toward centralization should come, the pace would undoubtedly be slow. Imp1igations for educational equality. According to available data, a trend toward centralization seems to exist both in federal-states relationships and in state-local relationships. For example, in the administration of wel- fare, social security, and highway construction, there seems to be a strong shift away from control and support by many small administrative units to control and support by state 10 . . . . Philo T. Fernswarth, Adaptation Processes 1p_Public Schgg1 Systems (New York: Columbia University, 1940); and Walter Cocking, Regional Introduction p§_Educational Practices 1p_Urban Schoo1_Systems pf ppp_gp;ted States (New York: Columbia University, 1951). Although these studies were not necessarily concerned with the matter of administrative systems as such, the results of the studies may well be re— lated to the very system of educational administration and school finance. (Prflii’ -' claim * H growth 21 agencies. The advocate of strong state control of education holds that his View is in harmony with this trend. While various interpretations are offered as to the causes of these trends, expansion and centralization of government appear to be associated with industrialism and technology. Some people claim that the trends are merely a rational response to the growth of interdependence, the increase in the pressures which fall upon the individual in an industrial as opposed to an agrarian economy. This vieWpoint claims that fundamental changes in the economy, such as the relatively rapid increase of income and other forms of taxable capacity besides tangible property, and the differences in fiscal capacity of states and localities under modern conditions, have made it neces- sary that state and federal tax agencies play a larger role in raising revenue for essential public services. From the standpoint of education, the conviction that adequate educational opportunities should be available to all children, the mobility of the population, and the great inequalities in the financial ability to support schools are potent factors on the side of the centralist. The slow progress character- istic of extreme localism, as reported by Mort and Cornell,11 11 Paul H. Mort and F. G. Cornell, American Schools La Transition (New York: Bureau of Publications, Teachers College, Columbia University, 1941), pp. 405 ff. 22 support this argument. Commenting on the possible culmination of the centralized trend Morrison argues: The logic of the enlarging political and fiscal unit evidently tends toward the State itself becoming the unit, comprehensive of all schools in respect to both control and financial support. At that point the local instrumentalities of the State disappear, and the govern- ment of the state assumes the burden of maintaining and governing and administering its school system, in an executive as well as in a legis1ative and judicial sense. One of the strongest arguments comes from Kochnower: In the past ten years or so our country has attempted with increased vigor and'dedication to improve the edu- cational opportunities offered to youth. Yet the lag between the goal and the actuality remains considerable. I submit that our efforts have been largely fruitless because of a fragmentation of authority, a scattering of resources so that no one cohesive plan of action has materialized. . . . It is reasonable to assume that the local district, confused by a myriad of choices, will cling desperately to the comfort of the familiar. Be- cause of the difficult and time-consuming problem of evaluation and the lack of centralization, the develop- *ment of new proqrams will be slow and costly. . . . Are most our frustrations the result of the great emphasis we place on decentralization and on autonomy for the local school district? . . . If so, then let a central agency or regional agencies be instituted—-free from political dominatiOn, to be sure--but let there be direction. . . . If, as is generally agreed, the future wellbeing of our nation, its position in the world, and the peace and progress of this planet are related to the mobilization of our educational resources, let us not commit this mobilization to chance.13 2 Henry Clinton Morrison, American Schools, A Critical Study pf Our School System (Chicago: University of Chicago Press, 1943), p. 276. William Kochnower, "The Case for Centralization," in Phi Delta Kappan, 15:9 (Bloomington, Indiana: Phi Delta Kappa, June, 1961), pp.393~4. m E 23 Calling for effective federal support, Johnston states: State and local funds for education are mortgaged to the hilt. But still more money is needed. It is here, on the federal level, where the support of our school system has been most neglected and from where support must inevitably come. . . . We can afford the education we need. . . . Our economy has the capacity. . . . The choice we must make, therefore, is whether education will rank high or low in our scale of priorities. The issue is not one of ability. The nation has this ability. The issue is one of educational vision and of willingness to match this vision with appropriate fiscal action. Furthermore, such action would be an investment paying handsome returns in individual satisfactions and national wellbeing.l4 Johnston did not necessarily imply federal control; however, there are those who advocate in principle an in- crease in the amount of federal participation in and control of education in the states. They contend that the same social and fiscal factors which have broughtatcentralization trend in other spheres apply to education and should result in similar responses. In general, education is subject to many of the influences leading toward centralization which have affected other spheres of the culture; and it seems that centralism claims to be more closely siding with the idea of equal educational opportunity. 14 . . Eric Johnston, former PreSident of the U. S. Chamber of Commerce, "Financing Tomorrow's Schools," American Ag: sociation p£_School Administrators (Washington, D.C.: The Association, 1960), pp. 9 and 19. 24 The majority of citizens, however, including educators, are generally agreed that local control and administration of education are desirable. The sentiments have been ex- pressed by the Educational Policies Commission as follows: Centralization in the control, administration, and financing of education is very apt to lead to a mediocre school system and a lack of progressive development of the program of public education. With well—developed local units for the administration of schools, it is certain that some communities will develop leadership which will be effective in improving education. . . . Most of the great reforms in education have originated in the schools of some local community; they were not decreed by central authority.15 The advocate of local control fears that regimentation and bureaucracy will result from centralization, that edu- cation will lose its dynamic character and become stagnant. Major emphasis is almost universally placed upon the im- portance of retaining and fostering local initiative, in- terest, and support. The localist would not, as a rule, deny state or federal financial aid or research and advisory services, but he would want this assistance extended with no strings attached. A typical expression of this stand would be: Hallmark of freedom is diversity. Federal concern about education must be one which recognizes local 5 . . . . . Educational PoliCies CommiSSion, The Structure and Administration p§_Education ;p_5merican Democracy (Washing- ton, D.C.: National Education Association, 1938), p. 79. 25 control. We do not want our educational standards established either in Washinton or, for that matter, in the state capitol, and made absolutely uniform for all of the people and all of the students in all of the schools."16 Defending the decentralist's position, Burke even strong- ly advocates that differences in educational opportunity resulting from decentralization are unavoidable and should not be eliminated. He propounds that the objective of central finance is not the removing of inequalities in edu- cational opportunities. In a summary of his book, he states: Inequalities cannot be removed even in a state- operated school system. Inequalities caused by the able, vigorous, and willing communities raising their standards and improving their programs constitute the most powerful force for improving educational oppor- tunities in all school systems. Centrally directed improvements are slow-moving at best and hardly lead to a balanced improvement of the whole school pro- gram. . . . Within limits, central finance can be used to aid in the enforcement of state minimum standards, but this is a dangerous policy to pursue in a de- centralized structure. . . . The test of state equalization policy is the adequacy of programs avail- able at the lowest end of the scale of ability levels in the state. . . . However, in lifting education at the bottom of the scale, a state must be certain that it is doing everything possible to enable other localities to move as far as possible toward providing the kind of education required in our type of civili- zation.l7 16Richard M. Nixon's reply to the question of the fed- eral government's role in support of education, Phi Delta Kappan, XLI:8 (Bloomington, Indiana, Phi Delta Kappa, May, 1960), p. 349. l7Arvid J. Burke, pp, cit., pp. 586-9. IT! 26 Burke's stand described briefly above appears to be commendable, when we consider the ideological values and the traditions that have been prevalent in American education. However, there seems to be a serious dilemma in his argu- ments. That is, one may well ask if his state will really be able to enhance the real adequacy of educational programs available for the poorer districts, while it is doing every- thing possible to enable the wealthier districts to move as far as possible? What are the sound standards of the ade- quacy of educational proqrams for the poorer districts as compared with those of the wealthier districts? It is not an easy task for a state to maintain the adequacy of educa- tional services in the poor districts without raising money through levying of taxes on the more wealthy parts of the state for expenditures in poorer sections. Yet, wealthy dis- tricts themselves may not be fully satisfied with their own school programs. Thus, the very ideals of local control of education might hamper the sound total advancement of educa- tional standards in a state. It may be the case that while the arguments from the standpoint of social justice and the various interpretations of the very concept of democracy would never end, the factual unfavorable inequalities in education among school districts having differences in ability continue to exist, so long as the people cling to the idea of local me _ "no ‘7 F\‘ t“c\. In :3 . . “but 27 control of education in its original form. Nobody would deny Burke's arguments that inequalities cannot be removed even in a state-operated school system. But too much gap between the wealthy districts and the poor districts, or too many unfavorable inequalities among school districts within a state, would be untolerable even for many decentralists. Available research data reported so far reveal that there are extensive areas where the children never can have ade- quate school facilities, and that it may be too long a time before poor districts attain the benefits of the ideals of equal educational opportunity. It has generally been agreed that in order to provide anything like equal educational op- portunities, the poorer districts must bear a burden many times greater than that of the richer districts. One of the outcomes of this situation has been the sincere efforts to reduce the number of small school districts, on the assumption that financial abilities are closely related to sizes of school districts. But it may often happen that districts lying next to each other having about the same number of pupils differ greatly in assessable property. The implications of the foregoing discussions and of the situation for educational equality can be summarized as follows: 1. Any change in education and school finance systems is subject to social change, based on both the me It 28 technological advancement and the ideological values held by the people. 2. Although decentralism has been prevalent so far, a trend toward centralization seems to exist today in American education and school finance. The states that introduced tax-supported education in the eighteenth century depended largely on local support; those that introduced tax— supported education during the first half of the nineteenth century gave somewhat more impetus to support through state aid; those that initiated their public school systems in the latter half of the nineteenth century went still farther in state support, as shown in Tables I and II.18 3. Judging from the present situation, for a long period to come the functional approach appears to be the most productive method of effecting a compromise between the two schools of thought-- centralism and decentralism. For some aspects 18 Paul R. Mort, Walter C. Reusser, and John W. Polley, Public School Finance, Its Background, Structure and Opera- tion, Third edition (New York: McGraw—Hill Book Company, Inc., 1960). PP. 196-219. 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The trend toward general purpose and equalizing support of education in Michigan has been in accordance with that of the nation,42 and has been interpreted as the policy to reduce the unfavorable financial and educa— tional differences among school districts. Ppgticipation millage. A minimum uniform effort must be made on the part of the individual school district to obtain its state share. In this regard, the State Aid Act provides as follows: No school district, except those coming under the provisions of Section 20 of this Act shall be allotted or paid any sum under the provisions of this act in any year unless it has voted to raise and there has been levied in the fiscal year in which allotment is made, at least a 6 mill tax on the state equalized valuation of the property within the district, for the purposes included in the operation cost of the dis- trict as defined in Section 14 of this Act, and has certified such fact to the superintendent of public instruction. If the district does not levy at least an 8 mill tax for the above purposes, the amount allotted or paid shall be reduced to an amount which bears the same proportion to the total amount allotted or paid as the actual levy bears to 8 mills.43 This system is commonly referred to as a participation millage. Millage that local districts must levy in order 42 . . . . The U. S. Office of Education, State Fund Distribu- tions pp_Local School Systems, pp, cit., pp. 2, 9, and 10. 4 . . . . . 3The State of Michigan, Section 35 of the State Aid Act, 1959-60. 55 to participate in state support has been raised one mill. Previously only seven mills levied was required for full state aid and it prorated, if less, to a minimum of five mills. Summarily described, in order to obtain its state share, the individual district must have an operation tax, including the 3—1/4 mills, of at least 6 mills. To obtain all of the calculated state funds, the operation tax must be at least 8 mills. Although it is a matter of discussion if these provisions do carry much impact upon the sound deve- lopment toward educational equality, the main point of this provision is in its emphasis upon local initiative and the increment of effort required of local districts to attain partnership status with the state in the support of a mini- mum foundation program, irrespective of the membership size or the local financial ability. There are other provisions similar to those of parti- Cipation millage described above, requiring local effort to Obtain state financial assistance, such as the "distressed— school-district-aid" provisions and the constitutional arrangement for the "school bond loan program." The state may extend additional (above the partner- Ship $205) aid if a district is comparatively poor (below $9,000 SEV) and levies a total school district tax in ex- Cess of 20 mills. The State Aid Act provides: 56 A school district experiencing financial hardship and eligible to receive additional aid under the pro- visions of section 6 of this act shall meet all the following conditions: (a) The total tax rate levied in the district for operating and debt retirement pur- poses for the fiscal year in which such additional aid is allowed shall be at least 20 mills on the state equalized valuation of the district. . . .44 Thus, a district meeting the conditions prescribed in the Act may apply for the additional aid. The amount of aid ranges from $5 to $2 per resident pupil membership. This is called the "hardship-aid" or the "distressed-school—district- aid." Since the state gives financial aid for operation, maintenance, salaries, etc., but not for the cost of build- ings and sites, the costs of constructing and equipping buildings and providing sites are borne entirely by property taxation at the local level. In the cases that the burden on the part of the school district is unbearable because of the lack of taxable—property resources, the state may borrow money needed for the local school district. The constitutional Provision in this regard is as follows: The state may borrow from time to time such amounts as may be required but not to exceed an aggregate of $1000,000,000.00, pledge its faith and credit and issue its notes or bonds therefor, for the purpose of making loans to school districts for the payment of principal and interest on school bonds heretofore or hereafter 44The State of Michigan, Section 15, State Aid Act, 1959- 57 issued for acquiring, constructing, enlarging, im- proving and equipping school buildings and sites and for the funding or refunding of obligations incurred for l or more of the aforesaid purposes. . . .After a school district shall have received such a loan or loans from the state, it shall thereafter levy each year not less than the said 13 mills until the amount loaned has been repaid and any tax collections in any year over and above the minimum requirements for principal and interest shall be used towards the re- payment of such loan or loans. . . .45 This constitutional provision specifies that if a school district levies a local property tax of 13 mills to buy sites and construct buildings, and if this 13 mills is not sufficient, the state will extend state funds to be re- paid in order that the district may obtain the necessary facilities. IV. Summary Hitherto, the literature concerning the issues of local control of education and equal educational opportunity, the relationships between school finance and the quantity and quality of educational services, and the Michigan State Aid Formula has been reviewed. The purpose of the review was to clarify some of the fundamental issues and principles in American educational administration and school finance systems, and to establish a frame of reference in 45 . . . . The State of Michigan, Section 27, Article X of the Michigan Constitution. 58 comprehending the factual differences of financial and edu- cational factors among different types of school districts in Michigan. It has been understood that the two concepts of local control of education and equal educational opportunity are the fundamentals which set the tone and the characteristics of education and public school finance systems in the United States. Since the two concepts are often conflicting, con- current implementation of the two ideals is not an easy task in many cases. Thus, the issue of centralization versus de- centralization comes into the picture. In this regard, the functional approach appears to be the most productive method of effecting a compromise between the two extremes of cen- tralism and decentralism. It would be the best hope for both modifying the traditional decentralists' view of school district independence and forestalling those unwholesome and undemocratic results which, as many people fear, a strong state centralization might produce. It has also been understood that money by itself will not create excellence in school finance systems or in edu- cational services. Yet, sufficient money and effective finance systems are expected to enhance the better chances of obtaining, maintaining, and increasing the quantity and quality of education. Generally stated, the differences in 59 financial ability to support public school education tend to increase the potentiality of unfavorable differences in the quantity and quality of educational services among school districts. In the final analysis, the purpose of school finance in a democratic society is to maintain and enhance the equality of educational opportunities. An ultimate test of financial systems, policies, and practices in a democratic society, then, is the soundness of educational conditions in each school district, regardless of its geographical location, its community size, or its financial ability. The answers to the questions of "what are the sound educational conditions?" are conditioned by the social demands and are determined according to the value concepts held by the people. In Michigan, the philosophy has been accepted that the state must pay a major share of the cost of educating its children. This goes without question. A look at the State Aid plans in effect shows that Michigan has taken steps that are intended to assure reasonably adequate educational opportunities for all children in properly organized school districts. However, this indication does not necessarily mean that the present Michigan State Aid Formula is, in itself, entirely adequate or sufficient to provide satis- factory educational opportunities for all children of the 60 state. There have been substantial evidences that Michigan has not found yet the best plan for financing its public school system. In fact, the inequality of taxability in the different sections is becoming increasingly notice- able as has been reported by a few studies; and the problems arising from the disparity of ability distribution as re- lated to the quantity and quality of educational services among school districts have not yet been settled. The obser- vation is warranted that while it would be rather absurd to assert that the quality of the best programs should be reduced to produce a negligible improvement in the others, it would also be difficult to justify the wide unfavorable differences existing between the educational programs of the poorest and the privileged districts. One of the basic keys for attaining the ideals of equal educational opportunity lies probably in the reformation of the taxation system so as to obtain an actual increase of school revenue, along with effective measures of school dis- trict reorganization. The state should be making continuous examinations of what is happening in local operations, and the level of support should be adjusted to keep pace with the improvement and progress possible at any time. Unbiased ex- aminatioms of the situation and true understandings of the 61 factual differences existing among school districts should precede other efforts in this direction. 62 CHAPTER III CLASSIFICATION OF THE SCHOOL DISTRICTS I. Introduction One of the most clearcut bases of classifying the public school districts in Michigan is either by the popu- lation of inhabitants, according to the Federal census, or by the number of children between the ages of 5 and 20, as certified by the superintendent of public instruction. The former basis is applied in organizing the second class school districts, and the latter basis is applied in organ- izing the fourth, the third, and the first class school dis- tricts. While the classification of school districts in terms of either the population of inhabitants or the num- ber of pupils would have many advantages for general govern- mental administration, this system of district classifica- tion does not seem to carry by itself much meaning in con— sidering the effects of the state school aid programs. Hewever, besides the vantage points in administrative convenience, one of the general assumptions behind the 1The State of Michigan, The General School Laws, 1960 (340.21, 340.52, 340.102, 340.142, and 340.182, The numbers refer to the 1948 Michigan Complied Laws.) (Lansing, Michi- gan: Speaker-Hines and Thomas, Inc., 1960). 63 practice of classifying the school districts on the basis of the population of inhabitants or of the number of school age children seems to have been that financila need (member- ship) does have direct relationships with financial ability and effort. In this connection, one recent study, conducted by Turck, concluded that there is undoubtedly a relationship between the size of the membership and the taxable wealth, and that there is a tendency for a school district, as it increases in the size of membership, to expend more effort (tax rate) for the support of its program, even though there appears to be no consistent relationship between the ability of a high school district and its effort.2 In the light of the assumptions held in Michigan's school aid policies and judging from the results of the said study, it can reasonably be contended that even though each of the three variables may be an individually inade- quate basis, when they are taken altogether as a criterion, they can provide a sound basis of classifying and grouping the school districts for the purpose of analyzing the ef- fects of the financial system in Michigan. With these considerations in mind, and on the basis of the examination of the data, three comparative classifica- tion criteria--L (Low), M (Medium), and H (High)--in each 1 Merton James Turck, Jr., pp, cit., pp. 112-3. fr: kc) 64 of the three variables of financial need, ability and ef- fort are established in order to classify the school districts. Thus, in theory, there can be 27 classification cate- gories created by the combinations of the criteria in each of the three variables of financial need, ability, and ef- fort, as shown in Figure 1. II. Classification py_Need An examination of the membership distribution among the 535 K-12 school districts, including the Detroit School District, revealed the following facts: 1. Total membership 1,451,703 2. Median 1,128 3. Mean 2,713 4. Standard Deviation 12,663 The examination of the data, as shown in Table IV and Figure 2, clearly indicated that the membership distribu- tion was highly uneven. Approximately 74 per cent of the total districts have less than 2,000 membership. More than 91 per cent of the total districts have less than 5,000 membership. Looking at the situation in another way, a group of less than 10 per cent of the districts holds nearly 60 per cent of the total membership. In short, there are many small school districts. r .1 i flu: ~=r:. 65 FIGURE 13 A THEORETICAL FRAME OF REFERENCE FOR CLASSIFYING THE SCHOOL DISTRICTS IN TERMS OF NEED, ABILITY, AND EFFORT Classification N. A. E. number (membership) (SEV per pupil) (millage) 1. L L L 2. M L L 3. H L L 4. L L M 5. M L M 6. H L M 7. L L H 8. M L H 9. H L H 10. L M L 11. M M L 12. H M L 13. L M M 14. M M M 15. H M M 16. L M H 17. M M H 18. H M H 19. L H L 20. M H L 21. H H L 22. L H M ’ 23. M H M 24. H H M 25. L H H 26. M H H 27. H H H 3 .-. N. represents Need; A., Ability; E., Effort; L. represents Low; M., Medium; and H., High. 1*“ t iriu. {5115‘ ‘V- NEED DISTRIBUTION OF THE 535 K-12 SCHOOL DISTRICTS IN MICHIGAN TABLE IV 66 Classification Membership Number Of districts Low . . . 1-999 239 Medium . 1,000-1,999 156 2,000-2,999 41 3,000-3,999 32 4,000-4,999 19 High . . 5,000-5,999 8 6,000-6,999 6 7,000-7,999 4 8,000-8,999 5 9,000-9,999 3 10,000-10,999 3 11,000-ll,999 4 12,000-12,999 5 l4,000-14,999 l l7,000-17,999 2 l9,000-l9,999 2 21,000-21,999 1 22,000-22,999 l 24,000-24,999 l 26,000-26,999 1 37,000-37,999 l 283,000-283,999 l 67 Aooo.H CH uHflDv @002 6.543210987654321 222222.2111111111 10 987654321 43 88 87098 22 33322 RENT mNH.H MHF.N m@®.NH .trrIL rli FIHILIIrIIIIrILIIFII L ”sweeps "gems "coHpMH>oQ pumpcmum Acmmasoaa an muoauumac Hoosom «Hus mmmc onesmHmech memmmmmzmac cmmz N mmDUHm _ ON cs 00 cm OOH ONH ova 00H omH oom CNN Gem Number of School Districts 1’ Fl. 68 With these facts, and considering both the pr0portion of the number of school districts and the distribution of membership among school districts, the following classifi- cations were made. Low (small). Each school district included in this category has less than 999 membership. The average member- ship is 564. In this category, 239 school districts, with a total membership of 134,832, are included. Medium. Each school district included in this cate- gory has 1,000 to 4,999 membership. The average membership is 2,057. In this category, 248 school districts, with a total membership of 510,181, are included. High (large). Each school district included in this category has more than 5,000 membership. The average mem- bership is 16,815. In this category, 48 school districts, with a total membership of 807,140, are included. These classification boundaries seem to be appropriate for the purpose of this study, under the present Michigan condition. In this connection, it is interesting to note that the low classification criterion is in accordance with Conant's observation. Defining high schools with a gradu- ating class of under 100 as "too small," Dr. Conant said 69 about 30 per cent of Michigan's schools fall in this classi- fication. III. Classification py_Abi1ity The examination of the ability distribution among 535 K-12 school districts, including the Detroit School District, shows the following facts: 1. Median 8,817 2. Mean 10,277 3. Standard deviation 5,764 The examination of the data, as shown in Table V and ~Figure 3, indicates that the disparity of wealth distribu- tion among school districts is great. To compensate for this situation the Michigan State Aid Act contains hardship aid provisions. According to Section 15 of the Act, there are four categories under which districts may be entitled to receive additional aid: namely, the districts having a state equalized valuation of $3,0000r less; the districts having a state equalized valuation of at least $3,001 but“ less than $5,001; the districts having a state equalized valuation of at least $5,001 but less than $7,001; the 4 . . . . . . . . Michigan Education Assoc1ation, Michigan Education Journal, 36:15 (April, 1959), p. 447. 70 H mam.m¢uooo.mv H mom.m¢uooo.ov H mmmtmenooo.mv H mmm.o¢rooo.o¢ H mmm.mmuooo.mm H mmm.~muooo.mm m mmm.mmuooo.m~ N mmm.m~rooo.mm m mmH.mHuooo.MH m mom.e~rooo.s~ am mmm.mHnooo.mH mm mam.HHuooo.HH H mam.mmnooo.m~ He mom.oHuooo.0H H mmm.¢~-ooo.¢~ we mmm.mrooo.m H mmm.m~uooo.mm em mam.mrooo.m H mmm.m~nooo.- we mmm.nrmmm.s . .asHpmz m mam.H~uooo.H~ a mmm.o~uooo.om m mmm.mHuooo.mH mm «mm.nrooo.s m mmm.mHuooo.mH om mmm.muooo.e m mmm.aHrooo.sH om mam.mrooo.m 0H mmm.oHuooo.oH om mmm.¢.ooo.v om mmm.mHuooo.mH m mmm.muooo.m om mam.eHuooo.¢H m mmm.~rooo.~ NH mmm.ermmH.mH . :mHm H mmm.HuH . . . 30H muoflnumfip coflumo muofiuumwp coaumo Ho .02 HHasa “we >mm -HuHmmmHo mo .02 HHmsm Hem >mm -HmHmmmHo > MAM4B Z¢GHEUHZ ZH mBUHmBmHQ AOOEOm NHIM mmm mma m0 ZOHBDMHMBwHQ NBHQHmfi Hoo.ooo.Hm cH uHasc EHHHHnm 09876543104 98 s444444444aunw22mnmmmnnmmmnmmmnmumgsves4321 rln 1 rlH, FILfiAHHshHHHHsJ _ m _ H . +,. . , . o .1 1.0H T. 13 : om rt .mm l lion .mm aHm.mm “amHems . . .1 ow new OHW .cmmz vos.mw "coHpmH>mc enmocmum :1 . me u.om I: 11 . mm 1 oo HammHsoHa cH mpoHnuch Hoosom mHus mmmv mo onesmHmemHn HHHmsm mum >mmv weHHHma 1 as m mmaon I: ma Number of School Districts 72 districts having a state equalized valuation of at least $7,001 but less than $9,001 on the basis of its resident pupil membership. If these categories of school districts can be considered as one of the bases in considering the definition of poor school districts, it is noteworthy that there are 277 K-12 school districts which have less than $9,000 SEV on the basis of their resident pupil membership. In this connection, Hecker observes: The "average” Michigan school district has approxi- mately $15,000 SEV per pupil. A district would be con- Sidered relatively "poor" if it had less than $10,000 per pupil and relatively "wealthy"'if'it had over $25,000 per pupil.5 If this observation should be applied, there are only 15 K-12 school districts which can be classified as wealthy districts; and there are 321 K—12 school districts which can be classified as poor districts. With these facts, the criteria were established for the purpose of this study,as follows: pr, Those school districts that fall beyond one-half standard deviation below the mean of the dispersion of fi- nancial ability are included in this category. This cate- gory in effect includes about the lower one-third of the ability distribution. Each school district included in this category has a SEV (state equalized valuation) per 5Stanley E. Hecker, pp, cit., p. 17. 73 pupil of less than $7,394. There are 177 school districts, and the average SEV per pupil is $5,790. Medium. Those school districts that fall within the range of one-half standard deviation below and above the mean of the dispersion of financial ability are included in this category. Each school district included in this category has a SEV per pupil of $7,395 to $13,158. There are 250 school districts, and the average SEV per pupil is $9,723. ‘gigp, Those school districts that fall beyond one-half standard deviation above the mean of the dispersion of fi- nancial ability are included in this category. This category in effect included about the upper one-third of the ability distribution. Each school district included in this category has a SEV per pupil of $13,159 or more. There are 108 school districts, and the average SEV per pupil is $18,911. IV. Claspif1cation py_Effort The examination of the effort distribution among the 535 K-12 school districts, as shown in Table VI, and Figure 4, indicated the following: 1. Median 16.10 mills 2. Mean 16.97 mills 3. Standard deviation 4.69 mills EFFORT DISTRIBUTION OF THE 535 K—12 SCHOOL DISTRICTS IN MICHIGAN —~—7 ‘1 TABLE VI 74 Classification Millage No. 9f districts Low . . . . . 1.00-7.00 0 8.00-8.99 18 9.00—9.99 4 10.00-10.99 12 11.00-11.99 20 12.00-12.99 38 13.00-13.99 56 14.00-14.62 41 Medium . . . 14.63-14.99 l7 15.00-15.99 46 16.00-16.99 48 17.00-17.99 36 18.00-18.99 42 19.00-19.32 11 High . . . . 19.33-19.99 l4 20.00-20.99 22 21.00-21.99 24 22.00-22.99 23 23.00-23.99 10 24.00-24.99 16 25.00-25.99 12 26.00-26.99 6 27.00-27.99 8 28.00-28.99 7 29.00-29.99 l 30.00-30.99 2 34.00-34.99 l 75 HmHHHa EH pHasv shoppe 64208642086420 3 3 .3 as 2 Hz or 2 2 .1 11 11 1 .1 0 .[.jm~ O full-1 F bH ll: mH am full F1 [1 Eu em mHHHs 0H.oH “:mems .mm mHHHe sm.oH names .11 IL .ov mHHHs mo.v "coHHMH>ec eumpcmpm me T... 1r! .om AcmmHnon :H muoHuuch Hoonom «Hrs mmmc :1 m .m onepmHmech Assam xmev excess rt goo v mmpon Number of School Districts With these facts, the criteria are set,as follows: ppy, Those school districts that fall beyond one-half standard deviation below the mean of the dispersion of fi- nancial effort are included in this category. This cate- gory in effect includes about the lower one-third of the effort distribution. Each school district included in this category levies less than a total of 14.62 mills. There are 189 school districts and the average millage is 12.39 mills. Medium. Those districts that fall within the range of one-half standard deviation below and above the mean of the dispersion of effort are included in this category. Each school district included in this category levies a total of 14.63 to 19.32 mills. There are 200 school districts in this category, and the average millage is 16.76 mills. gpgg, Those school districts that fall beyond one-half standard deviation above the mean of the dispersion are included in this category. This category in effect includes about the upper one-third of the ability distribution. Each7 school district included in this category levies a total of 19.33 or more mills. There are 146 school districts in this category, and the average millage is 23.17 mills. 77 TABLE VII CLASSIFICATION OF THE 535 K-12 SCHOOL DISTRICTS IN MICHIGAN, IN TERMS OF NEED, ABILITY, AND EFFORT —— —— -—-—— f Classification Number of Need Ability Effort number . . N. A. E. districts average average average 1. L L L 35 552 5,591 12.15 2. M L L 11 1,637 6,204 12.25 3. H L L 0 -- - -- 4. L L M 39 650 5,733 16.75 5. M L M 27 1,968 6,356 16.78 6. H L M 0 -- -- -- 7. L L H 32 514 5,299 23.53 8. M L H 27 2,000 5,827 24.36 9. H L H 6 9,936 6,463 26.98 10. L M L 53 615 9,701 12.32 11. M M L 42 1,850 9,968 12.51 12. H M L 1 8,270 11,863 14.50 13. L M M 33 590 9,424 16.65 14. M M M 59 1,715 9,907 16.66 15. H M M 2 11,988 11,279 16.83 16. L M H 13 496 9,362 22.47 17. M M H 34 2,386 9,378 22.44 18. H M H 13 7,814 9,811 22.71 19. L H L 21 496 17,921 12.16 20. M H L 20 2,275 19,276 12.72 21. H H L 6 13,924 17,139 13.26 22. L H M 12 323 18,392 16.70 23. M H M 19 2,614 22,287 17.02 24. H H M 9 43,654 18,482 17.27 25. L H H 1 461 15,471 22.26 26. M H H 9 3,314 17,173 21.39 21, H H H 11 12,480 17,927 22.25 Total 535 General Mean 2,713 10,277 16.97 78 V. Summary According to the criteria thus established, the 535 K-12 school districts, including the Detroit school Dis— trict, were grouped into 27 theoretical categories. It was found that there were no school districts which be- longed to the two theoretical categories (classification numbers 3 and 6). The result is shown in Table VII. An examination of the data clearly indicated that a high degree of disparity exists among school districts in each of the distributions of membership, ability, and ef— fort. Summarily stated, many of the K-12 school districts in Michigan are still small and poor. For the total group of the 535 K-12 school districts, the membership average is 2,713; the ability (SEV per pupil) average is $10,277; and the effort average is 16.97 mills. From these classified groups of school districts, the 22 groups are selected for the purpose of the analyses, as described in Chapter IV. 79 CHAPTER IV DESIGN OF THE STUDY The present study is based on a design that made possi— ble the comparison of the differences in each of the selected financial and educational factors among different types of school districts, and the identification of the general rela- tionships between the differences and the three variables of financial need, ability, and effort. I. Selection 9£_the School Districts Table VII indicates that the two classification cate— gories (classification numbers 3 and 6) have no school dis- tircts. The two categories (classification numbers 12 and 25) have only one school district, respectively, and one category (classification number 15) has only two school districts. These five categories (types) of school dis- tricts are eliminated from the analyses that will be made hereafter. They lack the representative characteristics as types of a group of school districts in Michigan. In addition, 11 school districts, including the Detroit School District, are excluded because the data from these school districts were incomplete or unsatisfactory for the purpose of this study. The Detroit School District was 80 eliminated because of its uniqueness in size, its 283,340 membership being nearly 20 per cent of the total membership in Michigan's K-12 school districts, and because of the in- complete data furnished. Thus, the 22 groups (types) of school districts, comprising the 520 K—12 districts, are selected. For the total group of the 520 selected K-12 school dis- tricts, the membership average is 2,142; the ability (SEV per pupil) average is $10,229; and the effort average is 16.99 mills. The summarized information, in terms of need, ability, and effort of the selected 22 groups of school dis— tricts is shown in Table VIII. II. Selection g§_Financia1 and Educational Factors A tentative list of financial and educational factors was developed and revised by the writer's committee chairman and the writer himself. Then a questionnaire containing the list of financial and educational factors was sent to ten school finance experts and professors of educational admin- istration and school finance at Michigan State University, asking them to rank the factors in order of their importance for the purpose of the analyses of this study. The returns were reviewed, and five financial factors and five educa- tional factors were selected. 81 TABLE VIII THE 22 SELECTED GROUPS OF K-lZ SCHOOL DISTRICTS, CLASSIFIED IN TERMS OF NEED, ABILITY, AND EFFORT 1’ J L t C1a881fication Number of Need Ability Effort numbe£f_ districts avera e avera e average N. A. E. g g (mills) 1. L L L 34 557 5,560 12.27 2. M L L 11 1,637 6,204 12.25 4. L L M 39 650 5,733 16.75 5. M L M 25 2,024 6,366 16.90 7. L L H 32 514 5,299 23.53 8. M L H 27 2,000 5,827 24.36 9. H L H 5 9,974 6,687 26.77 10. L M L 53 615 9,701 12.32 11. M M L 40 1,879 10,034 12.66 13. L M M .33 590 9,424 16.65 14. M M M 58 1,721 9,927 16.70 16. L M H 13 496 9,362 22.47 17. M M H 34 2,386 9,378 22.44 18. H M H 13 7,814 9,811 22.71 19. L H L 21 496 17,922 12.16 20. M H L 20 2,275 19,276 12.72 21. H H L 6 13,924 17,139 13.26 22. L H M 10 333 18,053 16.59 23. M H M 19 2,614 22,287 17.02 24. H H M 8 13,693 18,423 17.34 26. M H H 8 3,134 16,877 21.44 27. H H H 11 12,480 17,927 22.25 Total 520 General Mean 2,142 10,229 16.99 82 Selected Financial Factors 1. The annual total current expenditures per pupil. 2. The average salary of the teaching staff. 3. The percentage of the capital outlay budget in relation to the total amount of expenditures. 4. The percentage of the total amount of state revenue receipts in relation to the total receipts. The total receipts as used in this study include the following: a. The total general fund balance of July 1, 1959. b. The total revenue receipts. c. The total non-revenue receipts. The state receipts include the following: a. Primary fund. b. School Aid for 1959—60. c. Delinquent State Aid. d. Aid to hardship districts. 5. The percentage of the total amount of general fund property taxes (revenue receipts) in relation to the total receipts. 83 Selected Educational Factors 1. The percentage of the number of teachers holding Master's degrees or above to the total number of the teaching staff. 2. The percentage of the total number of teachers holding provisional, permanent, or life certifi- cates to the total number of the teaching staff. 3. The percentage of the number of secondary teachers teaching in subjects outside of certified majors and minors to the total number of the secondary teaching staff. 4. The percentage of the number of full-time teachers receiving over $7,000 annual salary to the total .number of the full-time teaching staff. 5. The pupil-teacher ratio. III. Analysis The significance of differences among means of selected factors in the 22 types of school districts is tested by an analysis of variance technique. 84 General Question Are there true (significant) differences among the means of each of the selected financial and educational factors in the 22 groups of school districts? . . , 1 Statistical Analysis 1. Statistically, the analysis of each of the finan- cial and educational factors involves a test of the null hypothesis--that there are no true differ- ences among the means of the 22 groups (types) of school districts. 2. To test whether differences among means are signi- ficant, the F test is used. A .05 level of signi— ficance is established for rejecting the null hy- pothesis. 1References: (a) Henry E. Garrett and R. S. woodworth, Statistics ip_Psychology and Education (New York: Longmans, Green and Company, 1958), pp. 276-308 and 372-5; (b) Allen L. Edwards, Statistical Methods for the Behavioral Sciences (New YOrk: Rinehart and Company, Inc., 1957), pp. 315-65: (c) Wilfrid J. Dixon and Frank J. Massey, Jr., Introduction 32 Statistical Analysis (New YOrk: McGraw-Hill Book Company, Inc., 1957), pp. 139-88; (d) George W. Snedecor and William G. Cochran, Statistical Methods Fifth edition (Ames, Iowa: The Iowa State College Press, 1959), pp. 190-2 and 237-90; and (e) Sidney Siegel, Nonparametric Statistics for the Behavioral Sciences (New YOrk: McGraw—Hill Book Company, Inc., 1956), pp. 202-13 and 284. 85 3. When the F test rejects the null hypothesis, the "t" test is used in order to determine those means which contributed to the differences. 2The following are the points for special consideration and the steps taken in testing the differences. (a) The 22 groups are unequal in their sizes. (b) In each factor analysis, the number of potential dif- ferences will be: 22 (22 - l)/2 = 231 (c) A general formula for calculating standard error of the difference between any two means in analysis of variance is: l 1 SE=SD —+— D w N N 1 2 where SED is the standard error of the differences between any two means, SDw is the within-groups standard deviation, and the N and N are the sizes of the groups being compared. 1 2 Since "t" = mean difference/SED mean differences = "t" x SED therefore, D.01 - t .01 x SED where D.01 is the value of significant difference, when the difference is tested by the "t" at the 01 level. (d) The means of any two groups are said to be signifi- cantly different at the .01 level of significance, if they differ by more than: |I--I 1- + 1 2 (e) Hence, for each factor analysis, a table of values of D.01 values for all 231 combinations of two means is es- tablished. Another table of mean differences is derived for each factor analysis, and these differences are judged to be significant if they exceed the corresponding value in t . he D.01 table D.01 = t .01 x SD‘w Z Z 86 Differences between pairs of means are held to be significant at the .01 level, if they exceed an amount determined by the method given in the foot- note 2. 4. In order to identify the general relationships, in terms of Low, Medium, and High concepts, between each of the three variables of financial need, abil- ity, and effort and the differences of each of the selected factors, Spearman's rank correlation method is employed.3 The rank correlation coefficients are tested at the .10 and .02 levels of significance (two—tailed tests). (a) This is a nonparametric method. (b) The rank correlation tests will be the tests of the null hypotheses of no significant relationships between each of the selected factors and each of the three variables of financial need, ability, and effort. (c) Spearman's rank correlation coefficient (r ) is given by: S 6 EN :12: r = 1 - i=1 3 N(N2-1) In our cases, N = 22, the number of groups; where the di '8 are differences in ranks of each of the 22 groups among 1the two measurements whose rank correlation is being calculated. 87 IV. Summary The 22 groups (types) of school districts, comprising tflu3520 K-12 school districts, were selected. Five finan- cial factors and five educational factors were chosen. The statistical tool identified as appropriate for analyzing differences among the means of the 22 groups of each of the 10 selected factors was the analysis of variance. Differen- ces among the means of the 22 groups will be tested by the F ratio and the "t" test. The Spearman's rank correlation coefficient technique was identified as an appropriate sta- tistical method for identifying the general relationships between the differences of each of the selected factors among different types of school districts and each of the three variables of financial need, ability, and effort. f “i CHAPTER V ANALYSIS OF SELECTED FINANCIAL FACTORS In this chapter, the five selected financial factors are analyzed. An analysis of variance technique is employed in order to test the significance of differences among means of each financial factor. The distribution of differences, the largest differences, and the total number of differences that are significant at the .01 level of significance, are examined. An inspection of the differences among means of the groups 1, 14, and 27 will be a matter of particular interest because the three groups have typical characteris- tics.1 In order to identify the general relationships, in terms of Low, Medium, and High concepts, between the five selected financial factors and the three variables of finan- cial need, ability, and effort, Spearman's rank correla- tion technique is employed. The tests of significance of rank difference coefficient will be at the .10 and .02 levels of significance. For the purpose of this analysis, first, the types of districts are ranked from highest to lowest on the bases of -‘ 1Note: Group 1 (L L L) holds the low categories of all three variables of financial need, ability, and effort; group 14 (M M M)holds the medium categories; and group 27 (H H H) holds the high categories. See: Table VIII. 89 the group averages of need, ability, and effort, as shown in Table IX; and the group mean distribution table of each selected factor is arranged from highest to lowest, so that each group has a rank for each factor. All results of the analyses are presented in summarized forms. 1. Analysis 9: Financial Factor 1 Factor. The annual current expenditures per pupil. Null hypothesis. There are no significant differences among the 22 group means of financial factor 1. Analysis g£_variance. A summary of the analysis of variance is shown in Table X. Conclusion: The null hypothesis is rejected and, therefore, it is concluded that the 22 group means of financial factor 1 do, in fact, differ signifi- cantly. Tests g£_gifference§_by_use gf_"§f. A summary of the results of the "t" tests is presented in Table XI. A close inspection of the mean differences shows the following: TABLE IX* 90 THE TWENTY-TWO GROUPS OF SCHOOL DISTRICTS ARRAYED IN ORDER OF THE GROUP AVERAGE OF NEED, ABILITY, AND EFFORT Need A'bilityfi—_—-__:====::rf:::===q 3,3222. $3,252... 252:; Rank Highest 21 l 23 1 9 l 24 2 20 2 8 2 27 3 24 3 7 3 9 4 22 4 18 4 18 5 27 5 16 5 26 6 19 6 l7 6 23 7 21 7 27 7 17 8 26 8 26 8 20 9 ll 9 24 9 5 10 14 10 23 10 8 11 18 11 11 ll 12 10 12 4 12 14 13 13 13 14 13 14 17 14 22 14 4 15 16 15 13 15 10 16 9 16 21 16 13 17 5 17 20 17 l 18 2 18 ll 18 7 l9 8 19 10 19 19 20 4 20 l 20 16 21 l 21 2 21 Lowest 22 22 7 22 19 22 *NOte: This table is derived from Table VIII. 91 TABLE X SUMMARY: ANALYSIS OF VARIANCE OF FINANCIAL FACTOR l Source of Sums of Mean squares . . df . SD variation squares (variance) w Among the 21 817,179 38,913.28 means Within 498 835,495 1,677.70 40.96 groups Total 519 1,652,674 " u = 38,913.28 _ P 1,677.70 23.19 df = 21 and df = 498‘ ll [.1 U1 \0 H l-‘ \D I-' "F" at .01 Ho: rejected 92 .Nm.OHmw ma muUAHumflp Hoonom ONm How mmmuw>m $39 any N ooN Ha .HfiH ma mucwuwmmav m th mN ucmoflmflcmwm mo Hones: amuoa Any v cam on . H HmN ¢m .wuchHmwcmflm m owN SN mo Hm>mH Ho. msu um unuoflmflnmfim oH mmm mm mum museum pmumuflccfl mo manmE Va HmN mm cww3umfl mmocwHGMMHp “map mwumofians any h NmN Nm HH gmN ov y a ma NOm mm a van m x a a s * s x a « SH HNM vm « s e s « s s s x * ON mmm ON * a a s s s s s x s 0H mmm MH * s s s x s s s s a ma mvm ma a * a e e s x s a s a ma mmm AN a s x a x a s s k * HN mom 0 s k x a s s * ¥ * x « s s s s MN mmm ma * t a s a s e x e a s k a a s NN mom OH x s a a x s s « ¥ « s x a s s * 0N Now m * a a a s s a a « s s x a s a # GN hdfi m s t s a s s s a s s * ¥ * s s s i hN MN¢w HH 5N @N 0N NN MN HN ma ma 0H ON SH m ma HH 5 vH OH m H w m N .OG saw: .2 macho H0855 adonw A:u= mo mmaflmu :Hv AHmDm mmm mmmDBHDzmmxm BZfiMMDU HN Wflmda A¢D22< ho ZOmHmm one ADV A mmAg gm MA Ammv MM .OAA mA mmocwHTMMAG OA hfifig mm acmogmgcmfim no “mass: Hmuoa inc 4 Hmew mm OA AOm¢ AN .mochAMAcmfim mo Hm>ma go. way mm moms 63 um unmoAMAcmAm mum masonv N Snug AA OwumoAOCA mo mammfi cmm3umfl a a m NOhfi MN mmucmumMMHc umnu mmumUAocH4 Ame 6H mesa ma * * ¢A mmhfl Om * s a m MMOO SN a a s a « AA ommfi Ow « a a s t * NA NOAm OM « s s a a s * ON Nme ON * a x a s * ON AhMm m s s a a a s a * MN NAvm OA 4 a a a x « m ommm m a x a s a a x s s x x x s x mA Mhmm MA * s « s .a s a a a a a a a a s x * vN MONO m s x a s a s k s a x x a x x s a a x « 5N gAmo AA a s a s a a « x a a a s a s s s a a t s * AN mMAmw 0 AN SN vN mA m MN ON ON NA AA m vA OA m N NN MA w OA MA A 5 .OG msouw 2mm: .z Hogan: msomm A=u= mo mmanmu cfiv mmmmomma mo mmHm¢qm mus mo zomHmamzoo H H HN nun—”mama. 98 11. Distribution of Mean Differences Frequency More than $3,001 14 2,001-3,000 22 1,001-2,000 43 l-l,000 152 Total 231 2. Largest difference exists between group 21 and group 7 (difference: $3,990). 3. Total number of differences, significant at the .01 level of significance is 116. 4. Differences among means of groups 1, l4, and 27. a. Group 27 vs. group 1: significant. b. Group 27 vs. group 14: significant. c. Group 14 vs. group 1: significant. Variables contributing 1:2 the differences. 1.- Need a. r = 0.8961. s b. Significant at the .10 and .02 levels. c. Positive relationship. 2. Ability a. r = 0.5935. s 99 b. Significant at the .10 and .02 levels. c. Positive relationship. Effort a. r = 0.3636 s b. Significant at the .10 level, but not at the .02 level. c. Positive relationship. Conclusion a. There is a very high positive relationship between financial factor 2 and need. b. There is a substantial positive relation- ship between financial factor 2 and ability. c. There is some relationship between financial factor 2 and effort. Therefore, it must be interpreted that the most contributive variable to the differences in the average salaries of the teachers is financial need, the sizes of the school districts. The relationship is positive. 100 III. Analysis 9f Financial Factor 3 Efiactor. The percentage of the capital outlay budget in relation to the total expenditures. b¢ull hypothesis. There are no significant differences mmarig; the 22 group means of financial factor 3. Analysis 2;“ variance. Table XIV shows the result of the analysis of variance. Conclusion: The null hypothesis is rejected and it is concluded that the 22 group means of financial factor 3 are significantly different. (Pests 25 differences by use 2f it". The results are surrunarized in Table XV. 1“. Distribution of Mean Differences Frequency More than 3.01% 6 2.01-3.00 27 1.01-2.00 90 .01-1.00 108 Total 231 Largest difference is between group 21 and group 18 (difference: 3.24%). 101 TABLE XIV SUMMARY: ANALYSIS OF VARIANCE OF FINANCIAL FACTOR 3 Source of Sums of Mean squares . . df . SD variation squares (variance) Among the meariss 21 338 16.095 Within 9r0ti£>s 498 2,703 5.427 2.33 Total 519 n u = 16.095 : F .5T427 2.965 df1 = 21 and df2 = 498 "F" at .05 = 1.59 "F" at .01 = 1.91 Ho: rejected 102 OA mM.A MA 0 ov.A m XSA.M mA mAOAHumAp SN m¢.A AA Aoonum ONm mg» Mom mmmum>w 0:9 on AN Mm.A O sN mm.A m .mN mA mwocmHmMMAp SA MO.N gm ucmoAMAsmAm mo Hones: Amuoe AQV m m¢.N MN AA mm.N os .mUGMUAMAcmAm mo Am>mA Ao. may ON oo.M m um unmoAMAcmAm mum mmsoum m So.M SN OmymoAOcA mo mamme cmm3umn s MA.M OM mmocmHmMMAO umnu mmumoAOcH« Amv S mA.M NN * 0A MN.M mm ON OM.M ON OA AM.M MA MN SM.M MA 4 s «A Mv.M Om N MS.M AA * k s s * MA NA.¢ MM * a « NN ON.¢ 0A. « a a a s s a « s A Om.¢ ¢M « « a s a s a MA XNO.¢ AN 0A A NN MA N «A MN OA ON CA S g m ON AA m SA gN AN SN OA .0: msouw saw: .2 Hones: QSOHO A:U.: MO mmHQNU GHV mmMDBHQmeXm ANBOB Mme OB zoESE 2H .5an >350 .2526 a; mo zermomomm a; mo 282528 >K flqmda 103 The total number of differences that are signifi- cant at the .01 level of significance is 29. Differences among groups 1, l4, and 27. a. Group 1 vs. group 27: significant. b. Group 1 vs. group 14: not significant. c. Group 14 vs. group 27: not significant. ‘Jariables contributing tg_the differences. 1. Need a. r = -0.8046. s b. Significant at the .10 and .02 levels. c. The relationship is inverse. Ability a. r = 0.0870. s b. Not significant at the .10 and .02 levels. c. Positive relationship. Effort a. r = -0.5325. s b. Significant at the .10 and .02 levels. c. Inverse relationship. 104 4. Conclusion a. There is a very high inverse relationship between financial factor 3 and need. b. There is practically no relationship between financial factor 3 and ability. c. There is a substantial inverse relation- ship between financial factor 3 and effort. 5. Therefore, it is interpreted that the most con- tributive variable to the differences in the proportion of the capital outlay budget in relation to the total expenditures is financial need. The relationship is inverse; that is, the small school districts seem to spend more money for capital outlay expenditures out of their total money available. IV. Analysis 9£_Financial Factor 4 Factor. The percentage of the total state revenue receipts in relation to the total receipts. Null hypothesis. There are no significant differences among the 22 group means of financial factor 4. AEELY§1§.2£.variance. As presented in Table XVI, the null hypothesis is rejected and, therefore, it is concluded 105 TABLE XVI SUMMARY: ANALYSIS OF VARIANCE OF FINANCIAL FACTOR 4 Source of df Sums of Mean squares SD variance squares (variance) w Among the means 21 41,120 1,958.095 Within groups 498 34,077 68.427 8.27 Total 519 75,197 1 958.095 II N = _i = F 68.427 28.615 : : 4 df1 21 and df2 98 .'F" at .05 = l. 59 0! ('1' O H II H KO H II F" H6: rejected 106 that the 22 group means of financial factor 4 do, in fact, differ significantly. Tests 9§_differences by_use gf_"t". Summarized re- sults are shown in Table XVII. 1. Distribution of Mean Difference Frequency More than 30.01% 6 20.01-30.00 53 10.01-20.00 62 .01-10.00 110 Total 231 2. Largest difference exists between group 27 and group 1 (difference: 33.99%). 3. Total number of differences which are significant at the .01 level of significance is 151. 4. Differences among the means of groups 1, l4, and 27: a. Group 1 vs. group 27: significant. b. Group 1 vs. group 14: significant. c. Group 14 vs. group 27: significant. Variables contributing t9_the differences. 1. Need 107 *SS.Om mA mpUAHu ImAO ONm wnu Mom mOmum>m one ADV SN mO.mN AA ON Om.AM m .AMA mA mocmumMMAO MN SM.NM OA AcmkoAsOAm mo Hones: Amuoe Any ON OM.NM m NN OO.SM OA mUCMUAMAcOAm mo Am>wA AO. mnu AN SO.SM O um unmoAMAsOAm mum museum « « OA OA.OO AN OwumoAccA mo mamme cmm3umn * « ON O0.00 ON mmocmu0MMA6 umnu mwumvocH« Ame * 4 T 4 mA Mm.mv MA * s a & OA Om.mO MA * a a « x * SA mA.OO OM * a a s s a s s s « OA OO.Am mm a s s s a a s a a x MA OO.Nm MM « « s s a a a a s s « AA mN.Mm OO s a s s s a « a a x a OA OM.Om Mm « s ¥ * a s s s s O O0.00 m a s a « a s a s s a s m SM.Om SN * a s a « s r a s a s a s O m0.0m OM x s a a a a s a s a a a s S MN.mm NM s s k s a a a s t a a a a s N O0.00 AA * s s a a a « s s « s a s a s m OO.AO ON a s % s k s s a a a a a t ¥ s a A XOO.NO OM N S O O O OA AA MA OA SA OA mA ON OA AN NN ON MN ON SN .OG macho 2mm: .2 Hones: QDOHO A:u: mo mmAQmu :AV mBmHmumm A4909 awe OB ZOHBfiAmm ZH mBmHmOmm MDZm>mm NBN mAmm 0:9 Ave N OO.SA AA m NM.OA ON .OOA mA mmocwumMMAU S A0.0N NM samuAmAcmAm 40 4402:: A4009 Age 4 4 m so.mm am 4 4 4 4 OA SA.ON mm .mochAmAcmAm mo Am>mA Ao. 0:» 4 4 4 4 mA m4.mm mm 04 unmUAMAcmAm mum mmsoum 4 4 4 4 4 AA mm.mm ow UwfimoAOGA «0 mcmwfi Gmm3umfl 4 4 4 4 4 4 OA OO.SN mm mmocmuomon 0mg» mmumoAch4 Ame 4 4 4 4 m om.om m 4 4 4 4 4 4 4 4 4 SA OS.OM OM 4 4 4 4 4 4 OA mm.OM MA 4 4 4 4 4 4 4 4 4 4 4 OA O0.0M AN 4 4 4 4 4 4 4 4 4 4 mA OO.SM MA 4 4 4 4 4 4 4 4 4 4 4 NN OS.OM OA 4 4 4 4 4 4 4 4 4 4 4 4 AN Mm.OM O 4 4 4 4 4 4 4 4 4 4 4 4 4 ON ON.NO ON 4 4 4 4 4 4 4 4 4 4 4 4 4 ON mm.NO m 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 SN OM.OO AA 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 ON M0.00 w 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 MN XO0.00 O MN ON SN ON ON AN NN mA OA OA SA O OA AA MA OA m S m N O A .OG Queue saw: .2 A0355: asouo A4»: mo mmAnmu cAO memAmomm A4909 may 09 zoAamqmm 2H mmXfiB Mammmomm QZDh Admmme ANBOB MIR m0 ZOHBMOmomm NEE m0 ZOOHmsA mmumoAccA 4 AGO .pmumoAOCA Aw>mA any um ucmoAMAcOAm no: mA uconAmmmoo umnu mmumUApcA x on .OmumoApcA mAm>0A mnu um unmoAMAcOAm mA uconAmmmoo was» mmumoAOcA O Any amommm oz<..weAAAm< .Ommz mo mmAm mummy mus mo moms oz< mmoeoA0Amom x x «AmA.o o o ~4mm.o o o oemm.o m 000044 AMAUachm mmum>cA x x 4AA6A.ou o o ieAmm.ou x x 4Aonm.ou a 4000mm AMAUGMGAM mmum>cA o o 4mmmm.o- x x owmo.o o o 4ovom.ou m 4000mm AMAUcmsAm 0>A0Amom x o ommm.o o o mmam.o o o Aomm.o m 400044 . AmAUcchm 0>A0Amom x x anAm.o o o ammh.o x o onmm.o A 4000mm AMAocchm mm m -ckoMAmu «0. 0A. mo. oA. mo. oA. mnw mo mocmoAMAchm mu moamuMMACOAm mu mUCMUAMAGUAm mu GOAuuquO mo mAm>mA mo mAm>mA mo mAm>mA Amumcmo unommm muAAAnm 6mmz H E 118 factor and each of the three variables. The results of the tests of the significance of rank correlation coefficients on each of the selected financial factors and each of the three variables of need, ability, and effort are shown in Table XXI. (The most contributive variables to the differences of sac}: of the selected financial factors were: (a) (b) (C) (d) (e) Ability, in financial factor 1: a high positive relationship. Need, in financial factor 2: a very high posi- tive relationship. Need, in financial factor 3: a very high in- verse relationship. Ability, in financial factor 4: a very high inverse relationship. Ability, in financial factor 5: a very high positive relationship. Thus,, in view of the foregoing results of the analyses, it seenm: apparent that financial effort does have very little suffect upon the existing differences of the selected financial factors among the 22 types of school districts in Michigani 119 CHAPTER VI ANALYSIS OF SELECTED EDUCATIONAL FACTORS This chapter is devoted to the analyses of the five se- lected educational factors. For an analysis of variance, a hypothesis for each factor analysis is stated in null form, and the significance of differences among means of each factor is tested by the F ratio and the "t" tests according to the formula and the procedures as described in Chapter IV. The distribution of differences, the largest differences, the total number of differences that are significant at the .01 level of significance, and the differences among means of the groups 1, l4, and 27 are examined. In order to identify the general relationships between the five selected educa- tional factors and the three variables of financial need, ability, and effort, the significance of the rank corre- lation coefficients is tested at the .10 and .02 levels of significance. All results of the analyses are presented in summarized forms. I. Analysis p§_Educational Factor 1 Factor. The percentage of the teachers holding M. A. degrees or above to the total number of teaching staff. ._. I. 120 Null hypothesis. There are no significant differences among the 22 group means of educational factor 1. Analysis pf variance. A summary of the analysis of variance is presented in Table XXII. Conclusion: The null hypothesis is rejected; therefore, it is concluded that the 22 group means of educational factor 1 do, in fact, differ signifi- cantly. Tests 0 difference§_py_use p£_"t". Table XXIII shows a summary of the results of the "t" tests. 1. Distribution of Mean Differences Frequency More than 20.01%. 27 10.01-20.00 72 l.01-10.00 80 0.01- 1.00 g; Total 231 2. Largest difference is between group 24 and group 7 (difference: 24.28%). 3. Total number of differences that are significant at the .01 level of significance is 112. 4. Differences among means of the groups 1, l4, and 27. TABLE XXII SUMMARY: ANALYSIS OF VARIANCE OF EDUCATIONAL FACTOR l 121 Source of Sums of Mean squares . . df . SD variation squares (variance) w Among the means 21 17,276 822.666 Within groups 498 26,469 53.151 7.29 Total 519 43,705 4 4 = 822.666 = F 53.151 15.478 dfl = 21 and df2 = 498 "F" at .05 = 1.59 "F" at .01 = 1.91 H6: rejected .E. 122 *mm.M mA muUAHumAU S NN. NM Aoosum 0mm 0:0 000 mmmnm>m 009 on 0A mm. MA O ON. OM .NAA mA mooCmH0MMAU OA OM. Mm 0:00A0AcmAm mo uwnesc A4009 Ase mA m4. mm A Om. OM .mocmoAMAcmAm mo A0>0A Ac. 0:0 N 46. AA 0m 0:00AMAGOAm mum mmsoum m OO. MN UmumoAOGA mo mammfi Gwm3uwfl AA OO. OO mmocmeMMAU umgp mmAMUAUCH4 Amv OA OA.A AN NN Om.A OA m Om.A SN OA ON.N mm SA OM.O OM 4 4 4 4 4 4 4 ON mS.O ON 4 4 4 4 4 4 4 4 4 4 4 4 4 4 O Om.MA m 4 4 4 4 4 4 4 4 4 4 4 4 4 4 AN S0.0A O 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 mA N0.0A MA 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 MN AA.mA OA 4 4 4. 4 4 4 4 4 4 4 4 4 4 4 4 ON mm.mA m 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 SN SN.NN AA 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 ON XO0.0N m ON SN ON MN mA AN O ON SA OA O NN OA AA m N A MA OA O OA S .OC maono cmmz .z Hones: Omaha A40: mo mmAnm0 cAO mmaem ozAmoama A0m¢ m0 mmmmwmfl .<.2 OZHQAOE mmmmodfifi HEB m0 ZOHBmOQOm HEB m0 ZOmHmm one on O OM.OS SN MA m0.0S MM .A mA mmocmeMMAO OA MM.OS Om ucmoAMAcOAm mo HmAEDG Amuoa ADV AA O0.0S OO OA AS.OS AN .wosmoAmAcOAm mo Am>mA AO. may OA OM.OO MA um unmkoAsOAm mum mmsouO O Am.OO OM OmumoAOGA mo momma omm3pmn OA NO.AO MO mmocmumOMAU 0m£0 moumoAOcH4 Amy A OO.AO OM SA OA.NO OM MN NM.MO OA S OO.MO NM ON ON.OO O N OO.mO AA O O0.00 m ON OM.OO ON SN MS.SO AA AN S0.00 O ON MO.AO O NN OO.NO OA 4 OA nRSSOO MA OA NN ON AN SN ON O N ON S MN SA A OA O OA OA AA OA MA O m .0: msouw cum: .2 HmAEoc moouo A:u: m0 mmAQmu GAO OEBO UZHmOAfimB m0 mmmfiDZ 455508 MFA. OH. OMBdonHBmmu OZHQAOE mmmmUOHB HEB m0 ZOHBMOQOMQ HEB m0 ZOOHMdmZOU >XX mAmm was AUV ON OM. O AN SO. O .OA mA moocwumMMAO ON OS. O AcMUAwAGOAm wo HmAEsc Amuoe AAV ON ON.A ON OA SS.A MA .mocmoAMAsOAm mo Am>mA AO. 030 AA OA.N OO 0m 0cm0AMAsOAm mum mmoouO O ON.N ON OmumoAucA mo mommE cmm3umn MN OO.N OA moosmummmAO unnu mmumoAOcH4 Amv OA MO.M OO SA NA.M OM O OO.M O N NO.M AA O MO.M SN A ON.O OM OA AN.S MO S SO.S NM O OM.O OM OA O0.0 AN 4 4 4 4 4 4 MA ON.AA MM NN OM.AA OA 4 4 4 4 4 4 4 4 OA XO0.0A MA OA NN MA OA O S OA A O N O SA OA MN O AA OA ON ON AN ON SN .0: moouw :00: .z Hones: asouw W A40. 40 mmAAm0 cAO hm49m OZHEU¢MB MOOQZOUMO m0 mmmZDZ AOBOB mmB OB OMOZHS QZ< MOOOS QMHmHBmmU m0 mQHOBDO d OBUmOmDm ZH OZHNUOMB mmmmoXX mdmda 133 Ability a. r = -0.4670. s b. Significant at the .10 level but not at the .02 level. c. Inverse relationship. Effort a. r = —0.1248. s b. Not significant at the .10 and .02 levels. c. Inverse relationship. Conclusion a. There is a very high inverse relationship between educational factor 3 and need. b. There is some inverse relationship between educational factor 3 and ability. c. There is practically no relationship between educational factor 3 and effort. Therefore, it is interpreted that need is the most contributive variable to the differences of the proportion of the secondary teachers teaching in subjects outside of certified major and minors to the total number of secondary teaching staff. The relationship is inverse. This fact implies that 134 the large school districts hold many more teachers who are qualified for their teaching in high schools, while small school districts are pretty much limited to maintain qualified teachers. IV. Analysis pf_Educational Factor 4 Eactgr, The percentage of the teachers receiving over $7,000 annual salary to the total number of teaching staff. Null_hypothesis. There are no significant differences among the 22 group means of educational factor 4. Analysis pf_variance. Table XXVIII presents a summary of the results of the analysis of variance. Conclusion: The null hypotheSis is rejected and, therefore, it is concluded that the 22 group means of educational factor 4 do, in fact, differ signifi- cantly. Tests pf differences py use p§_"t". Table XXIX shows the summarized results of the tests. 135 TABLE XXVIII SUMMARY: ANALYSIS OF VARIANCE OF EDUCATIONAL FACTOR 4 = Source of Sums of Mean squares . . df . SD variation squares (variance) w Among the means 21 13,352 635.809 Within groups 498 49,313 99.022 9.95 Total 519 62,665 " N = 635.809 = F 99.022 6'421 dfl = 21 and df2 = 498 "F" at .05 = 1.59 "F" at .01 = 1.91 Ho: rejected 136 l E III I, Ii illii llildlillii i=0. 00 mmApm0 cAO mm<9m 02900409 40 400202 A4909 009 09 .XSS.OA mA mquuumAO OA M0.0 MO Aoosom ONO 0:0 you mmmum>w one ADO OA N0.0 MA MA MM.OA MM .SO mA mmucmumMMAU NN O0.0A OA AGMUAMAcOAm mo HwAESG Amuoa Any O OO.AA OM A .OO.NA OM .wosmoAMACOAm mo Am>mA AO. 030 N AO.MA AA um 0:00AMAsmAm mum mODOHO O O0.0A ON OOAMUAOGA mo mammfi Gmm3AmQ OA OA.OA AN mmoamumOMAO umnu mmumoAOoH4 Ame O O0.0A SN 4 S O0.0A NM 4 4 4 4 4 AA O0.0A OO 4 4 4 4 4 SA A0.0A OM 4 4 4 4 4 4 OA S0.0A OO O O0.0A O 4 4 4 4 4 4 4 4 4 4 MN OS.ON OA 4 4 4 4 4 4 4 4 4 4 4 ON O0.0N ON 4 4 4 4 4 4 4 4 4 AN MM.ON O 4 4 4 4 4 4 4 4 4 4 4 OA O0.0N MA 4 4 4 4 4 4 4 4 4 4 4 4 ON O0.0N O 4 4 4 4 4 4 4 4 4 4 4 4 4 4 SN O0.0M AA 4 4 4 4 4 4 4 4 4 4 4 4 4 4 ON .XMA.AM O ON SN ON OA AN ON MN O OA SA AA S O OA O N A O NN MA OA OA .0: @5000 :00: .z Augean moose >m¢A0 OZH>HMUMM mmmfl00 0:9 on MN OA.NN OA NN ON.NN OA .NO 0A 000000000A0 0A ON.NN AN 0000AOA0OA0 mo 90AEs: A0005 AAV SN OO.MN AA MA O0.0N MM .00000AMAGOA0 mo A0>0A AO. 0:0 S O0.0N NM 00 0000AOA0OA0 0H0 mmsoum A O0.0N OM U0000AOCA MO 00005 000300: OA N0.0N MA 000:0H0MMA0 00:0 00000AOGH4 Ame ON OS.ON ON OA SS.ON MA 4 4 4 OA O0.0N MO 4 4 4 SA O0.0N OM 4 4 4 4 OA AM.ON OO 4 4 ON O0.0N O 4 4 4 4 AA OO.SN OO 4 4 4 4 4 O MA.SN OM 4 4 4 4 4 O OS.SN SN 4 4 4 O ON.ON O 4 4 4 4 4 4 4 O O0.0N ON 4 4 4 4 4 4 N O0.0N AA 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 AN SA.OM O AN N O O O O AA ON OA SA OA OA ON OA A S MA SN OA NN MN ON .0: @0090 0002 .Z H0AEsc 050mm ilitr A=0: mo 00A900 GAO 09900 0000009409000 009 00 0009000000 HNNX HAmdfi 1. 142 Distribution of Mean Differences Frequency More than 10.01 7 5.01-10.00 23 1.01- 5.00 '1 142 .01- 1.00 59 Total 231 Largest difference is between group 21 and group 26 (difference: 13.92). Total number of differences which are significant at the .01 level of significance is 62. Differences among means of the groups 1, l4, and 27. a. Group 14 vs. group 27: not significant. b. Group 14 vs. group 1: not significant. c. Group 1 vs. group 27: not significant. There seem to be no consistent relationships among the three groups in relation to educational factor 5. Variables gpntributing pp_the differences 1. Need a. r = 0.2693. s b. Not significant at the .10 and .02 levels. Sbi yoneupeiq quoip has I: quonp 4 ”0' '7:- ‘ AFL'JJIVI... 11:) '«.r .L ,i—l 5m'GQISF91 jnejaiamoo on ed 03 lo noijudiijaifl asunsieiiifl 069M 10.01 00.CI~IO.€ 00.8 -IO.I 00.1 ~10. nsdj eIcM 1630? msawjed ai sansxsiiib jespisJ :9009193110) 03 are doidw sooneiellib 30 :sdmun isjoT .20 Si sonsoiiinpie 30 isvai 10. ed? 35 "3 C C C H l C 9 L, (.3 (I) 0‘ Q U) 3 3 ‘U :1 O B (D 0.} (D U D, {2. H (3') (.0 (+5 b- I...) )fz'flgla J04 :TS quorp .av 01 qUOtf ‘ i):3_-813 ion :1 qOOIp ,2v #1 QLC . jngta ion :TS qUOTP .av 1 ‘(~: I 1.5'0w Ll quoxp said: 0:: , ’ in? W: Qflxjgd ' 143 c. Positive relationship. Ability a. r = -0.4049. s b. Significant at the .10 level but not at the .02 level. c. Inverse relationship. Effort a. r = 0.0017. s b. Not significant at the .10 and .02 levels. Conclusion a. There is a slight positive (but not signi- ficant) relationship between educational factor 5 and need. b. There is some inverse relationship between educational factor 5 and ability. c. There is almost no relationship between educational factor 5 and effort. It is interpreted that although there seems to be no consistent general direction of the relation- ship, the most contributive variable to the dif- ferences of the pupil-teacher ratio is ability. 144 The relationship is inverse, that is, the pupil- teacher ratio in the small school districts is higher than in the large districts. The other two variables do not seem to have much effect on the differences of the pupil-teacher ratio among the 22 types of school districts in Michigan. VI. Summary All null hypotheses of no significant differences among means of each of the selected five educational factors were rejected by the F test at the .05 level of significance. The significance of differences among means of each factor was further tested by the "t" tests. The contributive vari- ables to the differences of each of the selected five edu— cational factors were identified by the Spearman rank corre- lation coefficient method. 1. The results of the analysis of variance were shown in Tables XXII, XXIV, XXVI, XXVIII, and XXX in summarized forms. 2. The results of the tests of differences by use of "t" were shown in Tables XXIII, XXV, XXVII, XXIX, and XXXI. The total number of differences that were significant at the .01 level of significance was: 145 (a) 112, in educational factor 1. (b) l, in educational factor 2. (c) 14, in educational factor 3. (d) 97, in educational factor 4. (e) 62, in educational factor 5. The least number of significant differences existed in educational factor 2, the proportion of the teachers holding certificates to the total number of teaching staff. The greatest number of significant differences existed in edu- cational factor 1, the proportion of the teachers holding M. A. degrees or above to the total number of teaching staff. Clearly, the total number of significant differences of the selected educational factors was much less than that of the selected financial factors. 3. The groups having the largest differences of each of the five educational factors are shown in Table XXXII with reference to the group averages of the three variables of financial need, ability, and effort. Table XXXII does not seem to show any clear-cut relationships in terms of Low, Medium, and High concepts, between the selected educa- tional factors and the three variables. Also, the exami- nations of the differences among means of the groups 1, l4, and 27 did not seem to reveal the general direction of the relationships. TABLE XXXII 146 THE GROUPS HAVING THE LARGEST DIFFERENCE OF EACH OF THE FIVE EDUCATIONAL FACTORS (with references to the group averages of need, ability, and effort) Groups having the largest difference Differ- ence Educa— Group 24 (H H m) and Group 7 (L L H) 24.28% ;::::: N. 13,693 N. 514 1 A. $18,423 A. $5,299 E. 17.34 mills E. 23.53 mills Educa- Group 18 (H M H) and Group 5 (M L M) 21.85% ;::::: N. 7,814 N. 2,024 2 A. $9,811 A. $6,366 E. 22.71 mills E. 16.96 mills Educa- Group 16 (L M H) Group 27 (H H H) 13.83% tional and Factor N. 496 N. 12,480 3 A. $9,362 A. $17,927 E. 22.47 mills E. 22.25 mills Educa- Group 24 (H H M) and Group 10 (L M L) 21.60% 8:22;: N. 13,693 N. 615 4 A. $18,423 A. $9,701 E. 17.34 mills E. 12.32 mills Educa- Group 21 (H H L) and Group 26 (M H H) 13.92 ;::::: N. ‘13,924 N. 3,134 5 A. $17,139 A. $16,877 E. 13.26 mills E. 21.44 mills Note: (a) The figures under each group are the group aver- (b) See: ages of Need (N.), Ability (A.), and Table VIII. Effort (E.). 147 The tests of the significance of the Spearman rank cor- relation coefficient at the .10 and .02 levels of signifi- cance indicated the general relationships between each of the selected five educational factors and each of the three variables of financial need, ability, and effort. The re- sults of the tests of the significance of rank differences are shown in Table XXXIII. The general direction of the relationships were: (a) (b) (c) (d) (e) Positive relationship, in educational factor 1. Positive relationship, in educational factor 2. Inverse relationship, in educational factor 3. Positive relationship, in educational factor 4. N0 consistent relationship, in educational factor 5. The most contributive variables to the differences of each of the (a) (b) (C) (d) selected five educational factors were: Need, in educational factor 1: a very high positive relationship. Both need and ability, in educational factor 2: some positive relationship. 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