A quantitative study of the percentage of variance in student Terra Nova Assessment scores accounted for by the variance in school size and per pupil expenditure in Catholic elementary schools

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The purpose of this quantitative study was to determine the effect, if any, that school size and per pupil expenditure have on student achievement in Catholic elementary schools within a particular diocese. As decisions are made regarding the future viability and sustainability of Catholic schools, it is prudent to examine the relationship between the size of student populations and the per pupil expenditure in Catholic schools and student achievement in these schools. The research question for this study was, "What is the percentage of variance in student Terra Nova Assessment scores accounted for by the variance in school size and per pupil expenditure?" This study examined the five year period from 2008-2012. Terra Nova Assessment score data from 36 elementary schools in the diocese under study was used as the measure of student achievement in this study. The student score data examined was from students in grades 2 through 7. This study utilized correlation analysis to test the strength of the linear relationship between the independent variables and the dependent variable, and when a significant correlation was discovered for a particular case, regression analysis was then employed to further examine the relationship. The findings of this study support the assertion that the percentage of variance in student Terra Nova Assessment scores that is accounted for by school size and per pupil expenditure in the diocese under study is not at a level that makes the effect practical for decision making regarding the future of Catholic education in the diocese under study. School size and per pupil expenditure may be major factors when making decisions about the viability of Catholic schools in the diocese under study for other reasons aside from the level of student achievement, and the findings of this study suggest that such decisions that use school size and per pupil expenditure as factors can be made without major concern for the effect on student achievement.
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A QUANTITATIVE STUDY OF THE PERCENTAGE OF VARIANCE IN STUDENT TERRA NOVA ASSESSMENT SCORES ACCOUNTED FOR BY THE VARIANCE IN SCHOOL SIZE AND PER PUPIL EXPENDITURE IN CATHOLIC ELEMENTARY SCHOOLS A Dissertation Presented to Faculty of the Division of Education and Human Services of Neumann University In Partial Fulfillment of the Requirements for the Degree of Doctor of Education by Jason C. Briggs May 2013 UMI Number: 3581765 All rights reserved INFORMATION TO ALL USERS The quality of this reproduction is dependent upon the quality of the copy submitted. In the unlikely event that the author did not send a complete manuscript and there are missing pages, these will be noted. Also, if material had to be removed, a note will indicate the deletion. UMI 3581765 Published by ProQuest LLC (2014). Copyright in the Dissertation held by the Author. Microform Edition © ProQuest LLC. All rights reserved. This work is protected against unauthorized copying under Title 17, United States Code ProQuest LLC. 789 East Eisenhower Parkway P.O. Box 1346 Ann Arbor, MI 48106 - 1346 As the world's largest graduate research publisher, UMI provides access to the official Copy of Record for millions of graduate theses and dissertations and safeguards the scholarly record via digital and microfilm preservation. As the central repository of graduate research through the ProQuest Dissertations and Theses Database (PQDT), ProQuest makes dissertations and theses accessible to researchers worldwide, ensuring their place as an integral component to the literature in every discipline. NEUMANN UNIVERSITY Division of Education and Human Services Dissertation Signatory Page Title of Dissertation: A QUANTITATIVE STUDY OF THE PERCENTAGE OF VARIANCE IN STUDENT TERRA NOVA ASSESSMENT SCORES ACCOUNTED FOR BY THE VARIANCE IN SCHOOL SIZE AND PER PUPIL EXPENDITURE IN CATHOLIC ELEMENTARY SCHOOLS Author: Jason C. Briggs The dissertation cited above is approved by the undersigned dissertation committee chairperson and members: ___________________________________ ____________________ Rev. Philip J. Lowe, Ed.D. Date of Signature Committee Chairperson ___________________________________ ____________________ Rev. Edward J. Griswold, D.Min. Date of Signature Committee Member ___________________________________ ____________________ Peter Idstein, Ph.D. Date of Signature Committee Member Accepted by the Faculty of the Division of Education and Human Services of Neumann University in partial fulfillment of the requirements for the degree of Doctor of Education. __________________________________ _____________________ Joseph E. Gillespie, Ed.D. Date of Signature Dean, Division of Education and Human Services COPYRIGHT BY Jason C. Briggs 2014 DEDICATION This study is dedicated to my wife Heather, my son Anthony, and my daughter Emily. My family has been steadfast in supporting my academic endeavors during my entire time in graduate school. Despite the many nights and weekends I spent preparing for classes and working on this dissertation, my family continued to encourage me each step of the way. I am profoundly grateful to almighty God for blessing me with these three special people. iv ACKNOWLEDGEMENTS The doctoral dissertation process is a long and complex journey, and a dissertator must seek the counsel of experts in various fields in order to have any chance of success. My journey through the dissertation process was no different, and I am thankful to several individuals for their advice and support during the process of completing my dissertation. Foremost, I am grateful to my dissertation committee, Rev. Philip Lowe, Ed.D., Chairperson, Rev. Edward Griswold, S.T.L., D.Min., Committee Member, and Dr. Peter Idstein, Ph.D., Committee Member. The guidance and support that my committee provided me was at all times focused and direct, and I believe that my committee’s guidance pushed me to new levels of scholarship. I would like to acknowledge Dr. Margaret F. Boland, Ed.D., who shared with me her vast knowledge of standardized testing in general, and the Terra Nova Assessment specifically. I would also like to acknowledge Dr. Stephen Thorpe, Ph.D., who helped me to understand the relationship between regression analysis and its assumptions. v ABSTRACT A QUANTITATIVE STUDY OF THE PERCENTAGE OF VARIANCE IN STUDENT TERRA NOVA ASSESSMENT SCORES ACCOUNTED FOR BY THE VARIANCE IN SCHOOL SIZE AND PER PUPIL EXPENDITURE IN CATHOLIC ELEMENTARY SCHOOLS Jason C. Briggs Dissertation Committee Chairperson: Rev. Philip J. Lowe, Ed.D. The purpose of this quantitative study was to determine the effect, if any, that school size and per pupil expenditure have on student achievement in Catholic elementary schools within a particular diocese. As decisions are made regarding the future viability and sustainability of Catholic schools, it is prudent to examine the relationship between the size of student populations and the per pupil expenditure in Catholic schools and student achievement in these schools. The research question for this study was, “What is the percentage of variance in student Terra Nova Assessment scores accounted for by the variance in school size and per pupil expenditure?” This study examined the five year period from 2008-2012. Terra Nova Assessment score data from 36 elementary schools in the diocese under study was used as the measure of student achievement in this study. The student score data examined was from students in grades 2 through 7. This study utilized correlation analysis to test the strength of the linear relationship between the independent variables and the dependent variable, and when a significant correlation was discovered for a particular case, regression analysis was then employed to further examine the relationship. The findings of this study support the assertion that the percentage of variance in student Terra Nova Assessment scores that is accounted for by school size and per pupil expenditure in the diocese under study is not at a level that makes the vi effect practical for decision making regarding the future of Catholic education in the diocese under study. School size and per pupil expenditure may be major factors when making decisions about the viability of Catholic schools in the diocese under study for other reasons aside from the level of student achievement, and the findings of this study suggest that such decisions that use school size and per pupil expenditure as factors can be made without major concern for the effect on student achievement. vii TABLE OF CONTENTS DEDICATION. ……………………………………………………………………………. iv ACKNOWLEDGEMENTS……………………………………………………………….. v ABSTRACT………………………………………………………………………………... vi TABLE OF CONTENTS………………………………………………………………….. viii LIST OF TABLES…………………………………………………………………………. xi LIST OF FIGURES………………………………………………………………………... xiii LIST OF APPENDICES…………………………………………………………………… xiv CHAPTER I. INTRODUCTION……………………………………………………….... 1 Background of the Study …………………………………………………. 3 Statement of the Problem ……………………………………………….... 7 Purpose of the Study ……………………………………………………… 8 Significance of the Study…………………………………………………. 10 Definition of Terms……………………………………………………….. 12 Catholic School…………………………………………………… 12 Catholic Schools Office…………………………………………… 12 Diocese……………………………………………………………. 12 Elementary School………………………………………………… 12 Per Pupil Expenditure…………………………………………….. 13 Student Achievement……………………………………………… 13 Terra Nova Assessment…………………………………………… 13 Testing Year……………………………………………………….. 13 Research Question…………………………………………………………. 14 Hypotheses………………………………………………………………… 14 Null Hypothesis 1…………………………………………………. 14 Research Hypothesis 1……………………………………………. 14 Null Hypothesis 2…………………………………………………. 14 Research Hypothesis 2……………………………………………. 14 Null Hypothesis 3…………………………………………………. 14 Research Hypothesis 3……………………………………………. 14 Limitations of the Study…………………………………………………… 14 Geographic Footprint……………………………………………… 15 Testing Procedures………………………………………………… 15 School Closure…………………………………………………….. 15 Socioeconomic Status Indicator…………………………………… 15 Student Population………………………………………………… 16 Delimitations of the Study…………………………………………………. 16 viii TABLE OF CONTENTS (continued) School Selection…………………………………………………….16 Regular Education Test Result Data………………………………. 16 Assumptions……………………………………………………………….. 17 Organization of the Study………………………………………………….. 17 Conclusion…………………………………………………………………. 18 II. REVIEW OF THE LITERATURE………………………………………... 18 Introduction………………………………………………………………… 18 Methodological Criteria……………………………………………………. 19 Early School Size and Consolidation Movements……………………….... 20 Foundational Considerations on School District Consolidation…………… 22 Small Schools……………………………………………………………… 24 Large Schools……………………………………………………………….30 Comparing Small Schools to Large Schools………………………………. 34 The Effect of School Size on Schools……………………………………... 37 School Size and Student Achievement……………………………………. 39 Per Pupil Expenditure and Student Achievement………………………… 44 School Size and Per Pupil Expenditure……………………………………. 46 The Unique Position of Catholic Education………………………………. 47 Conclusion………………………………………………………………… 51 III. METHODOLOGY………………………………………………………… 52 Introduction……………………………………………………………….. 52 Selection of Participants…………………………………………………… 53 Instrumentation……………………………………………………………. 54 Validity……………………………………………………………. 56 Reliability………………………………………………………….. 57 Data Collection…………………………………………………………….. 58 Data Analysis………………………………………………………………. 59 Conclusion…………………………………………………………………. 62 IV. PRESENTATION AND ANALYSIS OF DATA………………………… 63 Introduction……………………………………………………………….. 63 Descriptive Statistics……………………………………………………… 66 Foundational Analyses of Independent Variables………………………… 71 Foundational Analyses of Dependent Variables………………………….. 76 Tests of Regression Assumptions………………………………………… 88 Data Appropriateness…………………………………………….. 89 Independence……………………………………………………… 89 Linearity………………………………………………………..…. 90 Distribution………………………………………………………. 90 Homoscedasticity………………………………………………… 94 Independence and Normality of Errors………………………….. 103 Testing the Research Hypotheses Using Regression Analysis…………… 105 ix TABLE OF CONTENTS (continued) Null Hypothesis 1…………………………………………………. 105 Research Hypothesis 1……………………………………………. 105 Null Hypothesis 2…………………………………………………. 105 Research Hypothesis 2……………………………………………. 105 Null Hypothesis 3…………………………………………………. 105 Research Hypothesis 3……………………………………………... 105 Conclusion…………………………………………………………………. 109 V. SUMMARY. DISCUSSION, AND CONCLUSIONS..…………………… 109 Introduction………………………………………………………………… 109 Summary of the Study……………………………………………………... 111 Discussion of the Findings………………………………………………..... 115 Implications for Practice…………………………………………………… 125 Recommendations for Further Research…………………………………... 126 Conclusion…………………………………………………………………. 128 REFERENCES…………………………………………………………………………….. 129 APPENDIX A……………………………………………………………………………… 139 APPENDIX B……………………………………………………………………………… 140 APPENDIX C……………………………………………………………………………… 141 APPENDIX D……………………………………………………………………………… 142 APPENDIX E……………………………………………………………………………… 143 APPENDIX F……………………………………………………………………………… 144 APPENDIX G……………………………………………………………………………… 145 x LIST OF TABLES 1. Mean School Size and Per Pupil Expenditure, Testing Years 2008-2012………… 67 2. Mean Terra Nova Assessment Scores for Each Grade Level, Testing Year 2008… 68 3. Mean Terra Nova Assessment Scores for Each Grade Level, Testing Year 2009… 68 4. Mean Terra Nova Assessment Scores for Each Grade Level, Testing Year 2010… 69 5. Mean Terra Nova Assessment Scores for Each Grade Level, Testing Year 2011… 70 6. Mean Terra Nova Assessment Scores for Each Grade Level, Testing Year 2012… 70 7. Pearson Correlation Coefficient of 2008 School Size and 2008 Terra Nova Assessment Scores…………………………………………………………………. 78 8. Pearson Correlation Coefficient of 2009 School Size and 2009 Terra Nova Assessment Scores…………………………………………………………………. 79 9. Pearson Correlation Coefficient of 2010 School Size and 2010 Terra Nova Assessment Scores…………………………………………………………………. 80 10. Pearson Correlation Coefficient of 2011 School Size and 2011 Terra Nova Assessment Scores…………………………………………………………………. 81 11. Pearson Correlation Coefficient of 2012 School Size and 2012 Terra Nova Assessment Scores…………………………………………………………………. 82 12. Pearson Correlation Coefficient of 2008 Per Pupil Expenditure and 2008 Terra Nova Assessment Scores………………………..…………………………………. 83 13. Pearson Correlation Coefficient of 2009 Per Pupil Expenditure and 2009 Terra Nova Assessment Scores………………………..…………………………………. 84 14. Pearson Correlation Coefficient of 2010 Per Pupil Expenditure and 2010 Terra Nova Assessment Scores………………………..…………………………………. 85 xi LIST OF TABLES (continued) 15. Pearson Correlation Coefficient of 2011 Per Pupil Expenditure and 2011 Terra Nova Assessment Scores………………………..…………………………………. 86 16. Pearson Correlation Coefficient of 2012 Per Pupil Expenditure and 2012 Terra Nova Assessment Scores………………………..…………………………………. 87 17. Shapiro-Wilk Test for Normal Distribution – Results for Surviving Data Sets…… 91 18. Shapiro-Wilk Test for Normal Distribution – Results for Surviving Data Sets Transformed………………………………………………………………….…….. 93 19. Shapiro-Wilk Test for Normal Distribution – Standardized Residuals……………. 104 20. Regression Results – Amount of Variance in Transformed Terra Nova Scores Accounted for by Variance in Transformed School Size………………………….. 107 21. Percentage of Variance in Terra Nova Assessment Scores Accounted for by the Variance in School Size……………………………………………………………. 124 xii LIST OF FIGURES 1. Independent Variable Scatterplot for 2008………………………………………… 72 2. Independent Variable Scatterplot for 2009………………………………………… 73 3. Independent Variable Scatterplot for 2010………………………………………… 74 4. Independent Variable Scatterplot for 2011………………………………………… 75 5. Independent Variable Scatterplot for 2012………………………………………… 76 6. Residual Plot for 2009 Grade 4……………………………………………………..94 7. Residual Plot for 2009 Grade 5……………………………………………………..95 8. Residual Plot for 2010 Grade 3……………………………………………………..96 9. Residual Plot for 2010 Grade 5…………………………………………………….. 97 10. Residual Plot for 2010 Grade 7…………………………………………………….. 98 11. Residual Plot for 2011 Grade 3…………………………………………………….. 99 12. Residual Plot for 2011 Grade 4…………………………………………………….. 100 13. Residual Plot for 2011 Grade 5…………………………………………………….. 101 14. Residual Plot for 2011 Grade 6…………………………………………………….. 102 15. Residual Plot for 2012 Grade 6…………………………………………………….. 103 xiii LIST OF APPENDICES 1. Appendix A – Raw School Size Data ……………………………………………... 139 2. Appendix B – Raw Per Pupil Expenditure Data…………………………………… 140 3. Appendix C – Raw Terra Nova Assessment Score Data -- 2008………………...... 141 4. Appendix D – Raw Terra Nova Assessment Score Data -- 2009………………...... 142 5. Appendix E – Raw Terra Nova Assessment Score Data -- 2010………………...... 143 6. Appendix F – Raw Terra Nova Assessment Score Data -- 2011………………...... 144 7. Appendix G – Raw Terra Nova Assessment Score Data -- 2012………………...... 145 xiv 1 Chapter I Introduction This quantitative study sought to determine the percentage of variance in student Terra Nova Assessment scores that can be accounted for by the variance in school size and per pupil expenditure in parish-based and regional Catholic elementary schools in a particular diocese in New Jersey. This study was designed to use multiple regression analysis to measure the percentage of variance in student Terra Nova Assessment scores that can be explained by the variance in school size and per pupil expenditure in a particular diocese; however, the characteristics of the data only allowed the use of simple regression analysis once the data were tested for the assumptions of regression analysis. The period of study was 2008-2012, with each year’s data analyzed separately. “Elementary school” was defined as a Catholic school which operates under the aegis of a Catholic parish or the Catholic Schools Office within the diocese being studied that houses grades kindergarten through 8 or grades preschool through 8. “School size” was defined as the number of students on roll on the first day of school in grades kindergarten through 8 as reported to the Catholic Schools Office. School size was an independent variable. “Per pupil expenditure” was defined as the quotient of the sum of all school expense lines in the operating budget divided by the school enrollment for each Catholic elementary school as reported to the Catholic Schools Office. Per pupil expenditure was an independent variable. “Student achievement” was defined as the total student score expressed in terms of the mean Normal Curve Equivalent (NCE) for each grade level in each individual school on the Terra Nova Assessment for each year over a five year period, 2008-2012. Whole school mean scores were also available to the 2 researcher but were not employed in order to test student achievement at individual grade levels. Use of grade level mean NCEs instead of whole school mean NCEs enabled the researcher to uncover any possible grade level trends during the five years in the study period. Student achievement was the dependent variable. The research question for this study was, “What is the percentage of variance in student Terra Nova Assessment scores accounted for by the variance in school size and per pupil expenditure?” This study was designed to examine three aspects of this question. First, the study was designed to use simple regression analysis to measure the percentage of variance in student Terra Nova Assessment scores accounted for by the variance in school size for each grade level, grades 2 through 7, in each year, 2008-2012. Second, the study was designed to use simple regression analysis to measure the percentage of variance in student Terra Nova Assessment scores accounted for by the variance in per pupil expenditure for each grade level, grades 2 through 7, in each year, 2008-2012. Third, the study was designed to use multiple regression analysis to measure the percentage of variance in student Terra Nova Assessment scores accounted for by the variance in school size and per pupil expenditure for each grade level, grades 2 through 7, in each year, 2008-2012. Prior to using regression analysis, all data were tested for the assumptions of regression analysis. Due to the per pupil expenditure data sets failing to meet the assumptions for regression analysis, the per pupil expenditure data were excluded from all regression analyses. Thus, the study did not employ simple regression analysis to measure the percentage of variance in student Terra Nova Assessment scores accounted for by the variance in per pupil expenditure as designed, nor did the study employ 3 multiple regression analysis to measure the percentage of variance in student Terra Nova Assessment scores accounted for by the variance in school size and per pupil expenditure. This chapter presents an introduction to the study, the background of the study, a statement of the problem, the purpose of the study, the significance of the study, definitions for key operational terms, hypotheses, limitations of the study, delimitations of the study, assumptions, and the organization of the study. Through the process of trying to account for two possible sources of the variance in student achievement using the independent variables of school size and per pupil expenditure, this study sought to provide relevant data to be considered when planning for the future of Catholic education in the diocese under study. Background of the Study When the history of school structure in the United States of America is examined, specific trends emerge from the literature on the size of schools. These trends reveal that public education generally moved from a time of small local schools to larger consolidated schools, and that this transformation was not without its critics. The trends in Catholic education reveal that there has been a general movement towar
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