TITLE PAGE ASSESSMENT OF THE EQUIVALENCE OF WAEC AND NECO MATHEMATICS MULTIPLE-CHOICE TESTS USING ITEM RESPONSE THEORY BY OGUOMA, CHINYERE CHINWEIKE 2010177002F A DISSERTATION PRESENTED TO THE DEPARTMENT OF EDUCATIONAL FOUNDATIONS, FACULTY OF EDUCATION NNAMDI AZIKWE UNIVERSITY, AWKA IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE AWARD OF THE DEGREE OF DOCTOR OF PHILOSOPHY (Ph. D) IN EDUCATIONAL MEASUREMENT AND EVALUATION JUNE, 2017 2 CERTIFICATION This is to certify that Oguoma Chinyere Chinweike with Registration Number 2010177002F is responsible for the work submitted in this dissertation, that the work is original except as specified in the acknowledgements and references. ------------------------------ Oguoma, Chinyere Chinweike 3 APPROVAL PAGE This Dissertation has been approved for the Department of Educational foundations, Faculty of Education Nnamdi Azikiwe University, Awka. ------------------------- --------------------------- Prof. Romy Okoye Date Supervisor ------------------------- --------------------------- Prof. N.N. Agu Date Head of Department ------------------------- --------------------------- Prof. O.S. Abonyi Date External Examiner ------------------------- --------------------------- Prof. O. Ibeneme Date Dean, Faculty of Education ------------------------- --------------------------- Prof. H. I. Odumegwu Date Dean, School of Post Graduate Studies 4 DEDICATION This research work is dedicated to my husband Hon. Chinweike Oguoma. 5 ACKNOWLEDGEMENTS The researcher’s sincere thanks go to her supervisor Prof. Romy Okoye, not only for his insightful comments and encouragement but also for his hard questions which spurred her to widen her research from various perspectives. These he was able to do continuously and patiently in spite of his academic and other schedules. The researcher is also of immense gratitude to Prof. N. Agu, Prof. N.P.M. Esomonu, Prof. G.C. Unachukwu, Prof. R.C. Ebenebe, Dr. O. Ikwuka, Late Mr. O. Gbenga and others who made valuable contributions at one point or another and encouraged her in the course of the study. Her special thanks go to Dr. Metibemu Micheal for his assistance in ensuring the completion of this work. The researcher cannot forget to thank all the mathematics teachers who helped in administering the tests, especially Mr. Onyenwuchi Iheanacho, Mr. Obasi Chinedu and Mr Maduforo Ikechukwu. This study would not have been possible without the help of some research assistants who contributed immensely to its realization. The researcher is greatly indebted to all of them. She also appreciate her little children, Ugochinyere and Nzechimere, for enduring the deprivations they suffered in the course of this study. Finally, the researcher’s greatest thanks go to the Almighty God for giving her the grace, vision, peace, good health and journey mercies throughout the period of this study. 6 TABLE OF CONTENTS CONTENTS PAGE TITLE PAGE i CERTIFICATION ii APPROVAL PAGE iii DEDICATION iv ACKNOWLEDGEMENTS v TABLE OF CONTENTS vi LIST OF TABLES viii LIST OF CHARTS xi ABSTRACT xii CHAPTER ONE: INTRODUCTION 1 Background to the Study 1 Statement of the Problem 15 Purpose of the Study 17 Significance of the Study 18 Scope of the Study 19 Research Questions 19 Hypotheses 20 7 CHAPTER TWO: REVIEW OF RELATED LITERATURE 21 Conceptual Framework 22 Unidimensionality of test items 22 Local independence and test items 23 Reliability of a test 24 Test score equating 25 Theoretical Framework 26 Item response theory (IRT) 26 Theoretical Studies 28 IRT models 28 Applications of IRT 32 Model-data fit 35 Different forms of estimating reliability 36 Test equating requirement 44 Empirical Studies 51 Unidimensionality of Tests 51 Local Independence of Test Items 52 Reliability of a Test 54 Summary of Review of Related Literature 57 CHAPTER THREE: METHOD 58 Research Design 58 8 Area of the Study 58 Population of the Study 59 Sample and Sampling Technique 59 Instrument for Data Collection 60 Validation of Instrument 60 Reliability of the Instrument 60 Method of Data Collection 60 Method of Data Analysis 61 CHAPTER FOUR: PRESENTATION AND ANALYSIS OF DATA 67 Summary of Major Findings 113 CHAPTER FIVE: DISCUSSION OF RESULTS, CONCLUSION AND RECOMMENDATIONS 115 Discussion of Results 115 Conclusion 121 Implications of the Study 121 Recommendations 122 Limitation of the Study 122 Suggestions for Further Studies 123 References 124 Appendices 136 9 LIST OF TABLES PAGES Table 1: Design table for the Single Group Design (SG) 22 Table 2: Equivalent group Design (EG) 22 Table 3: Counterbalanced Design (CB) 23 Table 4: None Equivalent Groups with Anchor test Design 23 Table 5: Analysis of Total Variance Explained by Major Components of 2011 NECO Mathematics Test 40 Table 6: Analysis of Total Variance Explained by Major Components of 2012 NECO Mathematics Test 41 Table 7: Analysis of Total Variance Explained by Major Components of 2013 NECO Mathematics Test 42 Table 8: Analysis of Total Variance Explained by Major Components of 2014 NECO Mathematics Test 43 Table 9: Analysis of Total Variance Explained by Major Components of 2011 WAEC Mathematics Test 44 Table 10: Analysis of Total Variance Explained by Major Components of 2012 WAEC Mathematics Test 45 10 Table 11: Analysis of Total Variance Explained by Major Components of 2013 WAEC Mathematics Test 46 Table 12: Analysis of Total Variance Explained by Major Components of 2014 WAEC Mathematics Test 47 Table 13: Inter-correlation matrix of the polyphonic/tetrachoric correlation among 2011 NECO mathematics test items 48 Table 14: Summary of terachoric correlation coefficient among the 60-item 2011 NECO mathematics test 48 Table 15: Inter-correlation matrix of the polyphonic/tetrachoric correlation among 2012 NECO mathematics test items 49 Table 16: Summary of terachoric correlation coefficient among the 60-item 2012 NECO mathematics test 50 Table 17: Inter-correlation matrix of the polyphonic/tetrachoric correlation among 2013 NECO mathematics test items 50 Table 18: Summary of terachoric correlation coefficient among the 60-item 2013 NECO mathematics test 51 11 Table 19: Inter-correlation matrix of the polyphonic/tetrachoric correlation among 2014 NECO mathematics test items 51 Table 20: Summary of terachoric correlation coefficient among the 60-item 2014 NECO mathematics test 52 Table 21: Inter-correlation matrix of the polyphonic/tetrachoric correlation among 2011 WAEC mathematics test items 54 Table 22: Summary of terachoric correlation coefficient among the 60-item 2012 WAEC mathematics test 54 Table 23: Inter-correlation matrix of the polychoric/tetrachoric correlation among 2012 WAEC mathematics test items 55 Table 24: Summary of terachoric correlation coefficient among the 60-item 2012 WAEC mathematics test 56 Table 25: Inter-correlation matrix of the polychoric/tetrachoric correlation among 2013 WAEC mathematics test items 57 Table 26: Summary of terachoric correlation coefficient among the 60-item 2013 WAEC mathematics test 57 12 Table 27: Inter-correlation matrix of the polychoric/tetrachoric correlation among 2014 WAEC mathematics test items 58 Table 28: Summary of terachoric correlation coefficient among the 60-item 2014 WAEC mathematics test 59 Table 29: Distribution of the correlation coefficients of pairs of the NECO and WAEC items’ falling within ranges ≤0.099 – 0.299 and 0.300 and above. 60 Table 30: Examinees’ Ability scores, Mean and Standard deviation of NECO and WAEC. 61 Table 31: Correlation coefficient of NECO and WAEC mathematics test 62 Table 32: Reduction in uncertainty index of NECO and WAEC mathematics tests 62 Table 33: Comparison of reliability coefficients of NECO and WAEC mathematics tests 63 13 Table 34: Distribution of ability scores of examinees on NECO mathematics test transformation to WAEC scale and ability scores of examinees on WAEC mathematics test transformed to the scale of NECO test. 64 Table 35 : Z-test of correlation between NECO and WAEC mathematics multiple-choice test unidimensionality 71 Table 36: Z-test of reliability estimate of NECO and WAEC multiple-choice test 72 14 LIST OF CHARTS PAGES Scatter plot of examinees ability scores on NECO mathematics test of year 2011 and the examinees ability scores on the scale of WAEC mathematics test of 2011. 89 Scatter plot of examinees ability scores on WAEC mathematics test of year 2011 and the examinees ability scores on the scale of NECO mathematics test of 2011. 90 Scatter plot of examinees ability scores on NECO mathematics test of year 2012 and the examinees ability score on the scale of WAEC mathematics test of 2012 91 Scatter plot of examinees ability scores on WAEC mathematics test of year 2012 and the examinees ability score on the scale of NECO mathematics test of 2012 91 Scatter plot of examinees ability scores on WAEC mathematics test of year 2013 and the examinees ability score on the scale of NECO mathematics test of 2013 92 15 Scatter plot of examinees ability scores on NECO mathematics test of year 2013 and the examinees ability score on the scale of WAEC mathematics test of 2013 93 Scatter plot of examinees ability scores on NECO mathematics test of year 2014 and the examinees ability score on the scale of WAEC mathematics test of 2014 94 Scatter plot of examinees ability scores on WACE mathematics test of year 2014 and the examinees ability score on the scale of NECO mathematics test of 2014 95 16 ABSTRACT The study assessed the equivalence of West African Examination Council and the National Examination Council mathematics multiple-choice tests, from 2011 to 2014