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University of Oklahoma Graduate College A UNIVERSITY OF OKLAHOMA GRADUATE COLLEGE A PSYCHOMETRIC ANALYSIS OF THE STATISTICS CONCEPT INVENTORY A DISSERTATION SUBMITTED TO THE GRADUATE FACULTY in partial fulfillment of the requirements for the degree of Doctor of Philosophy By ANDREA STONE Norman, Oklahoma 2006 UMI Number: 3208004 UMI Microform 3208004 Copyright 2006 by ProQuest Information and Learning Company. All rights reserved. This microform edition is protected against unauthorized copying under Title 17, United States Code. ProQuest Information and Learning Company 300 North Zeeb Road P.O. Box 1346 Ann Arbor, MI 48106-1346 Copyright by ANDREA STONE 2006 All Rights Reserved. ACKNOWLEDGEMENTS The researcher wishes to acknowledge the support provided by a grant from the National Science Foundation (DUE-0206977). Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author and do not necessarily reflect the views of the National Science Foundation. iv TABLE OF CONTENTS Chapter 1: Literature...........................................................................................................1 1.1 Force Concept Inventory........................................................................................... 5 1.2 Other Concept Inventories-Related Efforts ............................................................ 13 1.2.1 Determining and Interpreting Resistive Electric Circuit Concepts Test (DIRECT) ................................................................................................................. 14 1.2.2 Test of Understanding Graphs in Kinematics (TUG-K).................................. 15 1.2.3 Statics Concept Inventory................................................................................ 17 1.2.4 Force and Motion Conceptual Evaluation (FMCE)........................................ 19 1.2.5 Signals and Systems Concept Inventory (SSCI).............................................. 19 1.2.6 Conceptual Survey of Electricity and Magnetism (CSEM)............................. 22 1.2.7 Thermal and Transport Science Concept Inventory ........................................ 25 1.2.8 Wave Concept Inventory ................................................................................. 26 1.2.9 Dynamics Concept Inventory .......................................................................... 27 1.2.10 Fluid Mechanics Concept Inventory (FMCI) ................................................ 29 1.2.11 Chemistry Concept Inventory........................................................................ 29 1.2.12 Heat Transfer Concept Inventory (HTCI)...................................................... 31 1.2.13 Materials Concept Inventory (MCI) .............................................................. 32 1.2.14 Other Concept Inventories ............................................................................. 33 1.2.15 Common Themes........................................................................................... 37 1.3 Statistics Education Research ................................................................................. 39 1.3.1 Probabilistic Thinking/General Reasoning Frameworks................................. 39 1.3.2 Averages/Measures of Central Tendency ........................................................ 46 1.3.3 Sampling Distributions .................................................................................... 51 1.4 Other Instruments for Statistics Assessment........................................................... 54 1.5 Test Theory Background......................................................................................... 60 1.5.1 Classical Test Theory Model ........................................................................... 61 1.5.2 Reliability......................................................................................................... 62 1.5.3 Factor Analytic Model ..................................................................................... 66 1.5.4 Item Response Theory ..................................................................................... 68 1.5.5 Validity ............................................................................................................ 75 1.5.6 Summary.......................................................................................................... 78 Chapter 2: A Classical Test Theory Perspective .............................................................. 79 2.1 Development of the Statistics Concept Inventory .................................................. 79 2.2 Participants and Data Collection............................................................................. 89 2.3 Results..................................................................................................................... 94 2.3.1 Posttest Scores ................................................................................................. 94 2.3.2 Gains ................................................................................................................ 98 2.3.3 Correlation with Final Course Grades ............................................................. 99 2.3.4 Coefficient Alpha........................................................................................... 102 Chapter 3: An Item Analysis of the Statistics Concepts Inventory ................................ 104 3.1 Item Analysis Tools .............................................................................................. 104 3.2 Statistics Concept Inventory: Annotated Version................................................. 110 Chapter 4 An Item Response Theory Perspective .......................................................... 163 4.1 The Data Set.......................................................................................................... 163 v 4.2 The Two Parameter Logistic Model (2PL)........................................................... 166 4.2.1 Question Comparisons................................................................................... 168 4.2.2 The Test as a Whole....................................................................................... 178 4.3 The Nominal Response Model.............................................................................. 180 Chapter 5 Discussion and Directions for Future Research............................................. 192 5.1 Scoring .................................................................................................................. 192 5.1.1 Obtaining Ability Estimates........................................................................... 193 5.1.2 Gains .............................................................................................................. 196 5.2 Model-Data Fit...................................................................................................... 198 5.2.1 Unidimensionality Assumption ..................................................................... 199 5.2.2 Minimal Guessing Assumption...................................................................... 203 5.2.3 Non-speeded Assumption .............................................................................. 204 5.2.4 Model Features and Behavior ........................................................................ 205 5.3 Further analysis..................................................................................................... 214 5.3.1 Factor Analysis .............................................................................................. 214 5.3.2 Investigation of Test Bias .............................................................................. 215 5.3.3 Confidence Analysis ...................................................................................... 217 5.4 Future Revisions ................................................................................................... 218 5.5 Reliability and Validity......................................................................................... 220 5.6 Conclusions........................................................................................................... 224 References....................................................................................................................... 225 Appendix A..................................................................................................................... 236 Appendix B ..................................................................................................................... 256 vi LIST OF TABLES Table 1-1: A portion of the item classification for the Force Concept Inventory (Hestenes et al., 1992). ................................................................................................................ 6 Table 1-2: Summary of FCI pre and post outcome data, based on Halloun and Hestenes (1985b)........................................................................................................................ 8 Table 1-3: A portion of the taxonomy of misconceptions developed from the Force Concept Inventory (Hestenes et al., 1992).................................................................. 9 Table 1-4: Summary of results from the Determining and Interpreting Resistive Electric Circuit Concepts Test (DIRECT) (Engelhardt & Beichner, 2004)........................... 14 Table 1-5: A comparison of the percentage of students in each quartile on the Statics Concept Inventory and the final
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