Contents
Preface
Notation
1 Introduction and Concepts
1.1 Equating and Related Concepts
1.1.1 Test Forms and Test Specifications
1.1.2 Equating
1.1.3 Processes That Are Related to Equating
1.1.4 Equating and Score Scales
1.1.5 Equating and the Test Score Decline of the 1960s and 1970s
1.2 Equating and Scaling in Practice-A Brief Overview of This Book
1.3 Properties of Equating
1.3.1 Symmetry Property
1.3.2 Same Specifications Property
1.3.3 Equity Properties
1.3.4 Observed Score Equating Properties
1.3.5 Group Invariance Property
1.4 Equating Designs
1.4.1 Random Groups Design
1.4.2 Single Group Design
1.4.3 Single Group Design with Counterbalancing
1.4.4 ASVAB Problems with a Single Group Design
1.4.5 Common-Item Nonequivalent Groups Design
1.4.6 NAEP Reading Anomaly-Problems with Common Items
1.5 Error in Estimating Equating Relationships
1.6 Evaluating the Results of Equating
1.7 Testing Situations Considered
1.8 Preview
1.9 Exercises 2 Observed Score Equating Using the Random Groups Design
2.1 Mean Equating
2.2 Linear Equating
2.3 Properties of Mean and Linear Equating
2.4 Comparison of Mean and Linear Equating
2.5 Equipercentile Equating
2.5.1 Graphical Procedures
2.5.2 Analytic Procedures
2.5.3 Properties of Equated Scores in Equipercentile Equating
2.6 Estimating Observed Score Equating Relationships
2.7 Scale Scores
2.7.1 Linear Conversions
2.7.2 Truncation of Linear Conversions
2.7.3 Nonlinear Conversions
2.8 Equating Using Single Group Designs
2.9 Equating Using Alternate Scoring Schemes
2.10 Preview of What Follows
2.11 Exercises 3 Random Groups-Smoothing in Equipercentile Equating
3.1 A Conceptual Statistical Framework for Smoothing
3.2 Properties of Smoothing Methods
3.3 Presmoothing Methods
3.3.1 Polynomial Log-linear Method
3.3.2 Strong True Score Method
3.3.3 Illustrative Example
3.4 Postsmoothing Methods
3.4.1 Illustrative Example
3.5 Practical Issues in Equipercentile Equating
3.5.1 Summary of Smoothing Strategies
3.5.2 Equating Error and Sample Size
3.6 Exercises 4 Nonequivalent Groups-Linear Methods
4.1 Tucker Method
4.1.1 Linear Regression Assumptions
4.1.2 Conditional Variance Assumptions
4.1.3 Intermediate Results
4.1.4 Final Results
4.1.5 Special Cases
4.2 Levine Observed Score Method
4.2.1 Correlational Assumptions
4.2.2 Linear Regression Assumptions
4.2.3 Error Variance Assumptions
4.2.4 Intermediate Results
4.2.5 General Results
4.2.6 Classical Congeneric Model Results
4.3 Levine True Score Method
4.3.1 Results
4.3.2 First-Order Equity
4.4 Illustrative Example and Other Topics
4.4.1 Illustrative Example
4.4.2 Synthetic Population Weights
4.4.3 Mean Equating
4.4.4 Decomposing Observed Di.erences in Means and Variances
4.4.5 Relationships Among Tucker and Levine Equating Methods
4.4.6 Scale Scores
4.5 Appendix Proof that ó2 s (TX) = ã2 1ó2 s (TV ) Under the Classical Congeneric Model
4.6 Exercises 5 Nonequivalent Groups-Equipercentile Methods
5.1 Frequency Estimation Equipercentile Equating
5.1.1 Conditional Distributions
5.1.2 Frequency Estimation Method
5.1.3 Evaluating the Frequency Estimation Assumption
5.1.4 Numerical Example
5.1.5 Estimating the Distributions
5.2 Braun-Holland Linear Method
5.3 Chained Equipercentile Equating
5.4 Illustrative Example
5.4.1 Illustrative Results
5.4.2 Comparison Among Methods
5.4.3 Practical Issues in Equipercentile Equating with Common Items
5.5 Exercises 6 Item Response Theory Methods
6.1 Some Necessary IRT Concepts
6.1.1 Unidimensionality and Local Independence Assumptions
6.1.2 IRT Models
6.1.3 IRT Parameter Estimation

By providing an introduction to test equating which both discusses the most frequently used equating methodologies and covering many of the practical issues involved, this volume expands upon the coverage of the first edition by providing a new chapter on test scaling and a second on test linking.