The Kernel Method of Test Equating (Statistics for Social Science and Behavorial Sciences)

✍ Scribed by Alina A. von Davier Paul W. Holland Dorothy T. Thayer

• Year: 2003
• Tongue: English
• Leaves: 252
• Edition: 1
• Category: Library

✦ Synopsis

This book is aimed at (a) practitioners who need to equate tests-including those with these responsibilities in testing companies, state testing agencies and school districts; (b) statisticians and other research workers interested in the theory behind such work and the use of model based statistical methods of data smoothing in applied work; (c) advanced graduate students in psychometric and measurement programs. While there are other books on test equating, and books of the use of kernel smoothing, no one has published any work on the kernel method of test equating. It is something of a unifying idea in equating and brings together several methods into an organized whole rather than treating them as a group of disparate methods.

✦ Table of Contents

Contents......Page 12
Preface......Page 8
List of Notation......Page 16
1.1 Introduction......Page 24
1.2 The Notation Used in This Book......Page 28
1.3 The Linear Equating Function......Page 31
1.4 The Equipercentile Equating Function......Page 32
1.5 The Relationship Between Lin[sub(Y)] (x) and Equi[sub(Y)] (x)......Page 34
1.6 Data Collection Designs......Page 36
1.7 Sample Estimates......Page 37
1.8 A Summary of the New Material in This Book......Page 38
Part I—The Kernel Method of Test Equating: Theory......Page 40
2 Data Collection Designs......Page 42
2.1 The Equivalent-Groups Design (EG)......Page 44
2.2 The Single-Group Design (SG)......Page 45
2.3 The Counterbalanced Design (CB)......Page 50
2.4 Non-Equivalent groups with Anchor Test Design (NEAT)......Page 55
2.5 Random versus Spiraled Samples......Page 66
2.6 Summary......Page 67
3.1 The Five Steps of Kernel Equating: Overview......Page 68
3.2 Pre-smoothing Using Log-Linear Models......Page 70
3.3 Estimation of the Score Probabilities......Page 75
4.1 Continuization......Page 78
4.2 Equating......Page 87
5 Kernel Equating: The SEE and the SEED......Page 90
5.1 Introduction......Page 91
5.2 The δ-Method Divides the Problem in Three......Page 92
5.3 The SEE and the SEED for Kernel Equating......Page 96
5.4 The SEE and SEED for Chain Equating......Page 104
6 Kernel Equating versus Other Equating Methods......Page 110
6.1 KE versus Linear Equating......Page 111
6.2 KE versus the Percentile Rank Method......Page 113
6.3 Viewing PRM from the KE Perspective......Page 116
6.4 Advantages of KE over PRM......Page 117
Part II—The Kernel Method of Test Equating: Applications......Page 120
7 The Equivalent-Groups Design......Page 122
7.1 Pre-smoothing......Page 124
7.2 Estimation of the Score Probabilities......Page 126
7.3 Continuization......Page 127
7.4 Equating......Page 129
7.5 Standard Error of Equating......Page 131
7.6 Deciding Between ê[sub(Y)] (x) and Lin[sub(Y)] (x)......Page 133
8 The Single-Group Design......Page 136
8.1 Pre-smoothing......Page 139
8.2 Estimation of the Score Probabilities......Page 144
8.3 Continuization......Page 146
8.4 Equating......Page 147
8.5 Standard Error of Equating......Page 149
8.6 Deciding Between ê[sub(Y)] (x) and Lin[sub(Y)] (x)......Page 151
9 The Counterbalanced Design......Page 154
9.1 Pre-smoothing......Page 156
9.2 Estimation of the Score Probabilities......Page 162
9.3 Continuization......Page 164
9.4 Equating......Page 166
9.5 Standard Error of Equating......Page 168
9.6 Deciding Between ê[sub(Y1)] (x) and ê[sub(Y½)] (x)......Page 171
9.7 Diagnosis of the Equating Process......Page 172
9.8 Deciding Between ê[sub(Y½)] (x) and Lin[sub(Y½)] (x)......Page 173
9.9 Appendix: The Data Used in This Chapter......Page 175
10 The NEAT Design: Chain Equating......Page 178
10.1 Pre-smoothing......Page 182
10.2 Estimation of the Score Probabilities......Page 190
10.3 Continuization......Page 191
10.4 Equating......Page 193
10.5 Standard Error of Equating......Page 197
10.6 Deciding Between ê[sub(Y(CE))] (x) and Lin[sub(Y)] (x)......Page 198
11 The NEAT Design: Post-Stratification Equating......Page 202
11.1 Estimation of the Score Probabilities......Page 204
11.2 Continuization......Page 206
11.3 Equating......Page 207
11.4 Standard Error of Equating......Page 210
11.5 The Choice of the Target Population......Page 211
11.6 Deciding Between ê[sub(½Y)] (x) and Lin[sub(½Y)] (x)......Page 213
11.7 Comparing the KE Functions for PSE and CE......Page 215
11.8 CE versus PSE: Which One to Choose?......Page 217
A: The δ-Method......Page 220
B: Bivariate Smoothing......Page 222
B.1 Assessing the Fit of the Log-Linear Models......Page 224
C: Other Univariate Moments......Page 226
D: Review of the Use of Matrices in This Book......Page 228
Bibliography......Page 240
M......Page 246
W......Page 247
C......Page 248
F......Page 249
N......Page 250
T......Page 251
W......Page 252