Test equating, scaling, and linking: methods and practices
Test equating methods are used with many standardized tests in education and psychology to ensure that scores from multiple test forms can be used interchangeably. In recent years, researchers from the education, psychology, and statistics communities have contributed to the rapidly growing statisti...
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| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York
Springer
2004
|
| Ausgabe: | 2. ed. |
| Schriftenreihe: | Statistics for social science and public policy
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Zusammenfassung: | Test equating methods are used with many standardized tests in education and psychology to ensure that scores from multiple test forms can be used interchangeably. In recent years, researchers from the education, psychology, and statistics communities have contributed to the rapidly growing statistical and psychometric methodologies used in test equating. This book provides an introduction to test equating which both discusses the most frequently used equating methodologies and covers many of the practical issues involved. This second edition expands upon the coverage of the first edition by providing a new chapter on test scaling and a second on test linking. Test scaling is the process of developing score scales that are used when scores on standardized tests are reported. In test linking, scores from two or more tests are related to one another. Linking has received much recent attention, due largely to investigations of linking similarly named tests from different test publishers or tests constructed for different purposes. The expanded coverage in the second edition also includes methodology for using polytomous item response theory in equating. |
| Beschreibung: | Frühere Aufl. u.d.T.: Kolen, Michael J.: Test equating |
| Beschreibung: | xxvi, 548 S. graph. Darst. 25 cm |
| ISBN: | 0387400869 |
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| 100 | 1 | |a Kolen, Michael J. |e Verfasser |0 (DE-588)1047378051 |4 aut | |
| 245 | 1 | 0 | |a Test equating, scaling, and linking |b methods and practices |c Michael J. Kolen ; Robert L. Brennan |
| 250 | |a 2. ed. | ||
| 264 | 1 | |a New York |b Springer |c 2004 | |
| 300 | |a xxvi, 548 S. |b graph. Darst. |c 25 cm | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Statistics for social science and public policy | |
| 500 | |a Frühere Aufl. u.d.T.: Kolen, Michael J.: Test equating | ||
| 520 | 3 | |a Test equating methods are used with many standardized tests in education and psychology to ensure that scores from multiple test forms can be used interchangeably. In recent years, researchers from the education, psychology, and statistics communities have contributed to the rapidly growing statistical and psychometric methodologies used in test equating. This book provides an introduction to test equating which both discusses the most frequently used equating methodologies and covers many of the practical issues involved. This second edition expands upon the coverage of the first edition by providing a new chapter on test scaling and a second on test linking. Test scaling is the process of developing score scales that are used when scores on standardized tests are reported. In test linking, scores from two or more tests are related to one another. Linking has received much recent attention, due largely to investigations of linking similarly named tests from different test publishers or tests constructed for different purposes. The expanded coverage in the second edition also includes methodology for using polytomous item response theory in equating. | |
| 650 | 4 | |a Examens - Correction | |
| 650 | 4 | |a Examens - Interprétation des résultats | |
| 650 | 4 | |a Examens - Élaboration | |
| 650 | 7 | |a Psychometrie |2 swd | |
| 650 | 7 | |a Statistisches Modell |2 swd | |
| 650 | 7 | |a Test |2 swd | |
| 650 | 4 | |a Tests et mesures en éducation - Normes | |
| 650 | 4 | |a Tests psychologiques - Normes | |
| 650 | 7 | |a Vergleich |2 swd | |
| 650 | 4 | |a Examinations |x Scoring | |
| 650 | 4 | |a Examinations |x Interpretation | |
| 650 | 4 | |a Examinations |x Design and construction | |
| 650 | 4 | |a Psychological tests |x Standards | |
| 650 | 4 | |a Educational tests and measurements |x Standards | |
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Datensatz im Suchindex
| _version_ | 1804135337241346048 |
|---|---|
| adam_text | Contents
Preface
vii
Notation
xxi
1
Introduction and Concepts
1
1.1
Equating and Related Concepts
................ 1
1.1.1
Test Forms and Test Specifications
.......... 2
1.1.2
Equating
........................ 2
1.1.3
Processes That
Áre
Related to Equating
....... 3
1.1.4
Equating and Score Scales
.............. . 4
1.1.5
Equating and the Test Score Decline of the
1960s
and
1970s.......................... ?
1.2
Equating and Scaling In Practice—
Â
Brief Overview of This
Book
............................... 7
1.3
Properties of Equating
..................... 9
1.3.1
Symmetry Property
.................. 10
1.3.2
Same Specifications Property
............. 10
1.3.3
Equity Properties
.................... 10
1.3.4
Observed Score Equating Properties
......... 12
1.3.5
Group Inmriaaee Properly
.............. 13
1.4
Equating Designs
........................ 13
1.4.1
Random Groups Desiga
................ 13
1.4.2
Single Croup Design
.................. 15
1.4.3
Siagle Group Design with CfeimterbslaneiBg
..... 15
xiv Contents
1.4.4
ASVAB
Problems
with a Single Group Design
... 17
1.4.5
Common-Item
Nonequivalent
Groups Design
.... 19
1.4.6
NAEP Reading Anomaly
—
Problems with Common
Items
.......................... 22
1.5
Error in Estimating Equating Relationships
......... 23
1.6
Evaluating the Results of Equating
.............. 24
1.7
Testing Situations Considered
................. 25
1.8
Preview
............................. 26
1.9
Exercises
............................ 27
2
Observed Score Equating Using the Random Groups De¬
sign
29
2.1
Mean Equating
......................... 30
2.2
Linear Equating
........................ 31
2.3
Properties of Mean and Linear Equating
........... 32
2.4
Comparison of Mean and Linear Equating
.......... 34
2.5
Equipercentile Equating
.................... 36
2.5.1
Graphical Procedures
................. 39
2.5.2
Analytic Procedures
.................. 43
2.5.3
Properties of Equated Scores in Equipercentile Equat¬
ing
............................ 46
2.6
Estimating Observed Score Equating Relationships
..... 48
2.7
Scale Scores
........................... 52
2.7.1
Linear Conversions
................... 54
2.7.2
Truncation of Linear Conversions
........... 55
2.7.3
Nonlinear Conversions
................. 56
2.8
Equating Using Single Group Designs
............ 62
2.9
Equating
Usißg
Alternate Scoring Schemes
......... 63
2.10
Preview of What Follows
................... 64
2.11
Exercises
............................ 64
3
Random Groups
—
Smoothing In Equipercentile Equating
67
3.1
A Conceptual Statistical Framework for Smoothing
..... 68
3.2
Properties of Smoothing Methods
............... 72
3.3
Presmootbing Methods
..................... 73
3.3.1
Polynomial Log-Linear Method
............ 74
3.3.2
Strong Tfrue Score Method
............... 75
3.3.3
Itostrative Example
.................. 77
3.4
Postsmoothiag Methods
.................... 84
3.4.1
Illustrative Example
.................. 89
3.5
Practical Issues in fkplpereeiitie Equating
.........
il
3.5.1
Ѕшшшгу
of Smoothing Strategies
.......... §1
8.SJ Equating Error
äad
Sample
Sìa»
. ,......... 98
3-І
Exercises
............................ 100
Contents xv
Nonequivalent
Groups
—
Linear Methods
103
4.1
Tucker Method
......................... 105
4.1.1
Linear Regression Assumptions
............ 106
4.1.2
Conditional Variance Assumptions
.......... 106
4.1.3
Intermediate Results
.................. 107
4.1.4
Final Results
...................... 108
4.1.5
Special Cases
...................... 108
4.2
Levine
Observed Score Method
................ 109
4.2.1
Correlational Assumptions
............... 109
4.2.2
Linear Regression Assumptions
............ 110
4.2.3
Error Variance Assumptions
.............. 110
4.2.4
Intermediate Results
..................
Ill
4.2.5
General Results
.....................
Ill
4.2.6
Classical Congeneric Model Results
.......... 112
4.3
Levine
True Score Method
................... 115
4.3.1
Results
......................... 116
4.3.2
First-Order Equity
................... 118
4.4
Illustrative Example and Other Topics
............ 120
4.4.1
Illustrative Example
.................. 121
4.4.2
Synthetic Population Weights
............. 124
4.4.3
Mean Equating
..................... 125
4.4.4
Decomposing Observed Differences in Means and Vari¬
ances
.......................... 125
4.4.5
Relationships Among Tucker and
Levine
Equating
Methods
......................... 128
4.4.6
Scale Scores
....................... 130
4.5
Appendix: Proof
<Ą
(Τχ) = η σξ(Τγ)
Under Classical Con¬
generic Model
.......................... 131
4.6
Exercises
............................ 132
Nonequivalent Groups
—
Eqtiipereentlie Methods
135
5.1
Frequency Estimation EquipercentOe Equating
....... 135
5.1.1
Condiţional
Distributions
............... 136
5.1.2
Frequency Estimation Method
............ 136
5.1.3
Evaluating the Frequency Estimation Assumption
. 138
5.1.4
Numerical Example
.................. 139
5.1.5
Estimating the Distributions
............. 142
5.2
Вгашї
-Holand
Liaear Method
................ 144
5.3
Chaìaeé
Equipereenffle Equating
............... 145
5.4
Illustrative Example
...................... 147
5.4.1
Dlustrative Results
................... 147
5.4.2
ComparisoH
Anaong
Methods
............. 151
5.4.3
Practical Issues in Ikpipereentile Bqaatiag with Com¬
mon Items
........................ 152
5.5
Exercises
............................ 153
xvi Contents
6
Item Response Theory Methods
155
6.1
Some Necessary
IRT
Concepts
. ............... 156
6.1.1
Unidhnensionality and Local Independence Assump¬
tions
........................... 156
6.1.2
IRT
Models
....................... 157
6.1.3
IRT
Parameter Estimation
.............. 160
6.2
Transformations of
IRT
Scales
................. 161
6.2.1
Transformation Equations
............... 162
6.2.2
Demonstrating the Appropriateness of Scale Trans¬
formations
........................ 162
6.2.3
Expressing A and
В
Constants
............ 163
6.2.4
Expressing A and
В
Constants in Terms of Groups
of Items and/or Persons
................ 164
6.3
Transforming
IRT
Scales When Parameters Are Estimated
165
6.3.1
Designs
......................... 166
6.3.2
Mean/Sigma and Mean/Mean Transformation Meth¬
ods
............................ 167
6.3.3
Characteristic Curve Transformation Methods
. . . 168
6.3.4
Comparisons Among Scale Transformation Methods
173
6.4
Equating and Scaling
...................... 175
6.5
Equating True Scores
...................... 176
6.5.1
Test Characteristic Curves
............... 176
6.5.2
Trae
Score Equating Process
............. 176
6.5.3
The Newton-RaphsoK Method
............ 177
6.5.4
Using True Score Equating with Observed Scores
. . 180
6.6
Equating Observed Scores
................... 181
6.7
IRT
Trae
Score Versus
IRT
Observed Score Equating
.... 184
6.8
Illustrative Example
...................... 185
6.8.1
Item Parameter Estimation and Scaling
....... 185
6.8.2
ШТ
True Score Equating
............... 191
6-8.3
IRT
Observed Score Equating
............. 194
6.8.4 Rasch
Equating
..................... 198
6.9
Using
IRT
Calibrated Item Pools
............... 201
6.9.1
Common-Item Equating to a Calibrated Pool
.... 201
6.9.2
Item Preeqaating
.................... 205
6.9.3
Robustness to Violations of
IRT
Assumptions
.... 207
6.10
Equating with Polytomous
IRT
................ 208
6.10.1
Polytomous
IRT
Models for Ordered Responses
... 209
6.10.2
Scormg Functions, Item Response Riaction, and Test
Characteristic Curve
.................. 214
6.10.3
Parameter Estimation and Scale Transformation with
Poîytomous
IET
Models
................
2iS
6Д0.4
True Score Equating
.................. 210
§.10.5
Observed Score Equating
............... 219
6.10.6
Example Using the Graded Response Model
..... 220
Contents xvii
6.11
Practical Issues and Caveat
.................. 227
6.12
Exercises
............................ 228
Standard Errors of Equating
231
7.1
Definition of Standard Error of Equating
........... 232
7.2
The Bootstrap
......................... 235
7.2.1
Standard Errors Using the Bootstrap
......... 235
7.2.2
Standard Errors of Equating
............. 236
7.2.3
Parametric Bootstrap
................. 238
7.2.4
Standard Errors of Equipercentile Equating with Smooth¬
ing
............................240
7.2.5
Standard Errors of Scale Scores
............ 241
7.2.6
Standard Errors of Equating Chains
......... 242
7.2.7
Mean Standard Error of Equating
.......... 243
7.2.8
Caveat
.......................... 244
7.3
The Delta Method
....................... 245
7.3.1
Mean Equating Using Single Group and Random Groups
Designs
......................... 246
7.3.2
Linear Equating Using the Random Groups Design
. 247
7.3.3
Equipercentile Equating Using the Random Groups
Design
.......................... 248
7.3.4
Standard Errors for Other Designs
.......... 249
7.3.5
Approximations
..................... 251
7.3.6
Standard Errors for Scale Scores
........... 253
7.3.7
Standard Errors of Equating Chains
......... 254
7.3.8
Using Delta Method Standard Errors
......... 255
7.4
Using Standard Errors in Practice
.............. 261
7.5
Exercises
............................ 263
Practical Issues in Equating
2β?
8.1
Equating and the Test Development Process
......... 269
8.1.1
Test Specifications
................... 269
8.1.2
Characteristics of
Совшоп-ІІегв
Sets
........ 271
8.1.3
Changes in Test Specifications
............ 272
8.2
Data Collection: DesigH aad Implementation
........ 273
8.2.1
Choosing Among Equating Designs
.......... 273
8.2.2
Developing Equating Linkage Plans
......... 277
8.2.3
Examinee Groaps Used in Equating
......... 285
8.2.4
Sample Size Requirements
............... 288
8.3
Choosiag from Among the Statistical Procedures
...... 290
8.8.1
Equating Criteria in Research Studies
....... .
2§0
8-3.2
Characteristics of Equating Situations
........ 292
8.4
Choosing from Among Equating Results
........... 286
8.41
Equating Versus Not Equating
............ 296
8.4.2
Use of Robustness Cheeks
...............
2§§
xviii
Contents
8.4.3
Choosing from Among Results in the Random Groups
Design
.......................... 297
8.4.4
Choosing from Among Results in the Common-Item
Nonequivalent
Groups Design
............. 298
8.4.5
Use of Consistency Checks
............... 298
8.4.6
Equating and Score Scales
............... 300
8.4.7
Assessing First- and Second-Order Equity for Scale
Scores
.......................... 301
8.5
Importance of Standardization Conditions and Quality Con¬
trol Procedures
......................... 306
8.5.1
Test Development
................... 307
8.5.2
Test Administration and Standardization Conditions
307
8.5.3
Quality Control
..................... 309
8.5.4
Reequating
....................... 310
8.6
Conditions Conducive to Satisfactory Equating
....... 312
8.7
Comparability Issues in Special Circumstances
....... 312
8.7.1
Comparability
fettes
with Computer-Based Tests
. . 314
8.7.2
Comparability of Performance Assessments
..... 320
8.7.3
Score Comparability with Optional Test Sections
. . 323
8.8
Conclusion
........................... 324
8.9
Exercises
............................ 325
9
Score Scales
329
9.1
Scaling Perspectives
...................... 331
§.2
Score Transformations
..................... 336
9.3
Incorporating Normative Information
............ 337
§.3.1
Linear Transformations
................ 337
9.3.2
Nonlinear Transformations
.............. 338
9.3.3
Example: Normalized Scale Scores
.......... 340
9.3.4
Importance of Norm Group in Setting the Score Scale
344
9.4
Incorporating Score Precision Information
.......... 345
9.4.1
Rules of Thumb for Number of Distinct Score Points
345
9.4.2
Liaearly Transformed Score Scales with a Given Stan¬
dard Error of Measurement
.............. 348
9.4.3
Score Scales with Approximately Equal Conditional
Standard Errors of Measurement
.......... . 348
9.4.4
Example: Incorporating Score Precision
....... 351
8.4.5
Evaluating
Psychometrie
Properties of Scale Scores
. 354
9.4.6
The
ΙΚΓ
i-Scałe
as a Score Scale
........... 358
9.5
Incorporating Content Information
.............. 358
9.5.1
Item Mapping
..................... 358
9.5.2
Scale Anchoring
.................... 361
§.5.3
Standard Setting
.................... 361
0.5.4
Numerical Example
.................. 364
§.5.5
Practical UseMoeffi
.................. 366
Contents xix
9.6
Maintaining Score Scales
.................... 366
9.7
Scales for Test Batteries and Composites
........... 368
9.7.1
Test Batteries
...................... 368
9.7.2
Composite Scores
.................... 369
9.7.3
Maintaining Scales for Batteries and Composites
. . 371
9.8
Vertical Scaling and Developmental Score Scales
...... 372
9.8.1
Structure of Batteries
................. 373
9.8.2
Type of Domain Being Measured
........... 375
9.8.3
Definition of Growth
.................. 376
9.8.4
Designs for Data Collection for Vertical Scaling
. . . 377
9.8.5
Test Scoring
....................... 381
9.8.6
Hieronymus Statistical Methods
........... 381
9.8.7
Thurstone Statistical Methods
............ 383
9.8.8
IRT
Statistical Methods
................ 387
9.8.9
Thurstone Illustrative Example
............ 393
9.8.10
IRT
Illustrative Example
............... 401
9.8.11
Statistics for Comparing Scaling Results
....... 410
9.8.12
Some Limitations of Vertically Scaled Tests
..... 412
9.8.13
Research on Vertical Scaling
.............. 414
9.9
Exercises
............................ 418
10
Linking
423
10.1
Linking Categorization Schemes and Criteria
........ 424
10.1.1
Types of Linking
.................... 427
10.1.2
Mislevy/Linn Taxonomy
................ 429
10.1.3
Degrees of Similarity
.................. 433
10.2
Group
Invariance
........................ 437
10.2.1
Statistical Methods Using Observed Scores
..... 437
10.2.2
Statistics for Overall Group
Invariance
........ 441
10.2.3
Statistics for Pairwise Group
Invariance
....... 443
10.2.4
Example: ACT and ITED Science Tests
....... 444
10.3
Additional
Exampies
...................... 465
10.3.1
Extended Time
..................... 465
10.3.2
Test Adaptations and Translated Tests
........ 467
10.4
Discussion
............................ 469
10.5
Exercises
............................ 470
11
Current and Stature Challenges 4?3
11.1
Score Scales
........................... 473
11.2
Equating
........................... . 474
11.3
Vertical Scaling
.........................
4?5
11.4
Linking
............................. 475
11.5
Summary
............................
4?6
References 4?7
xx
Contents
Appendix A: Answers to Exercises
511
Appendix B: Computer Programs
533
Index
535
|
| adam_txt |
Contents
Preface
vii
Notation
xxi
1
Introduction and Concepts
1
1.1
Equating and Related Concepts
. 1
1.1.1
Test Forms and Test Specifications
. 2
1.1.2
Equating
. 2
1.1.3
Processes That
Áre
Related to Equating
. 3
1.1.4
Equating and Score Scales
. . 4
1.1.5
Equating and the Test Score Decline of the
1960s
and
1970s. ?
1.2
Equating and Scaling In Practice—
Â
Brief Overview of This
Book
. 7
1.3
Properties of Equating
. 9
1.3.1
Symmetry Property
. 10
1.3.2
Same Specifications Property
. 10
1.3.3
Equity Properties
. 10
1.3.4
Observed Score Equating Properties
. 12
1.3.5
Group Inmriaaee Properly
. 13
1.4
Equating Designs
. 13
1.4.1
Random Groups Desiga
. 13
1.4.2
Single Croup Design
. 15
1.4.3
Siagle Group Design with CfeimterbslaneiBg
. 15
xiv Contents
1.4.4
ASVAB
Problems
with a Single Group Design
. 17
1.4.5
Common-Item
Nonequivalent
Groups Design
. 19
1.4.6
NAEP Reading Anomaly
—
Problems with Common
Items
. 22
1.5
Error in Estimating Equating Relationships
. 23
1.6
Evaluating the Results of Equating
. 24
1.7
Testing Situations Considered
. 25
1.8
Preview
. 26
1.9
Exercises
. 27
2
Observed Score Equating Using the Random Groups De¬
sign
29
2.1
Mean Equating
. 30
2.2
Linear Equating
. 31
2.3
Properties of Mean and Linear Equating
. 32
2.4
Comparison of Mean and Linear Equating
. 34
2.5
Equipercentile Equating
. 36
2.5.1
Graphical Procedures
. 39
2.5.2
Analytic Procedures
. 43
2.5.3
Properties of Equated Scores in Equipercentile Equat¬
ing
. 46
2.6
Estimating Observed Score Equating Relationships
. 48
2.7
Scale Scores
. 52
2.7.1
Linear Conversions
. 54
2.7.2
Truncation of Linear Conversions
. 55
2.7.3
Nonlinear Conversions
. 56
2.8
Equating Using Single Group Designs
. 62
2.9
Equating
Usißg
Alternate Scoring Schemes
. 63
2.10
Preview of What Follows
. 64
2.11
Exercises
. 64
3
Random Groups
—
Smoothing In Equipercentile Equating
67
3.1
A Conceptual Statistical Framework for Smoothing
. 68
3.2
Properties of Smoothing Methods
. 72
3.3
Presmootbing Methods
. 73
3.3.1
Polynomial Log-Linear Method
. 74
3.3.2
Strong Tfrue Score Method
. 75
3.3.3
Itostrative Example
. 77
3.4
Postsmoothiag Methods
. 84
3.4.1
Illustrative Example
. 89
3.5
Practical Issues in fkplpereeiitie Equating
.
il
3.5.1
Ѕшшшгу
of Smoothing Strategies
. §1
8.SJ Equating Error
äad
Sample
Sìa»
. ,. 98
3-І
Exercises
. 100
Contents xv
Nonequivalent
Groups
—
Linear Methods
103
4.1
Tucker Method
. 105
4.1.1
Linear Regression Assumptions
. 106
4.1.2
Conditional Variance Assumptions
. 106
4.1.3
Intermediate Results
. 107
4.1.4
Final Results
. 108
4.1.5
Special Cases
. 108
4.2
Levine
Observed Score Method
. 109
4.2.1
Correlational Assumptions
. 109
4.2.2
Linear Regression Assumptions
. 110
4.2.3
Error Variance Assumptions
. 110
4.2.4
Intermediate Results
.
Ill
4.2.5
General Results
.
Ill
4.2.6
Classical Congeneric Model Results
. 112
4.3
Levine
True Score Method
. 115
4.3.1
Results
. 116
4.3.2
First-Order Equity
. 118
4.4
Illustrative Example and Other Topics
. 120
4.4.1
Illustrative Example
. 121
4.4.2
Synthetic Population Weights
. 124
4.4.3
Mean Equating
. 125
4.4.4
Decomposing Observed Differences in Means and Vari¬
ances
. 125
4.4.5
Relationships Among Tucker and
Levine
Equating
Methods
. 128
4.4.6
Scale Scores
. 130
4.5
Appendix: Proof
<Ą
(Τχ) = η\σξ(Τγ)
Under Classical Con¬
generic Model
. 131
4.6
Exercises
. 132
Nonequivalent Groups
—
Eqtiipereentlie Methods
135
5.1
Frequency Estimation EquipercentOe Equating
. 135
5.1.1
Condiţional
Distributions
. 136
5.1.2
Frequency Estimation Method
. 136
5.1.3
Evaluating the Frequency Estimation Assumption
. 138
5.1.4
Numerical Example
. 139
5.1.5
Estimating the Distributions
. 142
5.2
Вгашї
-Holand
Liaear Method
. 144
5.3
Chaìaeé
Equipereenffle Equating
. 145
5.4
Illustrative Example
. 147
5.4.1
Dlustrative Results
. 147
5.4.2
ComparisoH
Anaong
Methods
. 151
5.4.3
Practical Issues in Ikpipereentile Bqaatiag with Com¬
mon Items
. 152
5.5
Exercises
. 153
xvi Contents
6
Item Response Theory Methods
155
6.1
Some Necessary
IRT
Concepts
. . 156
6.1.1
Unidhnensionality and Local Independence Assump¬
tions
. 156
6.1.2
IRT
Models
. 157
6.1.3
IRT
Parameter Estimation
. 160
6.2
Transformations of
IRT
Scales
. 161
6.2.1
Transformation Equations
. 162
6.2.2
Demonstrating the Appropriateness of Scale Trans¬
formations
. 162
6.2.3
Expressing A and
В
Constants
. 163
6.2.4
Expressing A and
В
Constants in Terms of Groups
of Items and/or Persons
. 164
6.3
Transforming
IRT
Scales When Parameters Are Estimated
165
6.3.1
Designs
. 166
6.3.2
Mean/Sigma and Mean/Mean Transformation Meth¬
ods
. 167
6.3.3
Characteristic Curve Transformation Methods
. . . 168
6.3.4
Comparisons Among Scale Transformation Methods
173
6.4
Equating and Scaling
. 175
6.5
Equating True Scores
. 176
6.5.1
Test Characteristic Curves
. 176
6.5.2
Trae
Score Equating Process
. 176
6.5.3
The Newton-RaphsoK Method
. 177
6.5.4
Using True Score Equating with Observed Scores
. . 180
6.6
Equating Observed Scores
. 181
6.7
IRT
Trae
Score Versus
IRT
Observed Score Equating
. 184
6.8
Illustrative Example
. 185
6.8.1
Item Parameter Estimation and Scaling
. 185
6.8.2
ШТ
True Score Equating
. 191
6-8.3
IRT
Observed Score Equating
. 194
6.8.4 Rasch
Equating
. 198
6.9
Using
IRT
Calibrated Item Pools
. 201
6.9.1
Common-Item Equating to a Calibrated Pool
. 201
6.9.2
Item Preeqaating
. 205
6.9.3
Robustness to Violations of
IRT
Assumptions
. 207
6.10
Equating with Polytomous
IRT
. 208
6.10.1
Polytomous
IRT
Models for Ordered Responses
. 209
6.10.2
Scormg Functions, Item Response Riaction, and Test
Characteristic Curve
. 214
6.10.3
Parameter Estimation and Scale Transformation with
Poîytomous
IET
Models
.
2iS
6Д0.4
True Score Equating
. 210
§.10.5
Observed Score Equating
. 219
6.10.6
Example Using the Graded Response Model
. 220
Contents xvii
6.11
Practical Issues and Caveat
. 227
6.12
Exercises
. 228
Standard Errors of Equating
231
7.1
Definition of Standard Error of Equating
. 232
7.2
The Bootstrap
. 235
7.2.1
Standard Errors Using the Bootstrap
. 235
7.2.2
Standard Errors of Equating
. 236
7.2.3
Parametric Bootstrap
. 238
7.2.4
Standard Errors of Equipercentile Equating with Smooth¬
ing
.240
7.2.5
Standard Errors of Scale Scores
. 241
7.2.6
Standard Errors of Equating Chains
. 242
7.2.7
Mean Standard Error of Equating
. 243
7.2.8
Caveat
. 244
7.3
The Delta Method
. 245
7.3.1
Mean Equating Using Single Group and Random Groups
Designs
. 246
7.3.2
Linear Equating Using the Random Groups Design
. 247
7.3.3
Equipercentile Equating Using the Random Groups
Design
. 248
7.3.4
Standard Errors for Other Designs
. 249
7.3.5
Approximations
. 251
7.3.6
Standard Errors for Scale Scores
. 253
7.3.7
Standard Errors of Equating Chains
. 254
7.3.8
Using Delta Method Standard Errors
. 255
7.4
Using Standard Errors in Practice
. 261
7.5
Exercises
. 263
Practical Issues in Equating
2β?
8.1
Equating and the Test Development Process
. 269
8.1.1
Test Specifications
. 269
8.1.2
Characteristics of
Совшоп-ІІегв
Sets
. 271
8.1.3
Changes in Test Specifications
. 272
8.2
Data Collection: DesigH aad Implementation
. 273
8.2.1
Choosing Among Equating Designs
. 273
8.2.2
Developing Equating Linkage Plans
. 277
8.2.3
Examinee Groaps Used in Equating
. 285
8.2.4
Sample Size Requirements
. 288
8.3
Choosiag from Among the Statistical Procedures
. 290
8.8.1
Equating Criteria in Research Studies
. .
2§0
8-3.2
Characteristics of Equating Situations
. 292
8.4
Choosing from Among Equating Results
. 286
8.41
Equating Versus Not Equating
. 296
8.4.2
Use of Robustness Cheeks
.
2§§
xviii
Contents
8.4.3
Choosing from Among Results in the Random Groups
Design
. 297
8.4.4
Choosing from Among Results in the Common-Item
Nonequivalent
Groups Design
. 298
8.4.5
Use of Consistency Checks
. 298
8.4.6
Equating and Score Scales
. 300
8.4.7
Assessing First- and Second-Order Equity for Scale
Scores
. 301
8.5
Importance of Standardization Conditions and Quality Con¬
trol Procedures
. 306
8.5.1
Test Development
. 307
8.5.2
Test Administration and Standardization Conditions
307
8.5.3
Quality Control
. 309
8.5.4
Reequating
. 310
8.6
Conditions Conducive to Satisfactory Equating
. 312
8.7
Comparability Issues in Special Circumstances
. 312
8.7.1
Comparability
fettes
with Computer-Based Tests
. . 314
8.7.2
Comparability of Performance Assessments
. 320
8.7.3
Score Comparability with Optional Test Sections
. . 323
8.8
Conclusion
. 324
8.9
Exercises
. 325
9
Score Scales
329
9.1
Scaling Perspectives
. 331
§.2
Score Transformations
. 336
9.3
Incorporating Normative Information
. 337
§.3.1
Linear Transformations
. 337
9.3.2
Nonlinear Transformations
. 338
9.3.3
Example: Normalized Scale Scores
. 340
9.3.4
Importance of Norm Group in Setting the Score Scale
344
9.4
Incorporating Score Precision Information
. 345
9.4.1
Rules of Thumb for Number of Distinct Score Points
345
9.4.2
Liaearly Transformed Score Scales with a Given Stan¬
dard Error of Measurement
. 348
9.4.3
Score Scales with Approximately Equal Conditional
Standard Errors of Measurement
. . 348
9.4.4
Example: Incorporating Score Precision
. 351
8.4.5
Evaluating
Psychometrie
Properties of Scale Scores
. 354
9.4.6
The
ΙΚΓ
i-Scałe
as a Score Scale
. 358
9.5
Incorporating Content Information
. 358
9.5.1
Item Mapping
. 358
9.5.2
Scale Anchoring
. 361
§.5.3
Standard Setting
. 361
0.5.4
Numerical Example
. 364
§.5.5
Practical UseMoeffi
. 366
Contents xix
9.6
Maintaining Score Scales
. 366
9.7
Scales for Test Batteries and Composites
. 368
9.7.1
Test Batteries
. 368
9.7.2
Composite Scores
. 369
9.7.3
Maintaining Scales for Batteries and Composites
. . 371
9.8
Vertical Scaling and Developmental Score Scales
. 372
9.8.1
Structure of Batteries
. 373
9.8.2
Type of Domain Being Measured
. 375
9.8.3
Definition of Growth
. 376
9.8.4
Designs for Data Collection for Vertical Scaling
. . . 377
9.8.5
Test Scoring
. 381
9.8.6
Hieronymus Statistical Methods
. 381
9.8.7
Thurstone Statistical Methods
. 383
9.8.8
IRT
Statistical Methods
. 387
9.8.9
Thurstone Illustrative Example
. 393
9.8.10
IRT
Illustrative Example
. 401
9.8.11
Statistics for Comparing Scaling Results
. 410
9.8.12
Some Limitations of Vertically Scaled Tests
. 412
9.8.13
Research on Vertical Scaling
. 414
9.9
Exercises
. 418
10
Linking
423
10.1
Linking Categorization Schemes and Criteria
. 424
10.1.1
Types of Linking
. 427
10.1.2
Mislevy/Linn Taxonomy
. 429
10.1.3
Degrees of Similarity
. 433
10.2
Group
Invariance
. 437
10.2.1
Statistical Methods Using Observed Scores
. 437
10.2.2
Statistics for Overall Group
Invariance
. 441
10.2.3
Statistics for Pairwise Group
Invariance
. 443
10.2.4
Example: ACT and ITED Science Tests
. 444
10.3
Additional
Exampies
. 465
10.3.1
Extended Time
. 465
10.3.2
Test Adaptations and Translated Tests
. 467
10.4
Discussion
. 469
10.5
Exercises
. 470
11
Current and Stature Challenges 4?3
11.1
Score Scales
. 473
11.2
Equating
. . 474
11.3
Vertical Scaling
.
4?5
11.4
Linking
. 475
11.5
Summary
.
4?6
References 4?7
xx
Contents
Appendix A: Answers to Exercises
511
Appendix B: Computer Programs
533
Index
535 |
| any_adam_object | 1 |
| any_adam_object_boolean | 1 |
| author | Kolen, Michael J. Brennan, Robert L. |
| author_GND | (DE-588)1047378051 (DE-588)1047378590 |
| author_facet | Kolen, Michael J. Brennan, Robert L. |
| author_role | aut aut |
| author_sort | Kolen, Michael J. |
| author_variant | m j k mj mjk r l b rl rlb |
| building | Verbundindex |
| bvnumber | BV021570846 |
| callnumber-first | L - Education |
| callnumber-label | LB3060 |
| callnumber-raw | LB3060.77 |
| callnumber-search | LB3060.77 |
| callnumber-sort | LB 43060.77 |
| callnumber-subject | LB - Theory and Practice of Education |
| classification_rvk | QH 234 SK 830 |
| classification_tum | MAT 600f PSY 470f PSY 565f |
| ctrlnum | (OCoLC)54611281 (DE-599)BVBBV021570846 |
| dewey-full | 371.27/1 |
| dewey-hundreds | 300 - Social sciences |
| dewey-ones | 371 - Schools and their activities; special education |
| dewey-raw | 371.27/1 |
| dewey-search | 371.27/1 |
| dewey-sort | 3371.27 11 |
| dewey-tens | 370 - Education |
| discipline | Pädagogik Psychologie Mathematik Wirtschaftswissenschaften |
| discipline_str_mv | Pädagogik Psychologie Mathematik Wirtschaftswissenschaften |
| edition | 2. ed. |
| format | Book |
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| id | DE-604.BV021570846 |
| illustrated | Illustrated |
| index_date | 2024-07-02T14:38:16Z |
| indexdate | 2024-07-09T20:38:54Z |
| institution | BVB |
| isbn | 0387400869 |
| language | English |
| lccn | 2004045617 |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-014786659 |
| oclc_num | 54611281 |
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| physical | xxvi, 548 S. graph. Darst. 25 cm |
| publishDate | 2004 |
| publishDateSearch | 2004 |
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| publisher | Springer |
| record_format | marc |
| series2 | Statistics for social science and public policy |
| spelling | Kolen, Michael J. Verfasser (DE-588)1047378051 aut Test equating, scaling, and linking methods and practices Michael J. Kolen ; Robert L. Brennan 2. ed. New York Springer 2004 xxvi, 548 S. graph. Darst. 25 cm txt rdacontent n rdamedia nc rdacarrier Statistics for social science and public policy Frühere Aufl. u.d.T.: Kolen, Michael J.: Test equating Test equating methods are used with many standardized tests in education and psychology to ensure that scores from multiple test forms can be used interchangeably. In recent years, researchers from the education, psychology, and statistics communities have contributed to the rapidly growing statistical and psychometric methodologies used in test equating. This book provides an introduction to test equating which both discusses the most frequently used equating methodologies and covers many of the practical issues involved. This second edition expands upon the coverage of the first edition by providing a new chapter on test scaling and a second on test linking. Test scaling is the process of developing score scales that are used when scores on standardized tests are reported. In test linking, scores from two or more tests are related to one another. Linking has received much recent attention, due largely to investigations of linking similarly named tests from different test publishers or tests constructed for different purposes. The expanded coverage in the second edition also includes methodology for using polytomous item response theory in equating. Examens - Correction Examens - Interprétation des résultats Examens - Élaboration Psychometrie swd Statistisches Modell swd Test swd Tests et mesures en éducation - Normes Tests psychologiques - Normes Vergleich swd Examinations Scoring Examinations Interpretation Examinations Design and construction Psychological tests Standards Educational tests and measurements Standards Schulleistungsmessung (DE-588)4077202-0 gnd rswk-swf Schulleistungsmessung (DE-588)4077202-0 s 1\p DE-604 Brennan, Robert L. Verfasser (DE-588)1047378590 aut Digitalisierung UB Bamberg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014786659&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Kolen, Michael J. Brennan, Robert L. Test equating, scaling, and linking methods and practices Examens - Correction Examens - Interprétation des résultats Examens - Élaboration Psychometrie swd Statistisches Modell swd Test swd Tests et mesures en éducation - Normes Tests psychologiques - Normes Vergleich swd Examinations Scoring Examinations Interpretation Examinations Design and construction Psychological tests Standards Educational tests and measurements Standards Schulleistungsmessung (DE-588)4077202-0 gnd |
| subject_GND | (DE-588)4077202-0 |
| title | Test equating, scaling, and linking methods and practices |
| title_auth | Test equating, scaling, and linking methods and practices |
| title_exact_search | Test equating, scaling, and linking methods and practices |
| title_exact_search_txtP | Test equating, scaling, and linking methods and practices |
| title_full | Test equating, scaling, and linking methods and practices Michael J. Kolen ; Robert L. Brennan |
| title_fullStr | Test equating, scaling, and linking methods and practices Michael J. Kolen ; Robert L. Brennan |
| title_full_unstemmed | Test equating, scaling, and linking methods and practices Michael J. Kolen ; Robert L. Brennan |
| title_short | Test equating, scaling, and linking |
| title_sort | test equating scaling and linking methods and practices |
| title_sub | methods and practices |
| topic | Examens - Correction Examens - Interprétation des résultats Examens - Élaboration Psychometrie swd Statistisches Modell swd Test swd Tests et mesures en éducation - Normes Tests psychologiques - Normes Vergleich swd Examinations Scoring Examinations Interpretation Examinations Design and construction Psychological tests Standards Educational tests and measurements Standards Schulleistungsmessung (DE-588)4077202-0 gnd |
| topic_facet | Examens - Correction Examens - Interprétation des résultats Examens - Élaboration Psychometrie Statistisches Modell Test Tests et mesures en éducation - Normes Tests psychologiques - Normes Vergleich Examinations Scoring Examinations Interpretation Examinations Design and construction Psychological tests Standards Educational tests and measurements Standards Schulleistungsmessung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014786659&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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