Verfügbarkeit: Test equating, scaling, and linking | Technische Universität München

Test equating, scaling, and linking: methods and practices

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Bibliographische Detailangaben
Beteiligte Personen:	Kolen, Michael J. (VerfasserIn), Brennan, Robert L. (VerfasserIn)
Format:	Buch
Sprache:	Englisch
Veröffentlicht:	New York, NY [u.a.] Springer [2014]
Ausgabe:	Third edition
Schriftenreihe:	Statistics for social and behavioral sciences
Schlagwörter:	Schulleistungsmessung
Links:	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027260615&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
Umfang:	XXVI, 566 Seiten Diagramme
ISBN:	9781493903160

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Datensatz im Suchindex

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adam_text	Contents Introduction and Concepts ...................... 1.1 Equating and Related Concepts .............. .1.1 Test Forms and Test Specifications ...... .1.2 Equating ........................ Л.З Processes That are Related to Equating . . . .1.4 Equating and Score Scales ............ .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 ...................... .3.1 .3.2 .3.3 .3.4 .3.5 Symmetry Property ............ Same Specifications Property ..... Equity Properties ............. Observed Score Equating Properties Group Invariance Property ....... 1.4 Equating Designs .5 .6 .7 .8 .9 .4.1 Random Groups Design ................. .4.2 Single Group Design ................... .4.3 Single Group Design with Counterbalancing . . .4.4 AS VAB Problems with a Single Group Design .4.5 Common-Item Nonequivalent Groups Design. . .4.6 NAEP Reading Anomaly: Problems with Common Items ............ Error in Estimating Equating Relationships .......... Evaluating the Results of Equating ................ Testing Situations Considered ................... Preview ................................... Exercises .................................. References 2 2 3 4 7 8 9 9 9 11 12 12 13 14 14 16 18 20 21 22 23 24 25 26 Observed Score Equating Using the Random Groups Design .... 29 2.1 Mean Equating .................................. 30 2.2 Linear Equating ................................. 31 XIII Contents xiv 2.3 Properties of Mean and Linear Equating ................ 32 2.4 Comparison of Mean and Linear Equating ............... 33 2.5 Equipercentile Equating ............................ 36 2.5.1 Graphical Procedures ...................... 38 2.5.2 Analytic Procedures ....................... 42 2.5.3 Properties of Equated Scores in Equipercentile Equating ................... 45 2.6 Estimating Observed Score Equating Relationships ......... 46 2.7 Scale Scores ................................... 50 2.7.1 Linear Conversions ........................ 50 2.7.2 Truncation of Linear Conversions .............. 53 2.7.3 Nonlinear Conversions ..................... 54 2.8 Equating Using Single Group Designs ................. 60 2.9 Equating Using Alternate Scoring Schemes .............. 60 2.10 Preview of What Follows .......................... 61 2.11 Exercises ...................................... 62 References ......................................... 63 3 Random Groups: Smoothing in Equipercentile Equating ....... 65 3.1 A Conceptual Statistical Framework for Smoothing ........ 66 3.2 Properties of Smoothing Methods ..................... 69 3.3 Presmoothing Methods ............................ 70 3.3.1 Polynomial Log-Linear Method ............... 70 3.3.2 Strong True Score Method ................... 72 3.3.3 Illustrative Example ....................... 74 3.4 Postsmoothing Methods ............................ 80 3.4.1 Illustrative Example ....................... 85 3.5 The Kernel Method of Equating ...................... 89 3.6 Practical Issues in Equipercentile Equating .............. 93 3.6.1 Summary of Smoothing Strategies ............. 94 3.6.2 Smoothing and Population Distribution Irregularities ............................. 95 3.6.3 Equating Error, Sample Size, and Smoothing Method ..................... 96 3.7 Exercises ...................................... 98 References ......................................... 99 4 Nonequivalent Groups: Linear Methods ................... 103 4.1 Tucker Method ................................ 105 4.1.1 Linear Regression Assumptions ............... 105 4.1.2 Conditional Variance Assumptions ............. 106 4.1.3 Intermediate Results ....................... 107 4.1.4 Final Results ............................ Ю8 4.1.5 Special Cases ...................... Ю9 Contents xv 4.2 Levine Observed Score Method ...................... 1 09 4.2.1 Correlational Assumptions ................... 110 4.2.2 Linear Regression Assumptions ............... ПО 4.2.3 Error Variance Assumptions .................. 11 J 4.2.4 Intermediate Results ....................... Ill 4.2.5 General Results .......................... 112 4.2.6 Classical Congeneric Model Results ............ 1J3 4.3 Levine True Score Method ......................... 116 4.3.1 Results ................................ 117 4.3.2 First-Order Equity ......................... 119 4.4 Chained Linear Equating ........................... 121 4.4.1 Chained Linear Observed Score Equating ........ 122 4.4.2 Chained Linear True Score Equating ............ L23 4.5 Illustrative Example and Other Topics ................. 124 4.5.1 Illustrative Example ....................... 125 4.5.2 Synthetic Population Weights ................. 128 4.5.3 Mean Equating ........................... 128 4.5.4 Decomposing Observed Differences in Means and Variances ............................ 129 4.5.5 Relationships Among Linear Observed Score Methods ........................... 132 4.5.6 Relationships Involving Levine Methods ......... 135 4.5.7 Other Issues Involving Methods ............... 137 4.5.8 Scale Scores ............................. 137 4.6 Appendix: Proof that σ](Τχ) = γ[σ](Τν) Under the Classical Congeneric Model ...................... 139 4.7 Exercises ...................................... 139 References ......................................... 141 5 Nonequivalent Groups: Equipercentile Methods ............. 143 5. J Frequency Estimation Method ....................... 143 5.1.1 Conditional Distributions .................... 144 5.1.2 Assumptions and Procedures ................. 144 5.1.3 Numerical Example ........................ 147 5.1.4 Estimating the Distributions .................. 150 5.1.5 Special Case: Braun-Holland Linear Method ...... 151 5.1.6 Illustrative Example ....................... 152 5.2 Other Methods .................................. 158 5.2.1 Modified Frequency Estimation ............... 158 5.2.2 Chained Equipercentile Equating .............. 159 5.2.3 Illustrative Example ....................... 164 5.3 Practical Issues .................................. 165 5.4 Exercises ...................................... 166 References ......................................... 166 Contents XVI 6 Item Response Theory Methods l71 6.1 Some Necessary IRT Concepts ....................... 172 6.1.1 Unidimensionality and Local Independence Assumptions ............................. 172 6.1.2 IRT Models ............................. l73 6.1.3 IRT Parameter Estimation ................... 176 6.2 Transformations of IRT Scales ....................... 177 6.2.1 Transformation Equations ................... 177 6.2.2 Demonstrating the Appropriateness of Scale Transformations .................... 178 6.2.3 Expressing Aanć В Constants ................. 179 6.2.4 Expressing A and В Constants in Terms of Groups of Items and/or Persons ..................... 180 6.3 Transforming IRT Scales When Parameters are Estimated. ... 181 6.3.1 Designs ................................ 82 6.3.2 Mean/Sigma and Mean/Mean Transformation Methods ............................... 183 6.3.3 Characteristic Curve Transformation Methods ..... 184 6.3.4 Comparisons Among Scale Transformation Methods ............................... 189 6.4 Equating and Scoring ............................. 191 6.5 Equating True Scores ............................. 192 6.5.1 Test Characteristic Curves ................... 192 6.5.2 True Score Equating Process ................. 193 6.5.3 The Newton-Raphson Method ................ 193 6.5.4 Using True Score Equating with Observed Scores ...................... 196 6.6 Equating Observed Scores .......................... 197 6.7 IRT True Score Versus IRT Observed Score Equating ...... 201 6.8 Illustrative Example .............................. 201 6.8.1 Item Parameter Estimation and Scaling .......... 202 6.8.2 IRT True Score Equating .................... 206 6.8.3 IRT Observed Score Equating ................ 207 6.8.4 Rasch Equating .......................... 213 6.9 Using IRT Calibrated Item Pools and Other Designs ....... 214 6.9.1 Common-Item Equating to a Calibrated Pool ...... 215 6.9.2 Item Preequating ....................... 219 6.9.3 Other Designs .................... 221 6.10 Equating with Polytomous IRT .............. 221 6.10.1 Polytomous IRT Models for Ordered Responses. ... 222 6.10.2 Scoring Function, Item Response Function, and Test Characteristic Curve ............. 227 6.10.3 Parameter Estimation and Scale Transformation with Polytomous IRT Models ......... 228 Contents xvii 6Л0.4 True Score Equating ....................... 232 6.10.5 Observed Score Equating .................... 232 6.10.6 Example Using the Graded Response Model ...... 233 6.11 Robustness to Violations of the Unidimensionality Assumption .................................... 235 6.12 Practical Issues and Caveat ......................... 238 6.13 Exercises ...................................... 239 References ......................................... 241 7 Standard Errors of Equating ........................... 247 7.1 Definition of Standard Error of Equating ................ 248 7.2 The Bootstrap .................................. 250 7.2.1 Standard Errors Using the Bootstrap ............ 250 7.2.2 Standard Errors of Equating .................. 252 7.2.3 Parametric Bootstrap ....................... 253 7.2.4 Standard Errors of Equipercentile Equating with Smoothing .......................... 255 7.2.5 Standard Errors of Scale Scores ............... 256 7.2.6 Standard Errors of Equating Chains ............ 257 7.2.7 Mean Standard Error of Equating .............. 258 7.2.8 Caveat ................................. 259 7.3 The Delta Method ............................... 259 7.3.1 Mean Equating Using Single Group and Random Groups Designs ................. 260 7.3.2 Linear Equating Using the Random Groups Design ........................... 261 7.3.3 Equipercentile Equating Using the Random Groups Design ........................... 263 7.3.4 Standard Errors for Other Designs ............. 264 7.3.5 Illustrative Example ....................... 265 7.3.6 Approximations .......................... 267 7.3.7 Standard Errors for Scale Scores .............. 268 7.3.8 Standard Errors of Equating Chains ............ 269 7.3.9 Using Delta Method Standard Errors ............ 270 7.4 Using Standard Errors in Practice ..................... 276 7.5 Exercises ...................................... 278 References ......................................... 279 8 Practical Issues in Equating ............................ 283 8.1 Equating and the Test Development Process ............. 285 8.1.1 Test Specifications ........................ 285 8.1.2 Changes in Test Specifications ................ 286 8.1.3 Characteristics of Common-Item Sets ........... 287 Contents XVIII 8.2 Data Collection: Design and Implementation............. 289 8.2.1 Choosing Among Equating Designs ............ 289 8.2.2 Developing Equating Linkage Plans ............ 292 8.2.3 Examinee Groups Used in Equating ............ 300 8.2.4 Sample Size Requirements ................... 303 8.3 Choosing from Among the Statistical Procedures .......... 305 8.4 Equating Criteria and Designs in Research Studies ......... 310 8.4.1 Criteria and Designs Based on Error in Estimating Equating Relationships ..................... 310 8.4.2 Equating in a Circle ....................... 318 8.4.3 Criteria and Designs Based on Assessing Group Invariance of Equating Relationships ....... 319 8.4.4 Criteria and Designs Based on the Equity Property of Equating ....................... 320 8.4.5 Discussion of Equating Criteria and Designs ...... 325 8.5 Choosing from Among Equating Results in Operational Equating ...................................... 326 8.5.1 Equating Versus Not Equating ................ 326 8.5.2 Use of Robustness Checks ................... 327 8.5.3 Choosing from Among Results in the Random Groups Design ........................... 327 8.5.4 Choosing from Among Results in the Common-Item Nonequivalent Groups Design ...... 328 8.5.5 Use of Consistency Checks .................. 329 8.5.6 Equating and Score Scales ................... 330 8.6 Importance of Standardization Conditions and Quality Control Procedures ......................... 33] 8.6.1 Test Development ......................... 331 8.6.2 Test Administration and Standardization Conditions .............................. 331 8.6.3 Quality Control .......................... 333 8.6.4 Reequating .......................... 334 8.7 Conditions Conducive to Satisfactory Equating ........... 337 8.8 Comparability Issues in Special Circumstances ........... 337 8.8.1 Comparability Issues with Computer-Based Tests. .. 337 8.8.2 Comparability for Constructed-Response and Mixed-Format Tests ............... 344 8.8.3 Score Comparability with Optional Test Sections ... 348 8.9 Conclusion .................... -240 8.10 Exercises ................... References ................ Contents xix 9 Score Scales ........................................ 371 9.1 Scaling Perspectives .............................. 372 9.2 Unit Scores, Item Scores, and Raw Scores ............... 377 9.2Л Test Score Terminology .................... 377 9.2.2 Unit and Item Scores ...................... 378 9.2.3 Raw Scores (Y) .......................... 380 9.3 Scores on M ix ed- Format Tests ....................... 387 9.3.1 Weights Based on Numbers of Score Points ...... 388 9.3.2 Observed Score Effective Weights ............. 389 9.3.3 True Score Effective Weights ................. 390 9.3.4 Weights Chosen to Maximize Reliability ......... 390 9.3.5 Weighting Example ........................ 391 9.3.6 Some Other Weighting Criteria and Issues ........ 392 9.3.7 Weights in IRT .......................... 392 9.4 Score Transformations ............................. 393 9.5 Incorporating Normative Information .................. 394 9.5.1 Linear Transformations ..................... 394 9.5.2 Nonlinear Transformations ................... 395 9.5.3 Example: Normalized Scale Scores ............. 397 9.5.4 Importance of Norm Group in Setting the Score Scale ........................... 401 9.6 Incorporating Score Precision Information ............... 401 9.6.1 Rules of Thumb for Number of Distinct Score Points ............................. 402 9.6.2 Linearly Transformed Score Scales with a Given Standard Error of Measurement ............... 404 9.6.3 Score Scales with Approximately Equal Conditional Standard Errors of Measurement ...... 405 9.6.4 Example: Incorporating Score Precision ......... 407 9.6.5 Evaluating Psychometric Properties of Scale Scores ........................... 410 9.6.6 The IRT fl-Scale as a Score Scale .............. 413 9.7 Incorporating Content Information .................... 414 9.7.1 Item Mapping ............................ 414 9.7.2 Scale Anchoring .......................... 415 9.7.3 Standard Setting .......................... 417 9.7.4 Numerical Example ........................ 418 9.7.5 Practical Usefulness ....................... 420 9.8 Maintaining Score Scales ........................... 420 9.9 Scales for Test Batteries and Composites ............... 422 9.9.1 Test Batteries ............................ 422 9.9.2 Composite Scores ......................... 423 9.9.3 Maintaining Scales for Batteries and Composites . . . 424 Contents XX 9.10 Vertical Scaling and Developmental Score Scales ......... 425 9.10.1 Structure of Batteries ...................... 427 9.10.2 Type of Domain Being Measured .............. 428 9.10.3 Definition of Growth ....................... 429 9.10.4 Designs for Data Collection for Vertical Scaling ... 431 9.10.5 Test Scoring ............................. 434 9.10.6 Hieronymus Statistical Methods ............... 435 9.10.7 Thurstone Statistical Methods ................. 437 9.10.8 IRT Statistical Methods ..................... 440 9.10.9 Thurstone Illustrative Example ................ 445 9.10.10 IRT Illustrative Example .................... 454 9.10.11 Statistics for Comparing Scaling Results ......... 461 9.10.12 Some Limitations of Vertically Scaled Tests ...... 463 9.10.13 Vertical Scaling Designs with Variable Sections. . . . 465 9.10.14 Maintaining Vertical Scales .................. 466 9.10.15 Research on Vertical Scaling ................. 466 9.10.16 Score Scales and Growth Models .............. 471 9. 1 1 Exercises ...................................... 473 References ......................................... 475 10 Linking ........................................... 487 10.1 Linking Categorization Schemes and Criteria ............. 488 10.1.1 Types of Linking ......................... 491 10.1.2 Mislevy/Linn Taxonomy .................... 492 10.1.3 Holland and Dorans Framework ............... 496 10.1.4 Degrees of Similarity ...................... 498 10.1.5 Summary and Other Approaches .............. 500 10.2 Group Invariance ................................ 501 10.2.1 Statistical Methods Using Observed Scores ....... 501 10.2.2 Statistics for Overall Group Invariance .......... 505 10.2.3 Statistics for Pairwise Group Invariance ......... 507 10.2.4 Example: ACT and ITED Science Tests ......... 508 10.3 Additional Examples ................... 527 10.3.1 Extended Time ........................... 528 10.3.2 Test Adaptations and Translated Tests ........... 529 10.4 Discussion ...................... 53] 10.5 Exercises ....................... «532 References .................... c-ii Appendix A: Answers to Exercises .............. 537 Appendix B: Computer Programs ............. 559 ................................................ 56!
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spellingShingle	Kolen, Michael J. Brennan, Robert L. Test equating, scaling, and linking methods and practices 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_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	Schulleistungsmessung (DE-588)4077202-0 gnd
topic_facet	Schulleistungsmessung
url	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027260615&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
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