Applications of item response theory to practical testing problems:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | Undetermined |
| Veröffentlicht: |
Hillsdale, NJ
Erlbaum
1980
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| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XIII, 274 S. |
| ISBN: | 089859006X |
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| 100 | 1 | |a Lord, Frederic M. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Applications of item response theory to practical testing problems |c Frederic M. Lord |
| 264 | 1 | |a Hillsdale, NJ |b Erlbaum |c 1980 | |
| 300 | |a XIII, 274 S. | ||
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Datensatz im Suchindex
| _version_ | 1804119513396936704 |
|---|---|
| adam_text | Contents
Preface xi
PART I: INTRODUCTION TO ITEM RESPONSE THEORY
1. Classical Test Theory—Summary and Perspective 3
1.1. Introduction 3
1.2. True Score 4
1.3. Uncorrelated Errors 6
1.4. Parallel Test Forms 6
1.5. Envoi 7
Appendix 7
2. Item Response Theory—Introduction and Preview 11
2.1. Introduction 11
2.2. Item Response Functions 12
2.3. Checking the Mathematical Model 15
2.4. Unidimensional Tests 19
2.5. Preview 21
iii
iv CONTENTS
3. Relation of Item Response Theory to
Conventional Item Analysis 27
3.1. Item-Test Regressions 27
3.2. Rationale for Normal Ogive Model 30
3.3. Relation to Conventional Item Statistics 33
3.4. Invariant Item Parameters 34
3.5. Indeterminacy 36
3.6. A Sufficient Condition for the
Normal Ogive Model 39
3.7. Item Intercorrelations 39
3.8. Illustrative Relationships Among
Test and Item Parameters 40
Appendix 41
4. Test Scores and Ability Estimates
as Functions of Item Parameters 44
4.1. The Distribution of Test Scores for
Given Ability 44
4.2. True Score 45
4.3. Standard Error of Measurement 46
4.4. Typical Distortions in
Mental Measurement 49
4.5. The Joint Distribution of Ability
and Test Scores 51
4.6. The Total-Group Distribution of
Number-Right Score 51
4.7. Test Reliability 52
4.8. Estimating Ability From Test Scores 52
4.9. Joint Distribution of Item Scores
for One Examinee 54
4.10. Joint Distribution of All Item Scores
on All Answer Sheets 55
4.11. Logistic Likelihood Function 56
4.12. Sufficient Statistics 57
4.13. Maximum Liklihood Estimates 58
4.14. Maximum Likelihood Estimation for
Logistic Items with c( =0 59
4.15. Maximum Likelihood Estimation for
Equivalent Items 59
4.16. Formulas for Functions of the
Three-Parameter Logistic Function 60
4.17. Exercises 61
Appendix 63
CONTENTS V
5. Information Functions and Optimal Scoring Weights 65
5.1. The Information Function for a Test Score 65
5.2. Alternative Derivation of the
Score Information Function 68
5.3. The Test Information Function 70
5.4. The Item Information Function 72
5.5. Information Function for a
Weighted Sum of Item Scores 73
5.6. Optimal Scoring Weights 74
5.7. Optimal Scoring Weights Not Dependent on 8 76
5.8. Maximum Likelihood Estimate of Ability 77
5.9. Exercises 77
Appendix 78
PART II: APPLICATIONS OF ITEM RESPONSE THEORY
6. The Relative Efficiency of Two Tests 83
6.1. Relative Efficiency 83
6.2. Transformations of the Ability Scale 84
6.3. Effect of Ability Transformation on
the Information Function 84
6.4. Effect of Ability Transformation on
Relative Efficiency 88
6.5. Information Function of
Observed Score on True Score 89
6.6. Relation Between Relative Efficiency and
True-Score Distribution 90
6.7. An Appproximation for Relative Efficiency 92
6.8. Desk Calculator Approximation for
Relative Efficiency 94
6.9. Relative Efficiency
of Seven Sixth-Grade Vocabulary Tests 96
6.10. Redesigning a Test 101
6.11. Exercises 104
7. Optimal Number of Choices Per Item 106
7.1. Introduction 106
7.2. Previous Empirical Findings 107
7.3. A Mathematical Approach 107
7.4. Grier s Approach 108
7.5. A Classical Test Theory Approach 108
7.6. An Item Response Theory Approach 110
7.7. Maximizing Information at a Cutting Score 112
vi CONTENTS
8. Flexilevel Tests 114
8.1. Introduction 114
8.2. Flexilevel Tests 115
8.3. Scoring 116
8.4. Properties of Flexilevel Tests 117
8.5. Theoretical Evaluation
of Novel Testing Procedures 119
8.6. Conditional Frequency Distribution of
Flexilevel Test Scores 120
8.7. Illustrative Flexilevel Tests, No Guessing 122
8.8. Illustrative Flexilevel Tests, with Guessing 124
8.9. Conclusion 126
8.10. Exercises 127
9. Two-Stage Procedures and Multilevel Tests 128
9.1. Introduction 128
9.2. First Two-Stage Procedure—Assumptions 129
9.3. Scoring 130
9.4. Conditional Distribution of Test Score 6 131
9.5. Illustrative 60-Item Two-Stage Tests,
No Guessing 132
9.6. Discussion of Results for 60-Item Tests
with No Guessing 135
9.7. Illustrative 15-Item Two-Stage Tests
with No Guessing 136
9.8. Illustrative 60-Item Two-Stage Tests
with Guessing 138
9.9. Converting a Conventional Test to a
Multilevel Test 140
9.10. The Relative Efficiency of a Level 141
9.11. Dependence of the Two-Stage Test on
its Levels 142
9.12. Cutting Points on the Routing Test 144
9.13. Results for Various Two-Stage Designs 144
9.14. Other Research 146
9.15. Exercises 146
Appendix 147
10. Tailored Testing 150
10.1. Introduction 150
10.2. Maximizing Information 151
10.3. Administering the Tailored Test 153
CONTENTS Vii
10.4. Calibrating the Test Items 154
10.5. A Broad-Range Tailored Test 154
10.6. Simulation and Evaluation 156
10.7. Results of Evaluation 157
10.8. Other Work on Tailored Tests 159
11. Mastery Testing 162
11.1. Introduction 162
11.2. Definition of Mastery 163
11.3. Decision Rules 163
11.4. Scoring the Test: The Likelihood Ratio 164
11.5. Losses 166
11.6. Cutting Score for the Likelihood Ratio 166
11.7. Admissible Decision Rules 168
11.8. Weighted Sum of Item Scores 169
11.9. Locally Best Scoring Weights 170
11.10. Cutting Point for Locally Best Scores 170
11.11. Evaluating a Mastery Test 171
11.12. Optimal Item Difficulty 172
11.13. Test Length 173
11.14. Summary of Mastery Test Design 174
11.15. Exercises 175
PART in: PRACTICAL PROBLEMS AND FURTHER APPLICATIONS
12. Estimating Ability and Item Parameters 179
12.1. Maximum Likelihood 179
12.2. Iterative Numerical Procedures 180
12.3. Sampling Variances of Parameter Estimates 181
12.4. Partially Speeded Tests 182
12.5. Floor and Ceiling Effects 182
12.6. Accuracy of Ability Estimation 183
12.7. Inadequate Data and
Unidentifiable Parameters 184
12.8. Bayesian Estimation of Ability 186
12.9. Further Theoretical Comparison of Estimators 187
12.10. Estimation of Item Parameters 189
12.11. Addendum on Estimation 189
12.12. The Rasch Model 189
12.13. Exercises 190
Appendix 191
viii CONTENTS
13. Equating 193
13.1. Equating Infallible Measures 193
13.2. Equity 195
13.3. Can Fallible Tests be Equated? 196
13.4. Regression Methods 198
13.5. True-Score Equating 199
13.6. True-Score Equating
with an Anchor Test 200
13.7. Raw-Score Equating
with an Anchor Test 202
13.8. Illustrative Example 203
13.9. Preequating 205
13.10. Concluding Remarks 207
13.11. Exercises 207
Appendix 208
14. Study of Item Bias 212
14.1. Introduction 212
14.2. A Conventional Approach 213
14.3. Estimation Procedures 217
14.4. Comparing Item Response Functions
Across Groups 218
14.5. Purification of the Test 220
14.6. Checking the
Statistical Significance Test 221
Appendix 223
15. Omitted Responses and Formula Scoring 225
15.1. Dichotomous Items 225
15.2. Number-Right Scoring 225
15.3. Test Directions 226
15.4. Non-Reached Responses 226
15.5. Omitted Responses 226
15.6. Model for Omits Under Formula Scoring 227
15.7. The Practical Meaning of
an Item Response Function 227
15.8. Ignoring Omitted Responses 228
15.9. Supplying Random Responses 228
15.10. Procedure for Estimating Ability 229
15.11. Formula Scores 229
CONTENTS ix
PART IV: ESTIMATING TRUE-SCORE DISTRIBUTIONS
16. Estimating True-Score Distributions 235
16.1. Introduction 235
16.2. Population Model 236
16.3. A Mathematical Solution
for the Population 237
16.4. The Statistical Estimation Problem 239
16.5. A Practical Estimation Procedure 239
16.6. Choice of Grouping 241
16.7. Illustrative Application 242
16.8. Bimodality 244
16.9. Estimated Observed-Score Distribution 245
16.10. Effect of a Change in Test Length 245
16.11. Effects of Selecting on Observed Score:
Evaluation of Mastery Tests 247
16.12. Estimating Item True-Score Regression 251
16.13. Estimating Item Response Functions 252
17. Estimated True-Score Distributions for Two Tests 254
17.1. Mathematical Formulation 254
17.2. Bivariate Distribution of
Observed Scores on Parallel Tests 255
17.3. True-Score Equating 255
17.4. Bivariate Distribution of
Observed Scores on Nonparallel Tests 257
17.5. Consequences of Selecting on
Observed Score 259
17.6. Matching Groups 262
17.7. Test Norms 263
Answers to Exercises 265
Author Index 267
Subject Index 269
|
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| physical | XIII, 274 S. |
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| spelling | Lord, Frederic M. Verfasser aut Applications of item response theory to practical testing problems Frederic M. Lord Hillsdale, NJ Erlbaum 1980 XIII, 274 S. txt rdacontent n rdamedia nc rdacarrier Testtheorie (DE-588)4131939-4 gnd rswk-swf Itemanalyse (DE-588)4162624-2 gnd rswk-swf Itemanalyse (DE-588)4162624-2 s Testtheorie (DE-588)4131939-4 s DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=003316353&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Lord, Frederic M. Applications of item response theory to practical testing problems Testtheorie (DE-588)4131939-4 gnd Itemanalyse (DE-588)4162624-2 gnd |
| subject_GND | (DE-588)4131939-4 (DE-588)4162624-2 |
| title | Applications of item response theory to practical testing problems |
| title_auth | Applications of item response theory to practical testing problems |
| title_exact_search | Applications of item response theory to practical testing problems |
| title_full | Applications of item response theory to practical testing problems Frederic M. Lord |
| title_fullStr | Applications of item response theory to practical testing problems Frederic M. Lord |
| title_full_unstemmed | Applications of item response theory to practical testing problems Frederic M. Lord |
| title_short | Applications of item response theory to practical testing problems |
| title_sort | applications of item response theory to practical testing problems |
| topic | Testtheorie (DE-588)4131939-4 gnd Itemanalyse (DE-588)4162624-2 gnd |
| topic_facet | Testtheorie Itemanalyse |
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