Statistical theories of mental test scores:
Gespeichert in:
| Format: | Buch |
|---|---|
| Sprache: | Undetermined |
| Veröffentlicht: |
Reading, Mass. [u.a.]
Addison-Wesley
1974
|
| Ausgabe: | 2. print. |
| Schriftenreihe: | Addison-Wesley series in behavioral science : Quantitative methods
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XVII, 568 S. graph. Darst. |
| ISBN: | 0201043106 |
Internformat
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| 245 | 1 | 0 | |a Statistical theories of mental test scores |c Frederic M. Lord and Melvin R. Novick. With contributions by Allan Birnbaum |
| 250 | |a 2. print. | ||
| 264 | 1 | |a Reading, Mass. [u.a.] |b Addison-Wesley |c 1974 | |
| 300 | |a XVII, 568 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Addison-Wesley series in behavioral science : Quantitative methods | |
| 650 | 0 | 7 | |a Statistischer Test |0 (DE-588)4077852-6 |2 gnd |9 rswk-swf |
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| 700 | 1 | |a Lord, Frederic M. |e Sonstige |4 oth | |
| 700 | 1 | |a Novick, Melvin R. |e Sonstige |4 oth | |
| 700 | 1 | |a Birnbaum, Allan |e Sonstige |4 oth | |
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Datensatz im Suchindex
| _version_ | 1804122453390131200 |
|---|---|
| adam_text | CONTENTS
PART 1
The Foundations of Mental Measurement Theory
Chapter 1
Measurement in Psychology and Education
1.1 The need for a theory of mental testing 13
1.2 Psychological theory and its function 15
1.3 Measurement as a basis of model construction 16
1.4 The place of measurement in psychology 19
1.5 Levels of measurement 20
1.6 The specification of interval scales 21
1.7 Deterministic and probabilistic models 23
1.8 The assumptions underlying test theory models 24
Chapter 2
The Construction of True and Error Scores
2.1 Introduction 27
2.2 The distribution of measurements on a fixed person 29
2.3 True score as an expectation 30
2.4 The construction of the error random variable for a fixed person ... 31
2.5 The random selection of persons 32
2.6 Construction of the linear model 34
2.7 Derivation of the usual assumptions of the classical model 36
2.8 What is error? 38
2.9 The many concepts of true score 39
2.10 Experimental independence 44
2.11 Linear experimental independence 45
2.12 Replicate measurements 46
2.13 Parallel measurements and parallel forms 47
ix
X CONTENTS
PART 2
The Classical Test Theory Model
Chapter 3
Basic Equations of the Classical Model for Tests of Fixed Length
3.1 The classical linear model: restatement of assumptions 55
3.2 Expectations, variances, and correlations 56
3.3 Relationships based on parallel measurements 58
3.4 Definitions, interpretations, and applications 60
3.5 The validities of a test 61
3.6 An alternative statement of the classical model 63
3.7 Regression theory for the classical model 64
3.8 Errors of measurement, estimation, and prediction 66
3.9 Attenuation formulas 69
3.10 Elementary models for inferring true change 74
Chapter 4
Composite Tests
4.1 Introduction 82
4.2 Composite measurements with two components 83
4.3 Composite measurements with n components 85
4.4 Coefficient a. and the reliability of composite measurements .... 87
4.5 The internal structure of tests 95
4.6 Expectations, variances, and covariances of weighted composites ... 96
4.7 The correlation between two composite measurements 97
Chapter 5
Basic Equations of the Classical Model
for Homogeneous Teste of Variable Length
5.1 Test length as a test parameter 103
5.2 The classical model with a continuous test length parameter .... 104
5.3 Statement of the assumptions 105
5.4 The true score as the observed score of a person on a test
of infinite length 108
5.5 The fundamental theorem 108
5.6 Expectations and variances 109
5.7 Covariances 110
5.8 Correlations among observed, true, and error scores Ill
5.9 Expectations, variances, and correlations of lengthened tests .... Ill
5.10 The Spearman Brown formula 112
5.11 The effect of test length on validity 114
5.12 Comparing reliabilities and validities of tests of differing lengths . . . 118
5.13 The most reliable composite with a specified true score 119
CONTENTS xi
5.14 Maximizing the reliability of the composite when component
lengths are fixed 123
5.15 Maximizing the validity of a test battery as a function of
relative test lengths for a fixed total testing time 124
Chapter 6
Factors Affecting Measurement Precision,
Estimation, and Prediction
6.1 Introduction 129
6.2 Effect of group heterogeneity on test reliability 129
6.3 Speed and power tests 131
6.4 Conditions of measurement affecting reliability 133
6.5 Experimental problems in correcting for attenuation 137
6.6 Accuracy of the Spearman Brown prophecy formulas 139
6.7 Reliability as a generic concept 139
6.8 Effect of explicit and incidental selection on test validity:
the two variable case 140
6.9 The effect of selection on test validity: the three variable case . . . 144
6.10 The effect of selection on test validity: the general case 146
6.11 Accuracy of the selection formulas 147
Chapter 7
Some Estimates of Parameters of the Classical Model
7.1 Introduction 151
7.2 Estimating true score 152
7.3 An unbiased estimate of the specific error variance from
parallel measurements 153
7.4 The use of estimated error variances 159
7.5 Specific true score variance estimated from an analysis
of variance components 160
7.6 A general formulation of the estimation problem as
an analysis of variance components 162
7.7 An estimate of an upper bound on the specific error variance
from measurements that are not strictly parallel 166
PAET 3
Other Weak True Score Models
Chapter 8
Some Test Theory for Imperfectly Parallel Measurements
8.1 Defining true score 173
8.2 The generic error of measurement 176
8.3 The generic error variance 177
xii CONTENTS
8.4 Basic properties of generic errors of measurement 180
8.5 Generic true score variance 184
8.6 The relation between generic and specific true score variances .... 185
8.7 Estimating generic parameters describing a single test form .... 187
8.8 Comparisons of estimates of error variance 191
8.9 Substantive considerations regarding choice among estimates .... 194
Chapter 9
Types of Reliability Coefficients and Their Estimation
9.1 Introduction 198
9.2 Estimating the specific reliability coefficient 200
9.3 Statistical properties of an estimated variance ratio 201
9.4 Specific reliability theory for composite tests 203
9.5 Maximum likelihood estimation of reliability for normally
distributed scores 204
9.6 The frequency distribution of the estimated reliability 206
9.7 The generic reliability coefficient 208
9.8 Generic reliability for a single test 209
9.9 Use and interpretation of reliability coefficients 211
9.10 The reliability of ordinal measurements 214
9.11 Use of factor loadings as reliability coefficients 216
9.12 Estimating reliability without using parallel forms 216
Chapter 10
Some Test Theory for r Equivalent Measurements,
Including Estimation of Higher Order Moments
10.1 Introduction and definitions 224
10.2 An assumption of linear experimental independence 225
10.3 Immediate implications 226
10.4 Basic theorem for T equivalent measurements 227
10.5 Third order moments 228
10.6 Higher order moments and cumulants 230
10.7 Regression of true score on observed score 230
10.8 Implications, applications, and limitations 232
Chapter 11
Item Sampling in Test Theory and in Research Design
11.1 Introduction 234
11.2 Matrix sampling 236
11.3 Generalized symmetric means 238
11.4 First and second degree gsm s 241
11.5 Estimating true score moments 245
11.6 Estimating the relation of observed score to true score 248
11.7 Estimating the relation between scores on parallel test forms . . . 248
CONTENTS Xlii
11.8 Estimating the observed score statistics for lengthened tests .... 249
11.9 Frequency distribution of errors of measurement for binary items . . 250
11.10 Item sampling as a technique in research design 252
11.11 Estimating a mean from a single item sample 253
11.12 Estimating a mean by multiple matrix sampling 255
11.13 Estimating group mean differences 257
11.14 Estimating observed score variances by item sampling 259
PART 4
Validity and Test Construction Theory
Chapter 12
Validity
12.1 Introduction 261
12.2 Regression and prediction 262
12.3 Linear regression functions 264
12.4 Multiple and partial correlation 265
12.5 Partial and multiple correlation and regression in n variables . . . 267
12.6 The screening of predictor variables 269
12.7 Suppressor variables, moderator variables, and differential
predictability 271
12.8 Incremental validity 273
12.9 Validity and the selection ratio 275
12.10 Some remarks on the explication of the concept of validity
as a correlation coefficient 277
12.11 Construct validity 278
Chapter 13
The Selection of Predictor Variables
13.1 Introduction 284
13.2 Some sampling problems 284
13.3 Formal procedures for selecting predictor variables 288
13.4 Prediction in future samples 289
13.5 The effect of relative test lengths on reliability and validity:
the multiple predictor case 293
13.6 The determination of relative test lengths to maximize
the multiple correlation 295
Chapter 14
Measurement Procedures and Item Scoring Formulas
14.1 Introduction 302
14.2 Guessing and omitting 303
xiv CONTENTS
14.3 A simple formula score 305
14.4 Properties of the simple formula score 307
14.5 A simple regression model for scoring items 310
14.6 The regression method with a simple model that assumes
partial knowledge 312
14.7 Other item scoring formulas 313
14.8 An evaluation of partial knowledge 314
14.9 Methods for discriminating levels of partial knowledge
concerning a test item 315
14.10 Assumptions underlying the personal probability approach
to item scoring 319
14.11 Reproducing scoring systems 321
Chapter 15
Item Parameters and Test Construction
15.1 Introduction 327
15.2 Item difficulty 328
15.3 Item discriminating power 329
15.4 Item validity 332
15.5 Product moment correlations for dichotomous items 335
15.6 Biserial correlation 337
15.7 Comparison of biserial and point biserial coefficients 340
15.8 Tetrachoric correlation 345
15.9 A comparison of tetrachoric and phi coefficients 346
15.10 Considerations in the choice of test construction techniques .... 350
15.11 Formula scoring and corrections for chance success 352
15.12 Invariant item parameters 353
Chapter 16
Latent Traits and Item Characteristic Functions
16.1 Introduction 358
16.2 Latent variables 359
16.3 Local independence 360
16.4 Item test regression 363
16.5 The normal ogive model 365
16.6 Conditions leading to the normal ogive model 370
16.7 Correlation matrix with one common factor 371
16.8 A sufficient condition for normal ogive item characteristic curves . . 374
16.9 Normal ogive parameters: item difficulty 376
16.10 Normal ogive parameters: item discriminating power 377
16.11 Practical use of normal ogive item parameters 379
16.12 Conditional distribution of test scores 384
16.13 A relation of latent trait to true score 386
16.14 Typical distortions in mental measurement 387
CONTENTS XV
PART 5
Some Latent Trait Models
and Their Use in Inferring an Examinee s Ability
(Contributed by Allan Birnbaum)
Chapter 17
Some Latent Trait Models
17.1 Introduction 397
17.2 The logistic test model 399
17.3 Other models 402
17.4 The test as a measuring instrument: examples of classification
and estimation of ability levels by use of test scores 405
17.5 Information structure of a test and transformations of
scale of scores 410
17.6 Transformations of scales of ability 411
17.7 Calculations of distributions of test scores 414
17.8 Quantal response models in general 420
17.9 Estimation of item parameters 420
17.10 Validity of test models 422
Chapter 18
Test Scores, Sufficient Statistics,
and the Information Structures of Tests
18.1 Sufficient statistics: definition and interpretation 425
18.2 Conditions for sufficiency of a statistic 428
18.3 Test scores and sufficient statistics 429
18.4 Sufficiency and the logistic test model 431
18.5 Sufficiency and the information structures of tests 434
Chapter 19
Classification by Ability Levels
19.1 Classification rules for distinguishing two levels of ability .... 436
19.2 Two point classification problems 437
19.3 Locally best weights and classification rules 442
19.4 More general classification rules, composite scores, and
statistical efficiency in general 444
19.5 Quantitative appraisal and efficient design of classification rules . . . 446
Chapter 20
Estimation of an Ability
20.1 Introduction 453
20.2 Some algebra of information functions 453
20.3 More general methods of estimation: maximum likelihood .... 455
20.4 The information functions of various test items 460
Xvi CONTENTS
20.5 The information functions of various tests 465
20.6 Problems of test design and item selection 468
20.7 Relative precisions or efficiencies of various test designs,
test score formulas, and estimators 471
20.8 Efficiency of unweighted scores in the logistic model 472
PART 6
Strong True Score Theory
Chapter 21
Poisson Process Models
21.1 Introduction 480
21.2 Generating functions and the Poisson distribution 481
21.3 Derivation of the model for misreadings as a Poisson limit
of Bernoulli trials with variable probabilities 485
21.4 Statement of the Poisson model for misreadings 486
21.5 The separation of parameters in the model for misreadings .... 487
21.6 A parameter free distribution for testing the fit of
the model for misreadings 489
21.7 A stochastic process model for oral reading speed 489
21.8 Uncompleted texts 490
Chapter 22
Measurements with Independent Errors
of Known Distributional Form
22.1 Introduction 493
22.2 Moments of the true score distribution 494
22.3 Basic equations in latent trait theory 496
22.4 A formula for the distribution of true scores in terms of
the distribution of observed scores 497
22.5 Statistical inference problems 499
22.6 The regression of true score on observed score 500
22.7 The assumption of normally distributed errors 502
22.8 Conditions for linear regression of true score on observed score . . . 503
22.9 Conditions for linear multiple regression of true score on two or more
r equivalent observed scores 505
22.10 Conditions for linear regression of one measurement on another . . . 505
Chapter 23
Binomial Error Models
23.1 Introduction 508
23.2 Definitions and assumptions 509
23.3 Confidence intervals for true score 511
CONTEXTS Xvil
23.4 The fundamental equation 512
23.5 Regression of true score on observed score 513
23.6 Negative hypergeometric distribution of test scores 515
23.7 The beta distribution of true scores 520
23.8 Moments of the true score distribution 521
23.9 Relation of the binomial error model to more general test theory models 523
23.10 The compound binomial error model 524
23.11 Solving for the distribution of true scores 526
Chapter 24
True Scores, Factors, and Latent Traits
24.1 Introduction 530
24.2 The multiple factor analytic model 530
24.3 A comparison between the factor analytic and true score decompositions 535
24.4 Factors as latent traits 537
24.5 Conditional independence 538
24.6 A relationship between true scores and latent traits 541
24.7 A general latent trait model 543
24.8 Latent trait models for binary random variables 545
Author Index 551
Topic Index 557
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| genre_facet | Scores |
| id | DE-604.BV008083066 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T17:14:07Z |
| institution | BVB |
| isbn | 0201043106 |
| language | Undetermined |
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| physical | XVII, 568 S. graph. Darst. |
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| series2 | Addison-Wesley series in behavioral science : Quantitative methods |
| spelling | Statistical theories of mental test scores Frederic M. Lord and Melvin R. Novick. With contributions by Allan Birnbaum 2. print. Reading, Mass. [u.a.] Addison-Wesley 1974 XVII, 568 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Addison-Wesley series in behavioral science : Quantitative methods Statistischer Test (DE-588)4077852-6 gnd rswk-swf Intelligenztest (DE-588)4027254-0 gnd rswk-swf Scores gnd rswk-swf Intelligenztest (DE-588)4027254-0 s Scores f Statistischer Test (DE-588)4077852-6 s DE-604 Lord, Frederic M. Sonstige oth Novick, Melvin R. Sonstige oth Birnbaum, Allan Sonstige oth HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=005322383&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Statistical theories of mental test scores Statistischer Test (DE-588)4077852-6 gnd Intelligenztest (DE-588)4027254-0 gnd |
| subject_GND | (DE-588)4077852-6 (DE-588)4027254-0 |
| title | Statistical theories of mental test scores |
| title_auth | Statistical theories of mental test scores |
| title_exact_search | Statistical theories of mental test scores |
| title_full | Statistical theories of mental test scores Frederic M. Lord and Melvin R. Novick. With contributions by Allan Birnbaum |
| title_fullStr | Statistical theories of mental test scores Frederic M. Lord and Melvin R. Novick. With contributions by Allan Birnbaum |
| title_full_unstemmed | Statistical theories of mental test scores Frederic M. Lord and Melvin R. Novick. With contributions by Allan Birnbaum |
| title_short | Statistical theories of mental test scores |
| title_sort | statistical theories of mental test scores |
| topic | Statistischer Test (DE-588)4077852-6 gnd Intelligenztest (DE-588)4027254-0 gnd |
| topic_facet | Statistischer Test Intelligenztest Scores |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=005322383&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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