Psychometric theory:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York <<[u.a.]>>
McGraw-Hill
[200]6
|
| Ausgabe: | 3. ed., [Nachdr.] |
| Schriftenreihe: | MacGraw-Hill series in psychology
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XXIV, 752 S. graph. Darst. |
| ISBN: | 007047849X 9780070478497 |
Internformat
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| 245 | 1 | 0 | |a Psychometric theory |c Jum C. Nunnally ; Ira H. Bernstein |
| 250 | |a 3. ed., [Nachdr.] | ||
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Datensatz im Suchindex
| _version_ | 1804138183544274944 |
|---|---|
| adam_text | CONTENTS
PREFACE XXi
PART 1 INTRODUCTION 1
1 Introduction 3
CHAPTER OVERVIEW 3
MEASUREMENT IN SCIENCE 3
What Is “Meaningful” and “Useful”?
ADVANTAGES OF STANDARDIZED MEASURES 6
Objectivity / Quantification / Communication / Economy / Scientific
Generalization
MEASUREMENT AND MATHEMATICS 8
Measurement and Statistics
MEASUREMENT SCALES 11
Nominal scales / Ordinal scales / Interval scales / Ratio Scales /
Other Scales / Invariance
DECISIONS ABOUT MEASUREMENT SCALES 20
Ostensive Characteristics / Consequences of Assumptions / Convention
/ Classification as Measurement
RECENT TRENDS IN MEASUREMENT 27
The Impact of Computers / Closed versus Open-Form Solutions /
Computer Simulation
SUMMARY 29
SUGGESTED ADDITIONAL READINGS 30
PART 2 STATISTICAL FOUNDATIONS 31
2 Traditional Approaches To Scaling 33
CHAPTER OVERVIEW 33
ix
X CONTENTS
DATA MATRICES
More Complex Organizations / “Holes” in the Matrix (Missing Data)
EVALUATION OF MODELS 36
Scaling Stimuli versus Scaling People
A BRIEF INTRODUCTION TO PSYCHOPHYSICS 39
Psychophysical Methods / Absolute Thresholds / Simulating a
Threshold / Difference Thresholds / The Weber Fraction, Fechner s
Law, and Psychophysical Scaling / Direct Psychophysics and the
Plateau-Stevens Tradition / The Fullerton-Cattell Law / Signal
Detection Theory and Modern Psychophysics
TYPES OF STIMULI AND RESPONSES 5°
Judgments versus Sentiments / Absolute versus Comparative
Responses / Preferences versus Similarity Responses / Specified
versus Unspecified Attributes
METHODS FOR CONVERTING RESPONSES TO STIMULUS SCALES 53
Ordinal Methods / Interval Methods / Ratio Methods
MODELS FOR SCALING STIMULI 55
Direct (Subjective Estimate) Models / Indirect (Discriminant) Models /
Simulating Thurstone Scaling / A Comparison of the Two
Simulations / The Logistic Distribution and Luce s Choice Theory /
Averages as Scale Values / Checks and Balances / Multi-item
Measures / Item Trace Lines (Item Characteristics Curves) /
Difficulty and Discrimination
DETERMINISTIC MODELS FOR SCALING PEOPLE 71
The Guttman Scale / Evaluation of the Guttman Scale
PROBABILISTIC MODELS FOR SCALING PEOPLE 75
Nonmonotone Models / Monotone Models with Specified Distribution
Forms / Monotone Models with Unspecified Distribution Forms
SUMMARY 81
SUGGESTED ADDITIONAL READINGS 82
3 Validity 83
CHAPTER OVERVIEW 83
GENERAL CONSIDERATIONS 84
CONSTRUCT VALIDITY 84
Domain of Observables / Relations among Observables / Relations
among Constructs / Campbell and Fiske’s Contribution to Construct
Validation
PREDICTIVE VALIDITY 94
The Temporal Relation between Predictor and Criterion / The Criterion
Problem / Other Problems in Prediction / The “Composite Criterion” /
Validity Coefficients / Validity Generalization / Meta-analysis
CONTENT VALIDITY 101
EXPLICATION OF CONSTRUCTS 104
CONTENTS XI
Changing Substantive Theories versus Changing Measurement
Theories / A Commonsense Point of View
OTHER ISSUES CONCERNING VALIDITY 108
Relations among the Three Types of Validity / Other Names / The
Place of Factor Analysis
SUMMARY 112
SUGGESTED ADDITIONAL READINGS 113
4 Elements of Statistical Description and Estimation 114
CHAPTER OVERVIEW 114
CONTINUOUS VERSUS DISCRETE (CATEGORICAL) VARIABLES 115
VARIANCE 116
Transformations of Distributions
CORRELATION AND COVARIANCE AS CONCEPTS 120
THE PEARSON PRODUCT-MOMENT CORRELATION 120
The Meaning of Pearson Product-Moment Correlation / Computer
Applications / Covariance / Other Measures of Linear Relation /
Three Special Cases
ESTIMATES OF r 125
Biserial r (rbis) / Tetrachoric Correlation (rtet) and Related Estimates
PEARSON r VERSUS ESTIMATES OF PEARSON r 127
Some Related Issues in Categorization
ASSUMPTIONS UNDERLYING r 129
FACTORS INFLUENCING r 130
Restriction of Range / Distribution Form
A UNIVERSAL MEASURE OF RELATIONSHIP 135
PREDICTION, REGRESSION, AND STRUCTURAL EQUATIONS 139
Regression / Regression Based upon Raw Scores / The Standard
Error of Estimate / Partitioning of Variance / Structural Equations
STATISTICAL ESTIMATION AND STATISTICAL DECISION THEORY 147
Generalized Least-Squares Estimation / Maximum Likelihood
Estimation / Maximum Likelihood and the Testing of Hierarchical
Models / Bayesian Estimation / The Method of Moments / Equal
Weighting (The “It Don’t Make No Nevermind Principle”) / Properties
of Estimators
SUMMARY 156
SUGGESTED ADDITIONAL READINGS 158
5 Linear Combinations, Partial Correlation, Multiple Correlation, and
Multiple Regression 159
CHAPTER OVERVIEW 159
VARIANCES OF LINEAR COMBINATIONS 160
Variance of a Weighted Sum / Variance of a Sum of Standard Scores /
xii CONTENTS
Variance of Sums of Dichotomous Distributions / Numerical
Examples
CHARACTERISTICS OF SCORE DISTRIBUTIONS 166
Variances / Distribution Shape
COVARIANCE OF LINEAR COMBINATIONS 171
Correlation of Linear Combinations / Numerical Example
PARTIAL CORRELATION 175
An Example of Partialling / Higher-Order Partialling / Another Form of
Partialling
MULTIPLE CORRELATION AND MULTIPLE REGRESSION 182
The Two-Predictor Case / Numerical Example / The General Case /
Testing the Significance of R and Increments in ft /Determinants of
R / Categorical Predictors / Multicollinearity / Predictor Importance
SELECTION AND ALTERNATIVE WEIGHTINGS OF PREDICTORS 193
Stepwise Inclusion of Predictors / All Possible Subsets Approaches /
Hierarchical Inclusion of Variables / Combining Strategies /
Moderated Multiple Regression / Variable Weighting
RELATED TOPICS 203
The Analysis of Covariance / Nonlinear Relations / Residual
Analysis / Canonical Analysis
SUMMARY 205
SUGGESTED ADDITIONAL READINGS 208
PART 3 CONSTRUCTION OF MULTI-ITEM MEASURES 209
6 The Theory of Measurement Error 211
CHAPTER OVERVIEW 211
THE CONCEPT OF MEASUREMENT ERROR 212
ONE FORM OF CLASSICAL TEST THEORY 215
THE DOMAIN-SAMPLING MODEL 216
Multi-item Measures / Estimates of Reliability / The Importance of the
Reliability Coefficient
THE MODEL OF PARALLEL TESTS 223
PERSPECTIVES ON THE TWO MODELS 226
Factorial Composition
PRECISION OF RELIABILITY ESTIMATES 228
Variances of Items
FURTHER DEDUCTIONS FROM THE DOMAIN-SAMPLING MODEL 230
՝ Test Length / The Reliability of an Item Sample and Coefficient Alpha /
Numerical Example / Variance of True and Error Scores /
Estimation of True Scores / The Standard Error of Measurement /
Attenuation
CONTENTS XÎii
ALTERNATIVE MODELS 241
Factorial Domain-Sampling Model / The Binomial Model
RELIABILITY AS STABILITY OVER TIME 243
Difference Scores / One Other Consideration
SUMMARY 246
SUGGESTED ADDITIONAL READINGS 247
7 The Assessment of Reliability 248
CHAPTER OVERVIEW 248
SOURCES OF ERROR 249
Variation within a Test / Variation between Tests
ESTIMATION OF RELIABILITY 251
Internal Consistency / Alternative Forms / Other Estimates of
Reliability / Long-Range Stability
USES OF THE RELIABILITY COEFFICIENT 256
Corrections for Attenuation / Confidence Intervals / Effect of
Dispersion on Reliability
MAKING MEASURES RELIABLE 262
Test Length / Standards of Reliability / Limitations on the Reliability
Coefficient’s Utility
RELIABILITY OF LINEAR COMBINATIONS 266
Negative Elements / Weighted Sums / Principles Concerning the
Reliability of Linear Combinations
AN ANALYSIS OF VARIANCE APPROACH TO RELIABILITY 274
Some Basic Concepts / Application to the Study of Reliability
GENERALIZABILITY THEORY 279
Basic Concepts / Generalizability Studies and Decision Studies / A
Single Facet Design / Theoretical Considerations / Applying the
Results of a Single Facet G Study to a Study / A Fixed-Facet
Design / Higher-Order Designs
SUMMARY 290
SUGGESTED ADDITIONAL READINGS 292
8 Construction of Conventional Tests 293
CHAPTER OVERVIEW 293
CONSTRUCTION OF TESTS DESIGNED FOR CONTENT VALIDATION 295
The Domain of Content and Test Plan / Test Items / Test Length /
Sample of Subjects / Item Analysis / Item Selection / Norms / The
Role of External Correlates
CONSTRUCTION OF TESTS DESIGNED FOR CONSTRUCT VALIDATION 310
The Hypothesis and Domain of Content / Content Homogeneity /
Methodological Heterogeneity / Relations among Measures and
Constructs / The Role of Factor Analysis / Item Analysis and
Selection / The Inadequacy of Rational Approaches to Test
xiv CONTENTS
Construction / The inadequacy of Empirical (Criterion-Oriented)
Approaches to Test Construction / Norms / Applying the Measure /
Some Examples of Constructs in the Abilities Area
CONSTRUCTION OF TESTS DESIGNED FOR PREDICTIVE
VALIDATION
Item Analysis, Item Selection, and Norms
PROBLEMS UNIQUE TO CERTAIN TESTING SITUATIONS
Reversing the Direction of Keying / Unipolar versus Bipolar Attributes /
Discrimination at a Point / Equidiscriminating Tests / Weighting of
Items / Taking Advantage of Chance
SUMMARY
SUGGESTED ADDITIONAL READINGS
324
326
334
337
9 Special Problems in Classical Test Theory 338
CHAPTER OVERVIEW 338
GUESSING 340
The Blind Guessing Model and Abbott’s Formula / Effectsof Guessing
on Test Parameters / The Accuracy of the Correction for Blind
Guessing / Sophisticated Guessing Models / Practical
Considerations / Using the Model to Estimate Test Parameters /
Multiple-Choice versus Short Answer Tests
SPEED TESTS 348
The Internal Structure of Speed Tests / The Item Pool / Measurement
of Reliability / Factor Composition / Variables Relating to Speed /
Statistical Effects of Time Limits / One-Trial Measures of the Effects
of Time Limits / Correction for Guessing in Speed Tests / Timed-
Power Tests / Speed-Difficulty Tests / Factors Measured by Speed
and Power Tests / Implications
ADVERSE IMPACT, IMPROPER DISCRIMINATION, TEST
BIAS, AND DISPARITY 357
Definitions of Bias / Disparity and Bias / Test Bias, Regression, and
the Cleary Rule / Applying Linear Regression to Salary Disputes /
Reverse Regression / Residual Analysis / Simpson’s Paradox
Revisited / Bias in Content-Validated Measures / Barriers and
Cutoffs / Selection Fairness and Quotas / Pooled versus Separate
n Group Norms
HALO EFFECTS 373
Traditional Measures of Halo / Recent Developments in the Study of
Halo
RESPONSE BIASES AND RESPONSE STYLES 376
Sources of Bias / Changes in Test Scores as Personality Changes /
Carelessness and Confusion / The Role of Social Desirability /
Other Proposed Stylistic Variables
CONTENTS
XV
MULTISCALE TESTS
Item Overlap
SUMMARY
SUGGESTED ADDITIONAL READINGS
10 Recent Developments in Test Theory
CHAPTER OVERVIEW
ITEM RESPONSE THEORY
Conditional Independence / One-Parameter Models / Two-Parameter
Models / Three-Parameter Models / Item and Test Information /
The Bock Nominal Model I The Samejima Model for Graded
(Ordinal) Responses / A Nonparametric Approach / Other IRT
Models / Applications to Nonstandard Testing Conditions / Scoring
Algorithms
DIFFERENTIAL ITEM FUNCTIONING (ITEM BIAS)
A Substantive Example / A Simulated Example / Differential
Alternative Functioning / IRT Approaches to Assessing DIF /
Alternative IRT Approaches / Classical Approaches to Assessing
DIF / Content Bias
TAILORED TESTS AND COMPUTERIZED ADAPTIVE
TESTING
Tailored Testing and Psychophysical Thresholds / Applying the
Staircase Principle to Psychometrics / Flexilevel Tests / More
Complex Forms of Tailored Testing / Perspectives on Tailored Tests
COMMENTARY ON IRT
ACHIEVEMENT TESTS FOR MASTERY LEARNING
Nature of Mastery Learning / Test Construction / Definition of
“Mastery” / Practical Problems
SUMMARY
SUGGESTED ADDITIONAL READINGS
PART 4 FACTOR ANALYSIS
11 Factor Analysis I: The General Model and Variance
Condensation
CHAPTER OVERVIEW
USES OF FACTOR ANALYSIS
Factors as Groupings of Variables / Exploratory and Confirmatory
Analysis / Factor Analysis and Scientific Generalization / Variable
and Subject Selection
BASIC CONCEPTS
The General Factor Model / The Unit of Measurement / Estimating
386
388
392
393
393
394
416
428
433
436
438
442
445
447
447
449
454
XVI CONTENTS
Correlations / Structure Elements / Successive versus
Simultaneous Factoring / Geometric and Algebraic Interpretations /
Components of Variance / Types of Factors
CONDENSING VARIANCE IN EXPLORATORY FACTOR ANALYSIS
The Role of the Correlation Matrix / Properties of a Factor Solution
CENTROID CONDENSATION
PRINCIPAL COMPONENT AND PRINCIPAL AXIS
CONDENSATION
Principal Components / Mathematical Properties of Principal
Components / Principal Axis Solutions
MAXIMUM LIKELIHOOD AND RELATED FORMS OF CONDENSATION 477
Usefulness of ML Factoring / Variants on ML Factoring
OTHER METHODS OF CONDENSATION 481
DETERMINING THE NUMBER OF FACTORS 482
Consequences of Choosing a Given Number of Factors
CAUSAL INDICATORS 484
SUMMARY 485
SUGGESTED ADDITIONAL READINGS 490
12 Exploratory Factor Analysis II: Rotation and Other Topics
491
CHAPTER OVERVIEW
FACTOR ROTATION
Geometric Analogy / Visual Rotation / Further Mathematics of Rotation
/ Oblique Rotations / Simple and “Simpler՞ Structures / Reference
Vectors
ANALYTIC ROTATIONS
Quartimax / Varimax / Promax
ESTIMATION OF FACTOR SCORES
Practical Considerations in Obtaining Factor Scores
RELATIONS AMONG THE VARIOUS MATRICES
THE COMMON FACTOR MODEL
The Problem of Communality Estimation / Factorable Matrices / Matrix
Rank / Unities as Communality Estimates / Communalities Derived
from Hypotheses / Statistical Criteria of Rank / Iteration / Squared
Multiple Correlations / Reliability Coefficients / Direct Estimation /
Some Major Differences between Component and Common Factor
Solutions / Some Conceptual Problems with the Common Factor
Model / Effects of Number of Variables and Average Correlation upon
the Factor Structure
FACTOR ANALYTIC DESIGNS
Alternative Designs / Three-Mode Factor Analysis
AD-LIB FACTORING
HIGHER-ORDER FACTORS
HOW TO FOOL YOURSELF WITH FACTOR ANALYSIS
491
493
505
507
512
514
526
531
532
533
CONTENTS XVii
AN OUTLOOK ON EXPLORATORY FACTOR ANALYSIS 535
Practical Considerations in Factor Analysis
SUMMARY 536
SUGGESTED ADDITIONAL READINGS 541
13 Confirmatory Factor Analysis 542
CHAPTER OVERVIEW 542
SPEARMAN S GENERAL FACTOR SOLUTION 544
COMPARING FACTORS IN DIFFERENT ANALYSES 548
Classical Approaches to Testing Factor Invariance / Some Practical
Aspects of Comparing Factor Structures / Comparing Overall
Solutions / ACS Approaches
TESTING WEAK THEORIES (THEORIES CONCERNING GROUPINGS OF
VARIABLES) 554
Multiple Group Confirmatory Analysis / Procrustes
Confirmatory Analysis / ACS Confirmatory Analysis / A Comparison
of the Three Approaches
FACTORING CATEGORICAL VARIABLES (ITEM LEVEL FACTORING) 570
ACS and Related Approaches with PM Measures / Multiscale Analyses
TESTING STRONG THEORIES 576
Introduction to the Full ACS Model / ACS Notation / Assumptions /
Properties of Path Coefficients / A Note on Inferring Causality from
Correlational Data / Model Specification in ACS / Recursive and
Nonrecursive Models / Cross-lagged Correlation / Applying ACS /
Reapplying ACS / Classical Approaches to Strong Theories
SUMMARY 590
SUGGESTED ADDITIONAL READINGS 594
PART 5 ADDITIONAL STATISTICAL MODELS, CONCEPTS, AND ISSUES 595
14 Profile Analysis, Discriminant Analysis, and Multidimensional Scaling 597
CHAPTER OVERVIEW 597
CLUSTER ANALYSIS 598
PROBLEMS IN PROFILE ANALYSIS 599
Characteristics of Score Profiles
CLUSTERING OF PROFILES 601
Measures of Profile Similarity / Distance Measure / Hierarchical and
Overlapping Clustering
RAW-SCORE FACTOR ANALYSIS 604
An Example of Raw-Score Factor Analysis / How Raw-Score Factor
Analysis Works / Transformations of Variables / Transformations of
Profiles
xviii CONTENTS
DISCRIMINANT ANALYSIS
Geometric Interpretation of Discriminant Analysis / Linear Discriminant
Function / Multiple Linear Discriminant Functions / Placement /
Evaluation of Discriminant Analysis
PATTERN ANALYSIS
Discovering Latent Groups / Discriminating among Existing Groups /
Evaluation of Pattern Analysis
MULTIDIMENSIONAL SCALING
Spatial Conceptions of MDS / An Overview of Alternative Approaches
to MDS / Psychophysical Methods Based upon Similarity /
Psychophysical Methods Based upon Attribute Ratings / Indirect
Methods / Vector-Space Ratio Methods / Euclidian Distance Ratio
Methods / Interval Methods / Ordinal Methods and ALSCAL /
Some Empirical Properties of Alternative MDS Solutions / MDS of
Correlation Matrices / Scaling of Individual Differences / An
Example of the Use of MDS / Some Concluding Comments
DOMINANCE (PREFERENCE) SCALING
The Unfolding Concept / Multidimensional Unfolding and ALSCAL
SUMMARY
SUGGESTED ADDITIONAL READINGS
610
620
621
645
648
651
15 The Analysis of Categorical Data, Binary Classification, and Alternatives to
Geometric Representations
CHAPTER OVERVIEW
CATEGORICAL MODELING
Two-way Independence / Association (Nonindependence) /
Alternative Models for the 2x2 Case / Measures of Association in
the 2x2 Design / More about G2 / The Generalized Logit Variant /
Structural and Random Zeros / Multiple Levels on a Variable /
Higher-Order Designs / Predictor-Criterion Models / Multiple
Response Categories in Predictor-Criterion Models / Some Important
Assumptions / Log-linear Modeling and Item Response Theory /
More-Specific Categorical Models / Logistic Regression /
Comparing Groups with Logistic Regression / An Illustrative
Problem / A Note on Residuals / Predicting Categorical Criteria
BINARY CLASSIFICATION 680
Classical Signal Detection / Categorical Modeling Approaches to the
Equal Variance Gaussian Model / General Recognition Theory /
Application to Condensation Tasks / MDS, Dissimilarity Judgments,
and General Recognition Theory / Implications for Measurement
NONGEOMETRIC AND NON-EUCLIDIAN MODELS 696
Nearest Neighbors / Tree Representations / Network and Graph
Theoretic Approaches / Conclusions
652
652
654
CONTENTS XIX
SUMMARY 704
SUGGESTED ADDITIONAL READINGS 708
REFERENCES 709
INDEXES
Name Index 735
Subject Index 741
|
| adam_txt |
CONTENTS
PREFACE XXi
PART 1 INTRODUCTION 1
1 Introduction 3
CHAPTER OVERVIEW 3
MEASUREMENT IN SCIENCE 3
What Is “Meaningful” and “Useful”?
ADVANTAGES OF STANDARDIZED MEASURES 6
Objectivity / Quantification / Communication / Economy / Scientific
Generalization
MEASUREMENT AND MATHEMATICS 8
Measurement and Statistics
MEASUREMENT SCALES 11
Nominal scales / Ordinal scales / Interval scales / Ratio Scales /
Other Scales / Invariance
DECISIONS ABOUT MEASUREMENT SCALES 20
Ostensive Characteristics / Consequences of Assumptions / Convention
/ Classification as Measurement
RECENT TRENDS IN MEASUREMENT 27
The Impact of Computers / Closed versus Open-Form Solutions /
Computer Simulation
SUMMARY 29
SUGGESTED ADDITIONAL READINGS 30
PART 2 STATISTICAL FOUNDATIONS 31
2 Traditional Approaches To Scaling 33
CHAPTER OVERVIEW 33
ix
X CONTENTS
DATA MATRICES
More Complex Organizations / “Holes” in the Matrix (Missing Data)
EVALUATION OF MODELS 36
Scaling Stimuli versus Scaling People
A BRIEF INTRODUCTION TO PSYCHOPHYSICS 39
Psychophysical Methods / Absolute Thresholds / Simulating a
Threshold / Difference Thresholds / The Weber Fraction, Fechner's
Law, and Psychophysical Scaling / Direct Psychophysics and the
Plateau-Stevens Tradition / The Fullerton-Cattell Law / Signal
Detection Theory and Modern Psychophysics
TYPES OF STIMULI AND RESPONSES 5°
Judgments versus Sentiments / Absolute versus Comparative
Responses / Preferences versus Similarity Responses / Specified
versus Unspecified Attributes
METHODS FOR CONVERTING RESPONSES TO STIMULUS SCALES 53
Ordinal Methods / Interval Methods / Ratio Methods
MODELS FOR SCALING STIMULI 55
Direct (Subjective Estimate) Models / Indirect (Discriminant) Models /
Simulating Thurstone Scaling / A Comparison of the Two
Simulations / The Logistic Distribution and Luce's Choice Theory /
Averages as Scale Values / Checks and Balances / Multi-item
Measures / Item Trace Lines (Item Characteristics Curves) /
Difficulty and Discrimination
DETERMINISTIC MODELS FOR SCALING PEOPLE 71
The Guttman Scale / Evaluation of the Guttman Scale
PROBABILISTIC MODELS FOR SCALING PEOPLE 75
Nonmonotone Models / Monotone Models with Specified Distribution
Forms / Monotone Models with Unspecified Distribution Forms
SUMMARY 81
SUGGESTED ADDITIONAL READINGS 82
3 Validity 83
CHAPTER OVERVIEW 83
GENERAL CONSIDERATIONS 84
CONSTRUCT VALIDITY 84
Domain of Observables / Relations among Observables / Relations
among Constructs / Campbell and Fiske’s Contribution to Construct
Validation
PREDICTIVE VALIDITY 94
The Temporal Relation between Predictor and Criterion / The Criterion
Problem / Other Problems in Prediction / The “Composite Criterion” /
Validity Coefficients / Validity Generalization / Meta-analysis
CONTENT VALIDITY 101
EXPLICATION OF CONSTRUCTS 104
CONTENTS XI
Changing Substantive Theories versus Changing Measurement
Theories / A Commonsense Point of View
OTHER ISSUES CONCERNING VALIDITY 108
Relations among the Three Types of Validity / Other Names / The
Place of Factor Analysis
SUMMARY 112
SUGGESTED ADDITIONAL READINGS 113
4 Elements of Statistical Description and Estimation 114
CHAPTER OVERVIEW 114
CONTINUOUS VERSUS DISCRETE (CATEGORICAL) VARIABLES 115
VARIANCE 116
Transformations of Distributions
CORRELATION AND COVARIANCE AS CONCEPTS 120
THE PEARSON PRODUCT-MOMENT CORRELATION 120
The Meaning of Pearson Product-Moment Correlation / Computer
Applications / Covariance / Other Measures of Linear Relation /
Three Special Cases
ESTIMATES OF r 125
Biserial r (rbis) / Tetrachoric Correlation (rtet) and Related Estimates
PEARSON r VERSUS ESTIMATES OF PEARSON r 127
Some Related Issues in Categorization
ASSUMPTIONS UNDERLYING r 129
FACTORS INFLUENCING r 130
Restriction of Range / Distribution Form
A UNIVERSAL MEASURE OF RELATIONSHIP 135
PREDICTION, REGRESSION, AND STRUCTURAL EQUATIONS 139
Regression / Regression Based upon Raw Scores / The Standard
Error of Estimate / Partitioning of Variance / Structural Equations
STATISTICAL ESTIMATION AND STATISTICAL DECISION THEORY 147
Generalized Least-Squares Estimation / Maximum Likelihood
Estimation / Maximum Likelihood and the Testing of Hierarchical
Models / Bayesian Estimation / The Method of Moments / Equal
Weighting (The “It Don’t Make No Nevermind Principle”) / Properties
of Estimators
SUMMARY 156
SUGGESTED ADDITIONAL READINGS 158
5 Linear Combinations, Partial Correlation, Multiple Correlation, and
Multiple Regression 159
CHAPTER OVERVIEW 159
VARIANCES OF LINEAR COMBINATIONS 160
Variance of a Weighted Sum / Variance of a Sum of Standard Scores /
xii CONTENTS
Variance of Sums of Dichotomous Distributions / Numerical
Examples
CHARACTERISTICS OF SCORE DISTRIBUTIONS 166
Variances / Distribution Shape
COVARIANCE OF LINEAR COMBINATIONS 171
Correlation of Linear Combinations / Numerical Example
PARTIAL CORRELATION 175
An Example of Partialling / Higher-Order Partialling / Another Form of
Partialling
MULTIPLE CORRELATION AND MULTIPLE REGRESSION 182
The Two-Predictor Case / Numerical Example / The General Case /
Testing the Significance of R and Increments in ft /Determinants of
R / Categorical Predictors / Multicollinearity / Predictor Importance
SELECTION AND ALTERNATIVE WEIGHTINGS OF PREDICTORS 193
Stepwise Inclusion of Predictors / All Possible Subsets Approaches /
Hierarchical Inclusion of Variables / Combining Strategies /
Moderated Multiple Regression / Variable Weighting
RELATED TOPICS 203
The Analysis of Covariance / Nonlinear Relations / Residual
Analysis / Canonical Analysis
SUMMARY 205
SUGGESTED ADDITIONAL READINGS 208
PART 3 CONSTRUCTION OF MULTI-ITEM MEASURES 209
6 The Theory of Measurement Error 211
CHAPTER OVERVIEW 211
THE CONCEPT OF MEASUREMENT ERROR 212
ONE FORM OF CLASSICAL TEST THEORY 215
THE DOMAIN-SAMPLING MODEL 216
Multi-item Measures / Estimates of Reliability / The Importance of the
Reliability Coefficient
THE MODEL OF PARALLEL TESTS 223
PERSPECTIVES ON THE TWO MODELS 226
Factorial Composition
PRECISION OF RELIABILITY ESTIMATES 228
Variances of Items
FURTHER DEDUCTIONS FROM THE DOMAIN-SAMPLING MODEL 230
՝ Test Length / The Reliability of an Item Sample and Coefficient Alpha /
Numerical Example / Variance of True and Error Scores /
Estimation of True Scores / The Standard Error of Measurement /
Attenuation
CONTENTS XÎii
ALTERNATIVE MODELS 241
Factorial Domain-Sampling Model / The Binomial Model
RELIABILITY AS STABILITY OVER TIME 243
Difference Scores / One Other Consideration
SUMMARY 246
SUGGESTED ADDITIONAL READINGS 247
7 The Assessment of Reliability 248
CHAPTER OVERVIEW 248
SOURCES OF ERROR 249
Variation within a Test / Variation between Tests
ESTIMATION OF RELIABILITY 251
Internal Consistency / Alternative Forms / Other Estimates of
Reliability / Long-Range Stability
USES OF THE RELIABILITY COEFFICIENT 256
Corrections for Attenuation / Confidence Intervals / Effect of
Dispersion on Reliability
MAKING MEASURES RELIABLE 262
Test Length / Standards of Reliability / Limitations on the Reliability
Coefficient’s Utility
RELIABILITY OF LINEAR COMBINATIONS 266
Negative Elements / Weighted Sums / Principles Concerning the
Reliability of Linear Combinations
AN ANALYSIS OF VARIANCE APPROACH TO RELIABILITY 274
Some Basic Concepts / Application to the Study of Reliability
GENERALIZABILITY THEORY 279
Basic Concepts / Generalizability Studies and Decision Studies / A
Single Facet Design / Theoretical Considerations / Applying the
Results of a Single Facet G Study to a Study / A Fixed-Facet
Design / Higher-Order Designs
SUMMARY 290
SUGGESTED ADDITIONAL READINGS 292
8 Construction of Conventional Tests 293
CHAPTER OVERVIEW 293
CONSTRUCTION OF TESTS DESIGNED FOR CONTENT VALIDATION 295
The Domain of Content and Test Plan / Test Items / Test Length /
Sample of Subjects / Item Analysis / Item Selection / Norms / The
Role of External Correlates
CONSTRUCTION OF TESTS DESIGNED FOR CONSTRUCT VALIDATION 310
The Hypothesis and Domain of Content / Content Homogeneity /
Methodological Heterogeneity / Relations among Measures and
Constructs / The Role of Factor Analysis / Item Analysis and
Selection / The Inadequacy of Rational Approaches to Test
xiv CONTENTS
Construction / The inadequacy of Empirical (Criterion-Oriented)
Approaches to Test Construction / Norms / Applying the Measure /
Some Examples of Constructs in the Abilities Area
CONSTRUCTION OF TESTS DESIGNED FOR PREDICTIVE
VALIDATION
Item Analysis, Item Selection, and Norms
PROBLEMS UNIQUE TO CERTAIN TESTING SITUATIONS
Reversing the Direction of Keying / Unipolar versus Bipolar Attributes /
Discrimination at a Point / Equidiscriminating Tests / Weighting of
Items / Taking Advantage of Chance
SUMMARY
SUGGESTED ADDITIONAL READINGS
324
326
334
337
9 Special Problems in Classical Test Theory 338
CHAPTER OVERVIEW 338
GUESSING 340
The Blind Guessing Model and Abbott’s Formula / Effectsof Guessing
on Test Parameters / The Accuracy of the Correction for Blind
Guessing / Sophisticated Guessing Models / Practical
Considerations / Using the Model to Estimate Test Parameters /
Multiple-Choice versus Short Answer Tests
SPEED TESTS 348
The Internal Structure of Speed Tests / The Item Pool / Measurement
of Reliability / Factor Composition / Variables Relating to Speed /
Statistical Effects of Time Limits / One-Trial Measures of the Effects
of Time Limits / Correction for Guessing in Speed Tests / Timed-
Power Tests / Speed-Difficulty Tests / Factors Measured by Speed
and Power Tests / Implications
ADVERSE IMPACT, IMPROPER DISCRIMINATION, TEST
BIAS, AND DISPARITY 357
Definitions of Bias / Disparity and Bias / Test Bias, Regression, and
the Cleary Rule / Applying Linear Regression to Salary Disputes /
Reverse Regression / Residual Analysis / Simpson’s Paradox
Revisited / Bias in Content-Validated Measures / Barriers and
Cutoffs / Selection Fairness and Quotas / Pooled versus Separate
n Group Norms
HALO EFFECTS 373
Traditional Measures of Halo / Recent Developments in the Study of
Halo
RESPONSE BIASES AND RESPONSE STYLES 376
Sources of Bias / Changes in Test Scores as Personality Changes /
Carelessness and Confusion / The Role of Social Desirability /
Other Proposed Stylistic Variables
CONTENTS
XV
MULTISCALE TESTS
Item Overlap
SUMMARY
SUGGESTED ADDITIONAL READINGS
10 Recent Developments in Test Theory
CHAPTER OVERVIEW
ITEM RESPONSE THEORY
Conditional Independence / One-Parameter Models / Two-Parameter
Models / Three-Parameter Models / Item and Test Information /
The Bock Nominal Model I The Samejima Model for Graded
(Ordinal) Responses / A Nonparametric Approach / Other IRT
Models / Applications to Nonstandard Testing Conditions / Scoring
Algorithms
DIFFERENTIAL ITEM FUNCTIONING (ITEM BIAS)
A Substantive Example / A Simulated Example / Differential
Alternative Functioning / IRT Approaches to Assessing DIF /
Alternative IRT Approaches / Classical Approaches to Assessing
DIF / Content Bias
TAILORED TESTS AND COMPUTERIZED ADAPTIVE
TESTING
Tailored Testing and Psychophysical Thresholds / Applying the
Staircase Principle to Psychometrics / Flexilevel Tests / More
Complex Forms of Tailored Testing / Perspectives on Tailored Tests
COMMENTARY ON IRT
ACHIEVEMENT TESTS FOR MASTERY LEARNING
Nature of Mastery Learning / Test Construction / Definition of
“Mastery” / Practical Problems
SUMMARY
SUGGESTED ADDITIONAL READINGS
PART 4 FACTOR ANALYSIS
11 Factor Analysis I: The General Model and Variance
Condensation
CHAPTER OVERVIEW
USES OF FACTOR ANALYSIS
Factors as Groupings of Variables / Exploratory and Confirmatory
Analysis / Factor Analysis and Scientific Generalization / Variable
and Subject Selection
BASIC CONCEPTS
The General Factor Model / The Unit of Measurement / Estimating
386
388
392
393
393
394
416
428
433
436
438
442
445
447
447
449
454
XVI CONTENTS
Correlations / Structure Elements / Successive versus
Simultaneous Factoring / Geometric and Algebraic Interpretations /
Components of Variance / Types of Factors
CONDENSING VARIANCE IN EXPLORATORY FACTOR ANALYSIS
The Role of the Correlation Matrix / Properties of a Factor Solution
CENTROID CONDENSATION
PRINCIPAL COMPONENT AND PRINCIPAL AXIS
CONDENSATION
Principal Components / Mathematical Properties of Principal
Components / Principal Axis Solutions
MAXIMUM LIKELIHOOD AND RELATED FORMS OF CONDENSATION 477
Usefulness of ML Factoring / Variants on ML Factoring
OTHER METHODS OF CONDENSATION 481
DETERMINING THE NUMBER OF FACTORS 482
Consequences of Choosing a Given Number of Factors
CAUSAL INDICATORS 484
SUMMARY 485
SUGGESTED ADDITIONAL READINGS 490
12 Exploratory Factor Analysis II: Rotation and Other Topics
491
CHAPTER OVERVIEW
FACTOR ROTATION
Geometric Analogy / Visual Rotation / Further Mathematics of Rotation
/ Oblique Rotations / Simple and “Simpler՞ Structures / Reference
Vectors
ANALYTIC ROTATIONS
Quartimax / Varimax / Promax
ESTIMATION OF FACTOR SCORES
Practical Considerations in Obtaining Factor Scores
RELATIONS AMONG THE VARIOUS MATRICES
THE COMMON FACTOR MODEL
The Problem of Communality Estimation / Factorable Matrices / Matrix
Rank / Unities as Communality Estimates / Communalities Derived
from Hypotheses / Statistical Criteria of Rank / Iteration / Squared
Multiple Correlations / Reliability Coefficients / Direct Estimation /
Some Major Differences between Component and Common Factor
Solutions / Some Conceptual Problems with the Common Factor
Model / Effects of Number of Variables and Average Correlation upon
the Factor Structure
FACTOR ANALYTIC DESIGNS
Alternative Designs / Three-Mode Factor Analysis
AD-LIB FACTORING
HIGHER-ORDER FACTORS
HOW TO FOOL YOURSELF WITH FACTOR ANALYSIS
491
493
505
507
512
514
526
531
532
533
CONTENTS XVii
AN OUTLOOK ON EXPLORATORY FACTOR ANALYSIS 535
Practical Considerations in Factor Analysis
SUMMARY 536
SUGGESTED ADDITIONAL READINGS 541
13 Confirmatory Factor Analysis 542
CHAPTER OVERVIEW 542
SPEARMAN'S GENERAL FACTOR SOLUTION 544
COMPARING FACTORS IN DIFFERENT ANALYSES 548
Classical Approaches to Testing Factor Invariance / Some Practical
Aspects of Comparing Factor Structures / Comparing Overall
Solutions / ACS Approaches
TESTING WEAK THEORIES (THEORIES CONCERNING GROUPINGS OF
VARIABLES) 554
Multiple Group Confirmatory Analysis / Procrustes
Confirmatory Analysis / ACS Confirmatory Analysis / A Comparison
of the Three Approaches
FACTORING CATEGORICAL VARIABLES (ITEM LEVEL FACTORING) 570
ACS and Related Approaches with PM Measures / Multiscale Analyses
TESTING STRONG THEORIES 576
Introduction to the Full ACS Model / ACS Notation / Assumptions /
Properties of Path Coefficients / A Note on Inferring Causality from
Correlational Data / Model Specification in ACS / Recursive and
Nonrecursive Models / Cross-lagged Correlation / Applying ACS /
Reapplying ACS / Classical Approaches to Strong Theories
SUMMARY 590
SUGGESTED ADDITIONAL READINGS 594
PART 5 ADDITIONAL STATISTICAL MODELS, CONCEPTS, AND ISSUES 595
14 Profile Analysis, Discriminant Analysis, and Multidimensional Scaling 597
CHAPTER OVERVIEW 597
CLUSTER ANALYSIS 598
PROBLEMS IN PROFILE ANALYSIS 599
Characteristics of Score Profiles
CLUSTERING OF PROFILES 601
Measures of Profile Similarity / Distance Measure / Hierarchical and
Overlapping Clustering
RAW-SCORE FACTOR ANALYSIS 604
An Example of Raw-Score Factor Analysis / How Raw-Score Factor
Analysis Works / Transformations of Variables / Transformations of
Profiles
xviii CONTENTS
DISCRIMINANT ANALYSIS
Geometric Interpretation of Discriminant Analysis / Linear Discriminant
Function / Multiple Linear Discriminant Functions / Placement /
Evaluation of Discriminant Analysis
PATTERN ANALYSIS
Discovering Latent Groups / Discriminating among Existing Groups /
Evaluation of Pattern Analysis
MULTIDIMENSIONAL SCALING
Spatial Conceptions of MDS / An Overview of Alternative Approaches
to MDS / Psychophysical Methods Based upon Similarity /
Psychophysical Methods Based upon Attribute Ratings / Indirect
Methods / Vector-Space Ratio Methods / Euclidian Distance Ratio
Methods / Interval Methods / Ordinal Methods and ALSCAL /
Some Empirical Properties of Alternative MDS Solutions / MDS of
Correlation Matrices / Scaling of Individual Differences / An
Example of the Use of MDS / Some Concluding Comments
DOMINANCE (PREFERENCE) SCALING
The Unfolding Concept / Multidimensional Unfolding and ALSCAL
SUMMARY
SUGGESTED ADDITIONAL READINGS
610
620
621
645
648
651
15 The Analysis of Categorical Data, Binary Classification, and Alternatives to
Geometric Representations
CHAPTER OVERVIEW
CATEGORICAL MODELING
Two-way Independence / Association (Nonindependence) /
Alternative Models for the 2x2 Case / Measures of Association in
the 2x2 Design / More about G2 / The Generalized Logit Variant /
Structural and Random Zeros / Multiple Levels on a Variable /
Higher-Order Designs / Predictor-Criterion Models / Multiple
Response Categories in Predictor-Criterion Models / Some Important
Assumptions / Log-linear Modeling and Item Response Theory /
More-Specific Categorical Models / Logistic Regression /
Comparing Groups with Logistic Regression / An Illustrative
Problem / A Note on Residuals / Predicting Categorical Criteria
BINARY CLASSIFICATION 680
Classical Signal Detection / Categorical Modeling Approaches to the
Equal Variance Gaussian Model / General Recognition Theory /
Application to Condensation Tasks / MDS, Dissimilarity Judgments,
and General Recognition Theory / Implications for Measurement
NONGEOMETRIC AND NON-EUCLIDIAN MODELS 696
Nearest Neighbors / Tree Representations / Network and Graph
Theoretic Approaches / Conclusions
652
652
654
CONTENTS XIX
SUMMARY 704
SUGGESTED ADDITIONAL READINGS 708
REFERENCES 709
INDEXES
Name Index 735
Subject Index 741 |
| any_adam_object | 1 |
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| author | Nunnally, Jum C. Bernstein, Ira H. |
| author_facet | Nunnally, Jum C. Bernstein, Ira H. |
| author_role | aut aut |
| author_sort | Nunnally, Jum C. |
| author_variant | j c n jc jcn i h b ih ihb |
| building | Verbundindex |
| bvnumber | BV023535656 |
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| ctrlnum | (OCoLC)254935669 (DE-599)BVBBV023535656 |
| dewey-full | 150.287 |
| dewey-hundreds | 100 - Philosophy & psychology |
| dewey-ones | 150 - Psychology |
| dewey-raw | 150.287 |
| dewey-search | 150.287 |
| dewey-sort | 3150.287 |
| dewey-tens | 150 - Psychology |
| discipline | Psychologie |
| discipline_str_mv | Psychologie |
| edition | 3. ed., [Nachdr.] |
| format | Book |
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| id | DE-604.BV023535656 |
| illustrated | Illustrated |
| index_date | 2024-07-02T22:36:06Z |
| indexdate | 2024-07-09T21:24:08Z |
| institution | BVB |
| isbn | 007047849X 9780070478497 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-016855441 |
| oclc_num | 254935669 |
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| owner | DE-521 DE-473 DE-BY-UBG |
| owner_facet | DE-521 DE-473 DE-BY-UBG |
| physical | XXIV, 752 S. graph. Darst. |
| publishDateSearch | 2006 |
| publishDateSort | 2006 |
| publisher | McGraw-Hill |
| record_format | marc |
| series2 | MacGraw-Hill series in psychology |
| spelling | Nunnally, Jum C. Verfasser aut Psychometric theory Jum C. Nunnally ; Ira H. Bernstein 3. ed., [Nachdr.] New York <<[u.a.]>> McGraw-Hill [200]6 XXIV, 752 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier MacGraw-Hill series in psychology Theorie (DE-588)4059787-8 gnd rswk-swf Psychologie (DE-588)4047704-6 gnd rswk-swf Messtheorie (DE-588)4169537-9 gnd rswk-swf Psychometrie (DE-588)4176236-8 gnd rswk-swf Psychometrie (DE-588)4176236-8 s Theorie (DE-588)4059787-8 s 1\p DE-604 Messtheorie (DE-588)4169537-9 s Psychologie (DE-588)4047704-6 s 2\p DE-604 Bernstein, Ira H. Verfasser aut Digitalisierung UB Bamberg - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016855441&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 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Nunnally, Jum C. Bernstein, Ira H. Psychometric theory Theorie (DE-588)4059787-8 gnd Psychologie (DE-588)4047704-6 gnd Messtheorie (DE-588)4169537-9 gnd Psychometrie (DE-588)4176236-8 gnd |
| subject_GND | (DE-588)4059787-8 (DE-588)4047704-6 (DE-588)4169537-9 (DE-588)4176236-8 |
| title | Psychometric theory |
| title_auth | Psychometric theory |
| title_exact_search | Psychometric theory |
| title_exact_search_txtP | Psychometric theory |
| title_full | Psychometric theory Jum C. Nunnally ; Ira H. Bernstein |
| title_fullStr | Psychometric theory Jum C. Nunnally ; Ira H. Bernstein |
| title_full_unstemmed | Psychometric theory Jum C. Nunnally ; Ira H. Bernstein |
| title_short | Psychometric theory |
| title_sort | psychometric theory |
| topic | Theorie (DE-588)4059787-8 gnd Psychologie (DE-588)4047704-6 gnd Messtheorie (DE-588)4169537-9 gnd Psychometrie (DE-588)4176236-8 gnd |
| topic_facet | Theorie Psychologie Messtheorie Psychometrie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016855441&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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