Psychometric Methods

1. Introduction

1.1 Psychological Measurement and Tests
1.2 Tests and Samples of Behavior
1.3 Types of Tests
1.4 Origin of Psychometrics
1.5 Definition of Measurement
1.6 Measuring Behavior
1.7 Psychometrics and Its Importance to Research and Practice
1.8 Organization of This Book

Key Terms and Definitions

2. Measurement and Statistical Concepts
2.1 Introduction
2.2 Numbers and Measurement
2.3 Properties of Measurement in Relation to Numbers
2.4 Levels of Measurement
2.5 Contemporary View on the Levels of Measurement and Scaling
2.6 Statistical Foundations for Psychometrics
2.7 Variables, Frequency Distributions, and Scores
2.8 Summation or Sigma Notation
2.9 Shape, Central Tendency, and Variability of Score Distributions
2.10 Correlation, Covariance, and Regression
2.11 Summary

Key Terms and Definitions

3. Criterion, Content, and Construct Validity
3.1 Introduction
3.2 Criterion Validity
3.3 Essential Elements of a High-Quality Criterion
3.4 Statistical Estimation of Criterion Validity
3.5 Correction for Attenuation
3.6 Limitations to Using the Correction for Attenuation
3.7 Estimating Criterion Validity with Multiple Predictors: Partial Correlation
3.8 Estimating Criterion Validity with Multiple Predictors: Higher-Order Partial Correlation
3.9 Coefficient of Multiple Determination and Multiple Correlation
3.10 Estimating Criterion Validity with More Than One Predictor: Multiple Linear Regression
3.11 Regression Analysis for Estimating Criterion Validity: Development of the Regression Equation
3.12 Unstandardized Regression Equation for Multiple Regression
3.13 Testing the Regression Equation for Significance
3.14 Partial Regression Slopes
3.15 Standardized Regression Equation
3.16 Predictive Accuracy of a Regression Analysis
3.17 Predictor Subset Selection in Regression
3.18 Summary

Key Terms and Definitions

4. Statistical Aspects of the Validation Process
4.1 Techniques for Classification and Selection
4.2 Discriminant Analysis
4.3 Multiple-Group Discriminant Analysis
4.4 Logistic Regression
4.5 Logistic Multiple Discriminant Analysis: Multinomial Logistic Regression
4.6 Model Fit in Logistic Regression
4.7 Content Validity
4.8 Limitations of the Content Validity Model
4.9 Construct Validity
4.10 Establishing Evidence of Construct Validity
4.11 Correlational Evidence of Construct Validity
4.12 Group Differentiation Studies of Construct Validity
4.13 Factor Analysis and Construct Validity
4.14 Multitrait–Multimethod Studies
4.15 Generalizability Theory and Construct Validity
4.16 Summary and Conclusions

Key Terms and Definitions

5. Scaling
5.1 Introduction
5.2 A Brief History of Scaling
5.3 Psychophysical versus Psychological Scaling
5.4 Why Scaling Models Are Important
5.5 Types of Scaling Models
5.6 Stimulus-Centered Scaling
5.7 Thurstone’s Law of Comparative Judgment
5.8 Response-Centered Scaling
5.9 Scaling Models Involving Order
5.10 Guttman Scaling
5.11 The Unfolding Technique
5.12 Subject-Centered Scaling
5.13 Data Organization and Missing Data
5.14 Incomplete and Missing Data
5.15 Summary and Conclusions

Key Terms and Definitions

6. Test Development
6.1 Introduction
6.2 Guidelines for Test and Instrument Development
6.3 Item Analysis
6.4 Item Difficulty
6.5 Item Discrimination
6.6 Point–Biserial Correlation
6.7 Biserial Correlation
6.8 Phi Coefficient
6.9 Tetrachoric Correlation
6.10 Item Reliability and Validity
6.11 Standard Setting
6.12 Standard-Setting Approaches
6.13 The Nedelsky Method
6.14 The Ebel Method
6.15 The Angoff Method and Modifications
6.16 The Bookmark Method
6.17 Summary and Conclusions

Key Terms and Definitions

7. Reliability
7.1 Introduction
7.2 Conceptual Overview
7.3 The True Score Model
7.4 Probability Theory, True Score Model, and Random Variables
7.5 Properties and Assumptions of the True Score Model
7.6 True Score Equivalence, Essential True Score Equivalence, and Congeneric Tests
7.7 Relationship between Observed and True Scores
7.8 The Reliability Index and Its Relationship to the Reliability Coefficient
7.9 Summarizing the Ways to Conceptualize Reliability
7.10 Reliability of a Composite
7.11 Coefficient of Reliability: Methods of Estimation Based on Two Occasions
7.12 Methods Based on a Single Testing Occasion
7.13 Estimating Coefficient Alpha: Computer Programs and Example Data
7.14 Reliability of Composite Scores Based on Coefficient Alpha
7.15 Reliability Estimation Using the Analysis of Variance Method
7.16 Reliability of Difference Scores
7.17 Application of the Reliability of Difference Scores
7.18 Errors of Measurement and Confidence Intervals
7.19 Standard Error of Measurement
7.20 Standard Error of Prediction
7.21 Summarizing and Reporting Reliability Information
7.22 Summary and Conclusions

Key Terms and Definitions

8. Generalizability Theory
8.1 Introduction
8.2 Purpose of Generalizability Theory
8.3 Facets of Measurement and Universe Scores
8.4 How Generalizability Theory Extends Classical Test Theory
8.5 Generalizability Theory and Analysis of Variance
8.6 General Steps in Conducting a Generalizability Theory Analysis
8.7 Statistical Model for Generalizability Theory
8.8 Design 1: Single-Facet Person by Item Analysis
8.9 Proportion of Variance for the p x i Design
8.10 Generalizability Coefficient and CTT Reliability
8.11 Design 2: Single-Facet Crossed Design with Multiple Raters
8.12 Design 3: Single-Facet Design with the Same Raters on Multiple Occasions
8.13 Design 4: Single-Facet Nested Design with Multiple Raters
8.14 Design 5: Single-Facet Design Multiple Raters Rating on Two Occasions
8.15 Standard Errors of Measurement: Designs 1–5
8.16 Two-Facet Designs
8.17 Summary and Conclusions

Key Terms and Definitions

9. Factor Analysis
9.1 Introduction
9.2 Brief History
9.3 Applied Example with GfGc Data
9.4 Estimating Factors and Factor Loadings
9.5 Factor Rotation
9.6 Correlated Factors and Simple Structure
9.7 The Factor Analysis Model, Communality, and Uniqueness
9.8 Components, Eigenvalues, and Eigenvectors
9.9 Distinction between Principal Components Analysis and Factor Analysis
9.10 Confirmatory Factor Analysis
9.11 Confirmatory Factor Analysis and Structural Equation Modeling
9.12 Conducting Factor Analysis: Common Errors to Avoid
9.13 Summary and Conclusions

Key Terms and Definitions

10. Item Response Theory
10.1 Introduction
10.2 How IRT Differs from CTT
10.3 Introduction to IRT
10.4 Strong True Score Theory, IRT, and CTT
10.5 Philosophical Views on IRT
10.6 Conceptual Explanation of How IRT Works
10.7 Assumptions of IRT Models
10.8 Test Dimensionality and IRT
10.9 Type of Correlation Matrix to Use in Dimensionality Analysis
10.10 Dimensionality Assessment Specific to IRT
10.11 Local Independence of Items
10.12 The Invariance Property
10.13 Estimating the Joint Probability of Item Responses Based on Ability
10.14 Item and Ability Information and the Standard Error of Ability
10.15 Item Parameter and Ability Estimation
10.16 When Traditional IRT Models Are Inappropriate to Use
10.17 The Rasch Model
10.18 The Rasch Model, Linear Models, and Logistic Regression Models
10.19 Properties and Results of a Rasch Analysis
10.20 Item Information for the Rasch Model
10.21 Data Layout
10.22 One-Parameter Logistic Model for Dichotomous Item Responses
10.23 Two-Parameter Logistic Model for Dichotomous Item Responses
10.24 Item Information for the Two-Parameter Model
10.25 Three-Parameter Logistic Model for Dichotomous Item Responses
10.26 Item Information for the Three-Parameter IRT Model
10.27 Choosing a Model: A Model Comparison Approach
10.28 Summary and Conclusions

Key Terms and Definitions

11. Norms and Test Equating
11.1 Introduction
11.2 Norms, Norming, and Norm-Referenced Testing
11.3 Planning a Norming Study
11.4 Scaling and Scale Scores
11.5 Standard Scores Under Linear Transformation
11.6 Percentile Rank Scale
11.7 Interpreting Percentile Ranks
11.8 Normalized z- or Scale Scores
11.9 Common Standard Score Transformations or Conversions
11.10 Age- and Grade-Equivalent Scores
11.11 Test Score Linking and Equating
11.12 Techniques for Conducting Equating: Linear Methods
11.13 Design I: Random Groups—One Test Administered to Each Group
11.14 Design II: Random Groups with Both Tests Administered to Each Group, Counterbalanced (Equally Reliable Tests)
11.15 Design III: One Test Administered to Each Study Group, Anchor Test Administered to Both Groups (Equally Reliable Tests)
11.16 Equipercentile Equating
11.17 Test Equating Using IRT
11.18 IRT True Score Equating
11.19 Observed Score, True Score, and Ability
11.20 Summary and Conclusions

Key Terms and Definitions

Appendix. Mathematical and Statistical Foundations
References
Author Index
Subject Index
About the Author