Psychometric Methods

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