Contributions to Correlational Analysis - 1st Edition - ISBN: 9780127460505, 9781483266077

Contributions to Correlational Analysis

1st Edition

Authors: Robert J. Wherry
eBook ISBN: 9781483266077
Imprint: Academic Press
Published Date: 11th October 1984
Page Count: 478
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Contributions to Correlational Analysis provides information pertinent to the fundamental aspects of correlational analysis that can be used to replace and enhance many of the parametric and nonparametric inferential statistical tests. This book discusses the basic concern of correctional analysis, which is the relationship between two sets of measure.

Organized into 18 chapters, this book begins with an overview of the nature of correction analysis. This text then explains the simple linear relationships in which explains the simple linear relationships in which Y and X each consists of some single measurement per person and the relationship is assumed to be linear. Other chapters consider basic ways of expanding the process to include more or different measurements of either X or Y but with no attempt to find the best functions. This book discusses as well the topic of factor analysis. The final chapter deals with canonical correlation.

This book is a valuable resource for psychologists.

Table of Contents


1. Introduction

Historical Overview

Mathematical Background

What Correlation is. What the Book is About

2. Measures of Relationship Between Two Variables

Pearson r

What to do When Scores are not Interval: Special Equations

The Missing Special Equations

Significance Tests for r, rRI, and rDI

Significance Tests for rRR, rDR, and rDD

Significance Tests for rMI and rMD

Significance Test for rMR

Some Other Alternatives: Variable Transformation

Tables in Appendix A

3. Composite and Part Correlation

Weighted Standard Scores

Weighted Raw Scores

Correlation Between Two Composites

Part Variables

Semipartial Correlation Coefficients

Higher-Order Semipartial Correlation Coefficients

Relation of Semipartials to Multiple Correlation

Partial Correlation Coefficients

Higher-Order Partial Correlation Coefficients

Tests of Significance

4. Inferred Correlations and Reliability Measures

The Biserial Correlation Coefficient (rbis)

The Tetrachoric Correlation Coefficient (rtet)

Correction for Curtailment of Range

Correction for Overlap

Spearman-Brown Prophecy Equations

Correction for Attenuation: Upper Limits of Validity

Spearman-Brown Reliability Equation

The Kuder-Richardson Reliability Equations

Assumption of a Single Factor

Assumption of Equal Item Intercorrelations

Assumption of Equal Item Variance

Assumption of Equal Item Difficulties

Reliability of Ranks Assigned by Judges

5. Multiple and Composite Correlation

Solving the Simultaneous Equations

The Square-Root, Augmented Matrix Approach

Obtaining Standard Deviations of the Weights

The Doolittle Approach

Testing R for Significance and Predicting its Shrinkage

Obtaining the Gross Score Prediction Equation

Cross-Validation and Composite r

The Kelley-Salisbury Iteration Method

Extension of Multiple Regression to Nonlinear Terms

Multiple Regression as a Substitute for Curve Fitting

Multiple Regression as a Substitute for Analysis of Variance

Multiple Regression as a Substitute for Trend Analysis

6. Test Selection Techniques

Wherry Test-Selection Method

Solution of a Problem: The Added Tables

The Problem of Suppressor Variables

The Wherry-Gaylord (1946) Integral Weighting System

The Wherry-Hutchins Multiple Battery Method

Computer Programs for Test Selection

Moderated Coding Trees

7. Synthetic Validity: The J-Coefficient

A Fictitious Example

8. Test Analysis: Item Selection and Weighting

Improving the Reliability of a Test

Item Selection and Weighting with an External Criterion

The Horst Item-Selection Technique

The Flanagan Item-Weighting Technique

Computer Program TESREL

9. Factor Analysis: Early Models and Methods

Correlation between Two Variables

Correlation of a Variable with Itself

Finding the Factor Loadings

Spearman's Modified Group Factor Theory

The Bifactor Method

The Belongingness (B) Coefficients for Grouping Test into Clusters

10. Factor Extraction by Centroid Approaches

Thurstone Multiple Group Method

Computer Program and Subroutines

11. Factoring by the Principal-Axis Method

Iterative Extraction (One-at-a-Time) Methods

Original Hotelling Iteration Method

Direct Solution for All Factors: Modified Jacobi Method

12. Communality Estimation and Improvement

Estimating Initial Communalities

Postsolution Improvement

Stopping Extraction of Factors and Testing for Goodness of Fit

Stopping Rules for Initial Extraction of Factors

Upper Limit Cutoffs

Comparing Solutions with Varying Numbers of Factors

Computer and Subroutine Programs

13. The Rotation of Extracted Factors

Varimax Rotation

Oblique Factors

Hierarchical Rotation

More Complex Hierarchical Structure

Computer Programs and Subroutines

14. Practical Applications of Hierarchical Rotation

In the Area of Ability Testing

Hierarchical Factors in Morale Data

Application to Rating Scales: Multitrait-Multimethod Batteries

Overall Summary

15. Factoring Large Numbers of Items: Wherry-Winer Method

The Oblique Reference Vector Loadings: Items within Clusters

Corrections for Noncluster Items

Changing Intersubtest to Intercluster Correlations

Summary of Steps and Some Suggestions

An Empirical Example

Computer Program WHEWIN

16. Other Factor Applications: Profile Analysis

The Q Technique: Inverse Factoring

Profiles and Measures of Profile Similarity

An Example: Data and Methodology

Other Applications

17. Comparing Factors and Computing Factor Scores

Invariance or Reliability Measurement

Computing Factor Scores

Approximation Methods

18. Multiple Criteria: Canonical Correlation

Canonical Correlation

Testing the Significance of Canonical Correlations

Use with Two Batteries

Multiple Correlation as a Special Case

Used as a Basis for Discriminant Functions

The Wherry, Jr. K Coefficient: Use with Contingency Tables

Problems in Interpreting Canonical Composites

Lack of Meariingfulness of Canonical Factors

The Wherry, Jr. Reduced Matrix Approach

Programs for Two Data-Set Problems

Appendix A. Significance Tables

Appendix B. Regression Computer Programs

Appendix C. Factor Analysis Computer Programs

Appendix D. Special Computer Subroutines


Additional Readings

Author Index

Subject Index


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© Academic Press 1984
Academic Press
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About the Author

Robert J. Wherry

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