Contributions to Correlational Analysis

Preface1. Introduction Historical Overview Mathematical Background What Correlation is. What the Book is About2. 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 A3. 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 Significance4. 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 Judges5. 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 Analysis6. 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 Trees7. Synthetic Validity: The J-Coefficient A Fictitious Example8. 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 TESREL9. 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 Clusters10. Factor Extraction by Centroid Approaches Thurstone Multiple Group Method Computer Program and Subroutines11. Factoring by the Principal-Axis Method Iterative Extraction (One-at-a-Time) Methods Original Hotelling Iteration Method Direct Solution for All Factors: Modified Jacobi Method12. 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 Programs13. The Rotation of Extracted Factors Varimax Rotation Oblique Factors Hierarchical Rotation More Complex Hierarchical Structure Computer Programs and Subroutines14. Practical Applications of Hierarchical Rotation In the Area of Ability Testing Hierarchical Factors in Morale Data Application to Rating Scales: Multitrait-Multimethod Batteries Overall Summary15. 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 WHEWIN16. Other Factor Applications: Profile Analysis The Q Technique: Inverse Factoring Profiles and Measures of Profile Similarity An Example: Data and Methodology Other Applications17. Comparing Factors and Computing Factor Scores Invariance or Reliability Measurement Computing Factor Scores Approximation Methods18. 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 ProblemsAppendix A. Significance TablesAppendix B. Regression Computer ProgramsAppendix C. Factor Analysis Computer ProgramsAppendix D. Special Computer SubroutinesBibliographyAdditional ReadingsAuthor IndexSubject Index