Distributions of Correlation Coefficients

by Hoben Thomas

Overview

An important problem in personnel psychology, namely, the psychometric problem known as "validity generalization" is addressed in this volume. From a statistical point of view, the problem is how to make statements about a population correlation coefficient based on inferences from a collection of sample correlation coefficients. The first part of the book examines the largely ad hoc procedures which have been used to determine validity generalization. The second part develops a new model formulated from the perspective of finite mixture theory and, in addition, illustrates its use in several applications.

Product Details

ISBN-13:	9780387968636
Publisher:	Springer New York
Publication date:	04/18/1989
Edition description:	Softcover reprint of the original 1st ed. 1989
Pages:	95
Product dimensions:	6.10(w) x 9.25(h) x 0.01(d)

Table of Contents

1. Introduction.- 1.1 Motivation and Background.- 1.2 Conceptual Problems of Validity Generalization.- 1.3 An Alternative Formulation.- 2. A Validity Generalization Model.- 2.1 Introduction.- 2.2 Classical Test Theory.- 2.3 A Validity Generalization Random Model.- 2.4 The Joint Space of P and E.- 2.5 P and E Are Dependent Variables.- 2.6 The Distribution of R, c(r).- 2.7 Are P and E Correlated?.- 2.8 Identifiability.- 3. Estimation.- 3.1 Introduction.- 3.2 Lehmann’s Classification.- 3.3 Sample Data.- 3.4 The Basic Sample Estimates.- 3.5 The Estimator SP2 = SR2— S*2.- 3.6 Interpreting Estimators.- 3.7 The Expectation of SR2.- 3.8 The Expectation of S*2.- 3.9 The Expectation of SP2.- 3.10 Numerical Evaluation of—(SP2).- 3.11 The Distribution of Sp and the Power Problem.- 3.12 The Consistency of SP2.- 3.13 The Limiting Behavior of SR2.- 3.14 Multifactor Estimation Procedures.- 3.15 A Representative Multifactor Estimator.- 3.16 A Comment on Z Transformations.- 4. Summary and Discussion of Validity Generalization.- 4.1 Summary of Model Properties.- 4.2 Validity Generalization and Classical Test Theory.- 4.3 Summary of Estimation Procedures.- 4.4 Consistency and Identifiability.- 4.5 The Bayesian Connection.- 4.6 Computer Simulation Studies.- 5. A Conditional Mixture Model for Correlation Coefficients.- 5.1 Introduction.- 5.2 Finite Mixture Distributions.- 5.3 A Modeling Distribution for R.- 5.4 A Mixture Model Distribution for R.- 5.5 A Parent Distribution for Histograms of R.- 5.6 Comment.- 6. Parameter Estimation.- 6.1 Introduction.- 6.2 Estimation Equations.- 7. Examples and Applications.- 7.1 Introduction.- 7.2 Artificial Data, Example 1.- 7.3 How Many Components in the Mixture?.- 7.4 Electrical Workers, Example 2.- 7.5 Army Jobs, Example 3.- 7.6 Army Jobs,Example 4.- 7.7 College Grades, Example 5.- 7.8 Law School Test Scores and Grades, Example 6.- 8. Artifact Corrections and Model Assumptions.- 8.1 Artifact Corrections.- 8.2 Identifiability of Mixtures.- 8.3 Failure of Model Assumptions.- 8.4 Properties of the Maximum Likelihood Estimates.- 8.5 Miscellaneous Comments.- Notes.- References.- Author Index.