Distributions of Correlation Coefficients [Paperback]

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.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.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 Lehmanns 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 Prl³2