An overview of standards related to demonstrating evidence regarding relationships with criteria as it pertains to instrument development was presented, along with heuristic examples. Additional measures and a comprehensive design are necessary to establish evidence related to the use and interpretation of test scores for the validation of a…

When conducting experiments involving the measurement of physically related quantities, choosing an appropriate spacing for the experimental independent variable is a crucial procedure whose consequences may go beyond data graphical visualization. This is particularly true if the measured quantities are nonlinearly related and experimental errors…

A distinction is proposed between measures and predictors of latent variables. The discussion addresses the consequences of the distinction for the true-score model, the linear factor model, Structural Equation Models, longitudinal and multilevel models, and item-response models. A distribution-free treatment of calibration and…

Interval estimation of intraclass correlation coefficients in hierarchical designs is discussed within a latent variable modeling framework. A method accomplishing this aim is outlined, which is applicable in two-level studies where participants (or generally lower-order units) are clustered within higher-order units. The procedure can also be…

The paper obtains consistent standard errors (SE) and biases of order O(1/n) for the sample standardized regression coefficients with both random and given predictors. Analytical results indicate that the formulas for SEs given in popular text books are consistent only when the population value of the regression coefficient is zero. The sample…

Indefinite symmetric matrices that are estimates of positive-definite population matrices occur in a variety of contexts such as correlation matrices computed from pairwise present missing data and multinormal based methods for discretized variables. This note describes a methodology for scaling selected off-diagonal rows and columns of such a…

Learning about statistics is a lot like learning about science: the learning is more meaningful if you can actively explore. This seventh installment of "Explorations in Statistics" explores regression, a technique that estimates the nature of the relationship between two things for which we may only surmise a mechanistic or predictive…

A new effect size representing the predictive power of an independent variable from a multiple regression model is presented. The index, denoted as r[subscript sp], is the semipartial correlation of the predictor with the outcome of interest. This effect size can be computed when multiple predictor variables are included in the regression model…

Researchers in career and technical education often ignore more effective ways of reporting and treating missing data and instead implement traditional, but ineffective, missing data methods (Gemici, Rojewski, & Lee, 2012). The recent methodological, and even the non-methodological, literature has increasingly emphasized the importance of…

In behavioral research, interest is often in examining the degree to which the effect of an independent variable X on an outcome Y is mediated by an intermediary or mediator variable M. This article illustrates how generalized estimating equations (GEE) modeling can be used to estimate the indirect or mediated effect, defined as the amount by…

This note describes a procedure for estimating the range restriction component used in correcting correlations for unreliability and range restriction when an estimate of the reliability of a predictor is not readily available for the unrestricted sample. This procedure is illustrated with a few examples. (Contains 1 table.)

The computation and reporting of effect size estimates is becoming the norm in many journals in psychology and related disciplines. Despite the increased importance of effect sizes, researchers may not report them or may report inaccurate values because of a lack of appropriate computational tools. For instance, Pierce, Block, and Aguinis (2004)…

Among the varied analytical challenges institutional researchers face, examining faculty pay may be one of the most vexing. Although the literature on faculty compensation analysis dates back to the 1970s (Loeb and Ferber, 1971; Gordon, Morton, and Braden, 1974; Scott, 1977; Braskamp and Johnson, 1978; McLaughlin, Smart, and Montgomery, 1978),…

This paper contains information concerning the following: 1. An overview of multivariate analysis of variance, and discriminant (DA) and canonical (CA) analyses. 2. An introduction to specification and measurement errors, and collinearity. 3. The sparsity of information concerning specification and measurement errors and collinearity as they…

Nonlinear relationships and latent variable assumptions can lead to serious specification errors in structural models. A quadratic relationship, described by a linear structural model with a latent variable, is shown to have less predictive validity than a simple manifest variable regression model. Advocates the use of simpler preliminary…