Parallel analysis has been considered one of the most accurate methods for determining the number of factors in factor analysis. One major advantage of parallel analysis over traditional factor retention methods (e.g., Kaiser's rule) is that it addresses the sampling variability of eigenvalues obtained from the identity matrix, representing the…

There is a lack of research on the effects of outliers on the decisions about the number of factors to retain in an exploratory factor analysis, especially for outliers arising from unintended and unknowingly included subpopulations. The purpose of the present research was to investigate how outliers from an unintended and unknowingly included…

Two applications of Kristof's theorem on traces of matrix products are presented in order to highlight their utility for psychometric theory and studies. (Author/JKS)

A procedure for estimating the reliability of a factorially complex composite is considered. An application of its use with Scholastic Aptitude Test data is provided. (Author/JKS)

A subject by item matrix of test responses is shown to be a useful heuristic in criterion referenced and norm referenced test analysis, and in the teaching of measurement. The pattern of responses within the matrix provides indications of item interactions, weak deceptors, and conventional test statistics. The strong visual analogy between the…

This paper traces the course of the consequences of viewing test responses as simply providing dichotomous data concerning ordinal relations. It begins by proposing that the score matrix is best considered to be items-plus-persons by items-plus-persons, and recording the wrongs as well as the rights. (Author/CTM)

A method of factor extraction specific to a binary matrix, illustrated here as a person-by-item response matrix, is presented. The extraction procedure, termed ERGO, differs from the more commonly implemented dimensionalizing techniques, factor analysis and multidimensional scaling, by taking into consideration item difficulty. Utilized in the…

Attributional style as it has been operationalized in the Attributional Style Questionnaire (ASQ) was critically assessed. A sample of 538 senior high school and college students completed the ASQ. The resulting ASQ data were then intercorrelated, factor analyzed, and compared to hypothesized matrices for all items, good outcome items, and bad…

The Mastery-Learning test model is extended. Methods for estimating prior probabilities are described. The use of an adjustment matrix to transform a probability of mastery measure and empirical methods for estimating adjustment matrix parameters are derived. Adjustment matrices are interpreted as indicators of instructional effectiveness and as…