Richard J. Hofmann

Indices Descriptive of Factor Complexity

Summary This manuscript develops two indices for describing the complexity of a factor solution. One index indicates the complexity of the variables in terms of factors, while a second index indicates the complexity of the factors in terms of variables. With the use of the classic Thurstone box problem as an illustrative example, various orthogonal and oblique solutions are discussed with regard to these indices. It is concluded that the indices may serve to provide a measure of the attainment of simplicity of structure.

Achievement As a Momentary Event, As a Continuing State, Locus of Control: A Clarification.

The relationship between locus of control and achievement is clarified by disaggregating achievement into a momentary event (standardized test results) and continuing state (grade-point average) utilizing a path diagram approach. Although there are no substantial correlations among socioeconomic status, sex, and locus of control in this study, the three variables predict school achievement as a continuing state (R = 33) considerably better than they do as a momentary event (R = .56) of 174 students in Grade 8.

The Concept of Efficiency in Item Analysis

In this paper a new item analysis index, e, is derived as a function of difficulty and discrimination to represent item efficiency. It is demonstrated algebraically that the maximum discriminating power of an item may be determined from its difficulty and then item efficiency is defined as the ratio of observed discrimination to maximum discrimination. The magnitude of the e-index will range from zero to unity and will provide additional information for item analyses.

On Testing a Guttman Scale for Significance.

The Guttman scale is discussed from the viewpoint of errors in response patterns. The errors are assumed to be distributed as a binomial. A double-barreled significance test is suggested having two probabilities: high probability and low probability.

A Common Factor Structure of Bender Gestalt Protocols of Young Children

The common factor structure of the Bender is defined for 9-yr.-old children according to the Koppitz scoring procedure. Utilizing a new robust factor analytic interpretation strategy, it is demonstrated that the common factors correspond closely to the general error categories defined by Koppitz. A cross-validation study is suggested.

Multiple hierarchical analysis

A multivariate method for exploratory scalogram analysis of binary data is developed—Multiple Hierarchical Analysis (MHA). This method, based on certain factor analytic methodology, is demon strated using an illustrative data set. It is concluded that the MHA methodology will be functional in identifying underlying independent and noninde pendent scales in binary data.

A Modified Rule of Thumb for Evaluating Scale Reproducibilities Determined By Electronic Computers

The Goodenough technique for determining scale error is compared to the Guttman technique and demonstrated to be more conservative than the Guttman technique. Implications with regard to Guttmans evaluative rule of thumb for evaluating a reproducibility are noted.

LOCUS OF CONTROL: ITS STABILITY ACROSS DISTINCTLY DIFFERENT SUBGROUPS OF COLLEGE FRESHMEN

A modified version of the Nowicki-Strickland Locus of Control Scale is investigated. Utilizing four distinct subgroups (ns = 101) of college freshmen, education and noneducation majors, from a Bible College and a State University, a discriminant structure for the locus of control statements was defined. Two statistically significant discriminant functions showed a very clear external orientation for all four groups. The construct locus of control was less bipolar than anticipated.

A Generalized Regression Estimate Formula for Factor Scores: Its Application to Singular Data

Summary A generalized formula for determining regression estimate factor scores is developed for use with either singular or nonsingular data with either orthogonal or oblique factor solutions. Kaisers component scores are shown to be a specialized case of the generalized formula. With use of the formula, estimated factor scores and component scores are developed for an oblique solution of the singular data of the Thurstone box problem and then compared to the true factor scores.

Extended latent partition analysis

Utilizing an empirical data set, this article demonstrates and briefly discusses a multivariate technique that represents an extension of Wileys latent partition analysis, extended latent partition analysis.