This report gives some simple examples of stability for one factor and 2 x 2 factorial analysis of variance, reliability and correlations. The findings are very different: from superstability (no transformation whatsoever can change the result) to almost total instability. This is followed by a discussion of applications to multivariate analysis,…

INTERTAIL, the computer program which implements an approach to tailored testing outlined by Cliff (1975), was examined with errorless data in several Monte Carlo studies. Three replications of each cell of a 3 x 3 table with 10, 20 and 40 items and persons were analyzed. Mean rank correlation coefficients between the true order, specified by…

A correlation matrix of 21 structure-of-intellect (SOI) tests taken by 204 Marine officers at a military base in Southern California, which was intended to reflect aptitudes for military leadership, was reanalyzed through exploratory factor analysis and confirmatory maximum likelihood factor analysis. Higher order factors appeared to have…

In traditional factor analysis, the variance-covariance matrix or the correlation matrix has often been a form of inputting data. In contrast, in Bayesian factor analysis, the entire data set is typically required to compute the posterior estimates, such as Bayes factor loadings and Bayes unique variances. We propose a simple method for computing…

Mathematics majors' study of abstract algebra should provide these students with opportunities to connect what they are learning to their prior experiences with algebra in high school. This paper illustrates how such connections can be used to motivate the notion of binary operation and the axioms for a group.

Piaget has hypothesized that concrete and formal operations can be described by specific logical models. The present study focused on assessing various aspects of four concrete operational groupings and two variations of two formal operational characteristics. Six hundred twenty-two 9-14 year old students participating in the Human Sciences…

The report describes the Shared Process Evaluation System (SHAPES), a process analysis system designed to facilitate documenting, rationalizing, and evaluating community development projects. The evaluation process requires five steps. First, the project is described with respect to statements about the original problem situation and demographic…

Procedures for simultaneous confirmatory factor analysis in several populations are useful in a variety of problems. This is demonstrated with examples involving missing data, comparison of part correlations between groups, testing the equality of regression weights between groups with multiple indicators of each variable, and the formulation of…

The impact of the use of data arising from balanced incomplete block (BIB) spiralled designs on the chi-square goodness-of-fit test in factor analysis is considered. Data from BIB designs posses a unique pattern of missing data that can be characterized as missing completely at random (MCAR). Standard approaches to factor analyzing such data rest…

A Monte Carlo investigation of simplex fitting as a method of determining the dimensionality of binary data matrices was conducted. Examination of the fit of correlation matrices with a known factor structure to correlation matrices that represent the perfect simplex shows that simplex fitting is a feasible approach under some circumstances. (SLD)

An approach for multiple factor analysis of dichotomized variables is presented based on distribution of first and second order joint probabilities of binary scored items. The estimator is based on the generalized least squares principle. Standard errors and a test of the fit of the model is given. (Author/RC)

Three correlation matrices (PEARSON, POLYCHORIC, and TOBIT) were used to obtain reliability estimates on ordered polytomous variable models. A Monte Carlo study with different levels of variable asymmetry and 400 sample correlation matrices demonstrated that the PEARSON matrix did not perform as well as did the other 2 matrices. (SLD)

The use of stepwise regression has been criticized for both interpretive misunderstandings and statistical aberrations. A major statistical problem with stepwise regression and other procedures that involve multiple significance tests is the inflation of the Type I error rate. General approaches to control the family-wise error rate such as the…

This paper illustrates the transformation of a raw data matrix into a matrix of associations, and then into a factor matrix. Factor analysis attempts to distill the most important relationships among a set of variables, thereby permitting some theoretical simplification. In this heuristic data, a correlation matrix was derived to display…

This paper is an extended series of appendices to the report "Exploring the T.R.Q.: An Assessment of the Effectiveness of the Teachers' Rating Questionnaire," Report Number 123. It should be most useful to those familiar with multiple regression analysis and factor analysis and wishing a more complex record of the statistical procedures…