Decomposable models, which allow for the interdependence of structure among observable variables, are described. Each model is fully characterized by a set of conditional interdependence restrictions and can be visualized with an undirected as well as a special type of directed graph. (Author/JKS)

This paper discusses Bayesian m-group regression where the groups are arranged in a two-way layout into m rows and n columns, there still being a regression of y on the x's within each group. The mathematical model is then provided as applied to the case where the rows correspond to high schools and the columns to colleges: the predictor variables…

The Goodman technique of log linear analysis is ideal for family research, because it is designed for categorical (non-quantitative) variables. Variables are dichotomized (for example, married/divorced, childless/with children) or otherwise categorized (for example, level of permissiveness, life cycle stage). Contingency tables are then…

The stepwise regression method of selecting predictors for computer assisted multiple regression analysis was compared with forward, backward, and best subsets regression, using 16 data sets. The results indicated the stepwise method was preferred because of its practical nature, when the models chosen by different selection methods were similar…

This paper discusses the principles underlying discriminant analysis and constructs a simulated data set to illustrate its methods. Discriminant analysis is a multivariate technique for identifying the best combination of variables to maximally discriminate between groups. Discriminant functions are established on existing groups and used to…

Canonical correlation analysis is a multivariate statistical model which facilitates the study of interrelationships among multiple dependent variables and multiple independent variables. It identifies components of one set of variables that are most highly related linearly to the components of the other set of variables. The underlying logic of…

This report is about the problem of making transition or enrollment rate gains comparable. It is shown that measures based on the proportions themselves, i.e. the difference between proportions, the proportion ratio and the residual gain ratio do not make the gains comparable. Instead a non-linear transformation has to be done. Two such…

Three procedures used to control Type I error rate in stepwise regression analysis are forward selection, backward elimination, and true stepwise. In the forward selection method, a model of the dependent variable is formed by choosing the single best predictor; then the second predictor which makes the strongest contribution to the prediction of…

The effects of sample size, number of variables, and population value of the congruence coefficient on the sampling distribution of the congruence coefficient were examined. Sample data were generated on the basis of the common factor model, and principal axes factor analyses were performed. (Author/LMO)

In research, data sets often occur in which the variance of the distribution of the dependent variable at given levels of the predictors is a function of the values of the predictors. In this situation, the use of weighted least-squares (WLS) or techniques is required. Weights suitable for use in a WLS regression analysis must be estimated. A…

Meta-analysis is a technique for combining the summary statistics from previously conducted research studies to indicate the direction of results and provide an index of the magnitude of effect size. This paper focuses on the effect of the violation of the assumption of independence (that the value of any included statistic is in no way…

This paper is part of a series of applied statistics monographs intended to provide supplementary reading for applied statistics students. In the present paper, derivations of the unbiased standard error of estimate for both the raw score and standard score linear models are presented. The derivations for raw score linear models are presented in…

To examine and clarify background conditions for understanding variables which affect salary, the salary and compensation programs at two industrial and three educational organizations were subjected to a statistical audit. Data were available on 272 employees. Ten compensation variables were studied as having direct or indirect effects on salary:…

From some simple and schematic assumptions about information processing, a stochastic differential equation is derived for the motion of a student through a computer-assisted elementary mathematics curriculum. The mathematics strands curriculum of the Institute for Mathematical Studies in the Social Sciences is used to test: (1) the theory and (2)…

The general linear model was described, and the influence that measurement errors have on model parameters was discussed. In particular, the assumptions of classical true-score theory were used to develop algebraic relationships between the squared multiple correlations coefficient and the regression coefficients in the infallible and fallible…