When investigating differences between two sets of scores, the t test is appropriate. If the two sets of data are from two groups of subjects, then the independent t test is appropriate. If the two sets are from the same subjects, the dependent t test is required. In this paper, the authors describe the use of a third test when part of a data set…

A procedure for rapid screening of variables as potential moderators is presented and discussed. A moderator is defined as any variable which can be used to identify differentially predictable persons; or defined statistically by stating that if a predictor and a moderator are each divided into three or more categories and used as independent…

Statistics such as chi-square, phi, and Cramer's V are related to the R squared statistic of regression analysis. It is shown that the proportion of variance accounted for can be computed from many contingency table situations. (JKS)

The utility of a non-linear transformation of the criterion is established. The Pythagorean Theorem is used as the example to demonstrate the point. The functional relationships may be such (as in the Pythagorean Theorem) that an R-squared of 1.00 cannot be found without making a non-linear transformation of the criterion. The goal of…

The amount of variance accounted for by treatment can be estimated with omega squared or with the squared multiple correlation coefficient. Monte Carlo methods were employed to compare omega squared, the squared multiple correlation coefficient, and the squared multiple correlation coefficient to which a shrinkage formula had been applied, in…

Prediction for a number of criteria from a set of predictor variables in a system of regression equations is studied with the possibilities of linear transformations applied to both the criterion and predictor variables. Predictive composites representing a battery of predictor variables provide identical estimates of criterion scores as do the…

Evaluations in education often throw away important information because of a penchant for averages. Multiple regression techniques are used to estimate the average effect of policies across schools, and usually school performance is represented by the average score of its students on an achievement test. The author suggests some ways of broadening…

The implications of the report are that a knowledge of quantitative areas is becoming increasingly more important in the logistics career fields. Therefore the study has emphasized predicting academic performance in quantitative courses in graduate logistics. It was expected that a useful model of this type, in conjunction with the other models,…

Three simplifying conditions are given for obtaining least squares (LS) estimates for a nonlinear submodel of a linear model. If these are satisfied, and if the subset of nonlinear parameters may be LS fit to the corresponding LS estimates of the linear model, then one attains the desired LS estimates for the entire submodel. Two illustrative…

The purpose of the Neyman-Johnson statistical technique is to determine a region or span of values on r independent variables where the predicted criterion scores of two or more treatment groups are significantly different. Consequently, the technique should prove especially useful in research concerned with moderator variables or with the…

Longley proposed a set of data for use in testing regression programs. This paper shows that the numerically accurate solution is likely to be an unreasonable estimate of the regression coefficients for this problem. This is true because the accuracy of the data and appropriateness of the model may affect the solution more than the computational…

Many methodologists are aware that parametric tests associated with the analysis of variance and the analysis of covariance can be computed using regression procedures. It is shown that multiple linear regression can also be employed to compute the Kruskal-Wallis nonparametric analysis of variance. (Author)

The author is generally critical of the previous article (TM 503 686), which concerned the use of multiple regression for nonparametric analysis of variance. (JKS)

Issues in analysis of covariance, multiple regression analysis, and the analysis of variance such as the assumption of independence and directional hypotheses are discussed. (JKS)

The effects of the violation of the assumption of homogeneity of regression on the Type I error rate and on the power of analysis of covariance are investigated. The results indicate that analysis of covariance is robust when sample sizes are equal. (Author/JKS)