Applications of distribution theory for the squared multiple correlation coefficient and the squared cross-validation coefficient are reviewed, and computer programs for these applications are made available. The applications include confidence intervals, hypothesis testing, and sample size selection. (Contains 2 tables.)

Standard least squares analysis of variance methods suffer from poor power under arbitrarily small departures from normality and fail to control the probability of a Type I error when standard assumptions are violated. This article describes a framework for robust estimation and testing that uses trimmed means with an approximate degrees of…

Investigates the Tukey statistic for the empirical probability of a Type II error under numerous parametric specifications defined by Cohen (1969) as being representative of behavioral research data. For unequal numbers of observations per treatment group and for unequal population variancies, the Tukey test was simulated when sampling from a…

This paper demonstrates that multiple comparison tests using a pooled error term are dependent on the circularity assumption and shows how to compute tests which are insensitive (robust) to this assumption. (Author/GK)

The effects of variance heterogeneity on the empirical probability of a Type I error for the analysis of variance (ANOVA) F-test are examined. The rate of Type I error varies as a function of the degree of variance heterogeneity, and the ANOVA F-test is not always robust to variance heterogeneity when sample sizes are equal. (Author/JAC)

The need for multiple comparison procedures for repeated measures means employing a pooled estimate of error variance to conform to the sphericity assumptions of the design in order to provide a valid test is discussed. An alternative approach which does not require this assumption is presented. (Author/JKS)

This article shows how a multivariate approximate degrees of freedom procedure based on the Welch-James procedure as simplified by S. Johansen (1980) can be applied to the analysis of repeated measures designs without assuming covariance homogeneity. A Monte Carlo study illustrates the approach. (SLD)

The analysis of variance, Welch, and Brown and Forsyth tests for mean equality were compared using Monte Carlo methods. The tests' rates of Type I error and power were examined when populations were nonnormal, variances were heterogeneous, and group sizes were unequal. Recommendations for use are presented. (Author/JKS)