Recent research using single-stage procedures to test the equality of the means of J independent normal distributions when variances are unequal have proven unsatisfactory in controlling Type I errors and power. A method for dealing with the problem of unequal sample sizes while implementing two-stage procedures is discussed. (TJH)

This research is an empirical study, through Monte Carlo simulation, of the effects of violations of the assumptions for the oneway fixed-effects analysis of variance (ANOVA) and analysis of covariance (ANCOVA). Research reaffirms findings of previous studies that suggest that ANOVA and ANCOVA be avoided when group sizes are not equal. (SLD)

J. Barnette and J. McLean (1996) proposed a method of controlling Type I error in pairwise multiple comparisons after a significant omnibus F test. This procedure, called Alpha-Max, is based on a sequential cumulative probability accounting procedure in line with Bonferroni inequality. A missing element in the discussion of Alpha-Max was the…

Based on a Monte Carlo simulation, this study is designed to investigate the power of the Kruskal-Wallis's H-test compared to the power of the F-test for three equal moderate sample sizes drawn at random from distributions of common or different shapes but for which the population distributions have equal variances. The distributions are the…

This study integrates into one comprehensive Monte Carlo simulation a vast array of previously defined and substantively interrelated research studies of the robustness of analysis of variance (ANOVA) and analysis of covariance (ANCOVA) statistical procedures. Three sets of balanced ANOVA and ANCOVA designs (group sizes of 15, 30, and 45) and one…

This Monte Carlo study examines whether, given various numbers of variables, treatments, and sample sizes, in a one-way multivariate analysis of variance, Type I error rates of the test approximations provided by the BMDP program, the Statistical Analysis System (SAS), and the Statistical Package for the Social Sciences (SPSS) for Roy's largest…

An influential statistics test recommends a Levene text for homogeneity of variance. A recent note suggests that Levene's test is upwardly biased for small samples. Another report shows inflated Alpha estimates and low power. Neither study utilized more than two sample sizes. This Monte Carlo study involved sampling from a normal population for…

Concern over the validity of statistical tests performed on data that may not satisfy underlying assumptions has prompted methodological researchers to perform Monte Carlo studies for frequently used tests. Unfortunately, these studies appear to have had little impact on methodological practice. One reason is the lack of an overarching framework…

The purpose of this study is to help define the precise nature and limits of the tolerable range in which a researcher may be relatively confident about the statistical validity of his or her research findings, focusing specifically on the statistical validity of results when violating the assumptions associated with the one-way, fixed-effects…

The empirical performance of the technique proposed by P. O. Johnson and J. Neyman (1936) (the JN technique) and the modification of R. F. Potthoff (1964) was studied in simulated data settings. The robustness of the two JN techniques was investigated with respect to their ability to control Type I and Type III errors. Factors manipulated in the…

This paper presents 11 statistical procedures which test the equality of m coefficient alphas when the sample alpha coefficients are dependent. Several of the procedures are derived in detail, and numerical examples are given for two. (Author/LMO)

Accurate estimation of variance components used in generalizability theory is essential for the theory to be viewed as an efficacious mechanism for studying the reliability and validity of a measurement procedure. This paper explores two alternatives for dealing with the apparent instability of small sample size used in determining the accuracy of…

This study investigated seven methods for analyzing multivariate group differences. Bonferroni t statistics, multivariate analysis of variance (MANOVA) followed by analysis of variance (ANOVA), and five other methods were studied using Monte Carlo methods. Methods were compared with respect to (1) experimentwise error rate; (2) power; (3) number…