Type I error rates and power were estimated for 10 tests of variance equality under various combinations of the following factors: similar and dissimilar distributional forms, equal and unequal means, and equal and unequal sample sizes. (TJH)

For Y. Yao's and G. S. James' tests, Type I error rates were estimated for various combinations of the number of variables, sample-size and sample-size-to-variables ratios, and heteroscedasticity. These tests are alternatives to Hotelling's T(sup 2) and are intended for use when variance-covariance matrices are unequal for two independent samples.…

Determination of statistical power for analysis of variance procedures requires five elements: (1) significance level; (2) effect size; (3) number of means; (4) error variance; and (5) sample size. Significance levels are traditionally chosen to be 0.5, .01, or .001. Effect size is not discussed in this paper. The number of means is determined by…

In true experiments in which sample material can be randomly assigned to treatment conditions, most researchers presume that the condition of equal sample sizes is statistically desirable. When one or more a priori contrasts can be identified which represent a few overriding experimental concerns, however, allocating sample material unequally will…

THE PURPOSE OF THIS RESEARCH WAS TO STUDY THE EFFECT OF ERROR OF MEASUREMENT UPON THE POWER OF STATISTICAL TESTS. ATTENTION WAS FOCUSED ON THE F-TEST OF THE SINGLE FACTOR ANALYSIS OF VARIANCE. FORMULAS WERE DERIVED TO SHOW THE RELATIONSHIP BETWEEN THE NONCENTRALITY PARAMETERS FOR ANALYSES USING TRUE SCORES AND THOSE USING OBSERVED SCORES. THE…

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…

Type I error rates of four multivariate tests (Pilai-Bartlett trace, Johansen's test, James' first-order test, and James' second-order test) were compared for heterogeneous covariance matrices in 360 simulated experiments. The superior performance of Johansen's test and James' second-order test is discussed. (SLD)

This paper evaluates the logic underlying various criticisms of statistical significance testing and makes specific recommendations for scientific and editorial practice that might better increase the knowledge base. Reliance on the traditional hypothesis testing model has led to a major bias against nonsignificant results and to misinterpretation…

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…

The statistical properties of two methods of estimating gain scores for groups in quasi-experiments are compared: (1) gains in scores standardized separately for each group; and (2) analysis of covariance with estimated true pretest scores. The fan spread hypothesis is assumed for groups but not necessarily assumed for members of the groups.…