A test is developed for hypotheses about the grand mean in the analysis of variance, using the known relationship between the t distribution and the F distribution with 1 df (degree of freedom) for the numerator. (Author/RC)

Proposes three different multiple range tests based upon the Newman-Keuls philosophy with respect to significance levels. The three tests utilize the Fmax statistic, Cochran's statistic and a normalizing log transformation of the sample variances respectively. (Author/RC)

A Bayesian analysis for 2 to the k power factorial arrangements of treatments is presented in this paper. To perform the analysis, an experimenter must specify prior distributions on an orthogonal set of linear functions representing the main effects and interactions and on a function representing the grand mean. The solution is relatively…

The robustness of the statistic for complex contrasts in analysis of variance is compared to the statistic developed by Welch. The Welch statistic is recommended as the benchmark test for complex contrasts. (Author/JKS)

A procedure for testing heterogeneity of variance is developed which generalizes readily to complex, multi-factor experimental designs. Monte Carlo studies indicate that the Z-variance test statistic presented here yields results equivalent to other familiar tests for heterogeneity of variance in simple one-way designs where comparisons are…

Researchers often use the analysis of variance to test hypotheses about the means, followed by a multiple comparison technique when the F-test is significant. The technique is this study was developed by Newman (1939) and Keuls (1952). A flaw in the rationale underlying this technique was evaluated to determine whether the flaw is sufficiently…

The purposes of this paper are to: (1) describe some of the serious shortcomings in the current use of tests of statistical significance, (2) discuss how misuses are perpetuated in some widely used references, and (3) present an alternative significance testing model that overcomes some, but not all, of the shortcomings of the currently used…

The inferences allowable with a significant F in regression analysis are discussed. Included in this discussion are the effects of specificity of the research hypothesis, incorporation of covariates, directional hypotheses, and the manipulation of variables on the interpretation of significance for such purposes as causal and directional…

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…

Techniques for detecting synergistic effects in analysis of variance designs are presented and discussed. These techniques make it possible to apply some kinds of theoretical insights to the data analysis phase of a study: either by seeking synergistic effects implied or predicted by theory, or by seeking evidence of synergies as alternative…