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 standard statistical analysis of data classified in two ways (say into rows and columns) is through an analysis of variance that splits the total variation of the data into the main effect of rows, the main effect of columns, and the interaction between rows and columns. This paper presents an alternative Bayesian analysis of the same…

Although the Statistical Package for the Social Sciences (SPSS) contains no subprogram that is complete in itself for analyzing repeated measures or mixed designs analysis of variance, subprogram ANOVA can be used to obtain almost all the required sums of squares for repeated measures designs, mixed designs having repeated measures on some…

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 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…

The statistical power of nine k-sample tests against ordered location alternatives under completely randomized designs are investigated. The results are intended to aid researchers in selecting appropriate statistical procedures. (Author/JKS)

This paper reviews the distinctions between classical and partial eta square and derives a formula for use in those complex analysis of variance designs in which the investigator desires a measure of classical eta square and has access only to the F-tests and relevant degrees of freedom. (Author/BW)

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)

Many researchers draw the conclusion that one independent variable has more impact than another without testing the null hypothesis that their impact is equal. This paper presents and recommends a technique for testing the relative magnitude of effects, rather than basing conclusions solely on descriptive statistics. (Author/BW)

Disagreements have arisen about the robustness of the t test in normal populations with unequal variances. Employing liberal but objective standards for assessing robustness, it is shown that the t test is not always robust to the assumption of equal population variances even when sample sizes are equal. (Author/JKS)

Hollingsworth recently showed a posttest contrast for analysis of variance situations that, for equal sample sizes, had several favorable qualities. However, for unequal sample sizes, the contrast fails to achieve status as a maximized contrast; thus, separate testing of the contrast is required. (Author/GSK)

A problem in analysis of variance is that after rejection of the overall hypothesis, no contrasts of interest are found to be significant. A procedure for determining the contrast of significance is outlined, and the relationship between the "most significant" contrast and the overall test is shown. (Author/JKS)

A simple rationale for Scheffe's Method and Gabriel's Simultaneous Test Procedure is presented. Examples of both methods are provided. (Author)

An error is described that may occur in a posteriori testing, particularly when the original analysis of variance produces an F ratio that is just barely significant and the computer printout of the analysis does not provide the means that were used in the program. (Author/JKS)

The importance of measuring the size of an effect for fixed effects factorial analysis of variance designs is emphasized. Technical issues in such measurement are considered and examples are provided. (Author/JKS)