Motivation: In the exploding field of gene expression techniques such as DNA microarrays, there are still few general probabilistic methods for analysis of variance. Linear models and anova are heavily used tools in many other disciplines of scientific research. The usual F -statistic is unsatisfactory for microarray data, which explores many thousand genes in parallel, with few replicates. Res...

This research is to provide a solution of one-way ANOVA without using transformation when variances are heteroscedastic and group sizes are unequal. Parametric boothstrap test (Krishnamoorthy, Lu, & Mathew, 2007) has been shown to be competitive with many other methods when testing the equality of group means. We extend the parametric bootstrap algorithm to a multiple comparison procedure. Simu...

Kinematic and force trajectories are often normalized in time, with mean and variance summary statistic trajectories reported. It has been shown elsewhere, for simple one-factor experiments, that statistical testing can be conducted directly on those summary statistic trajectories using Random Field Theory (RFT). This technical note describes how RFT extends to two-factor designs, and how bizar...

In last week’s lecture we came across an example, from Field (2013), about the drug Viagra, which is a sexual stimulant (used to treat impotence), which is supposed to make men better lovers. Suppose we tested this belief by taking three groups of people and administering one group with a placebo (such as a sugar pill), one group with a low dose of Viagra and one with a high dose. The dependent...

For one-way fixed effects ANOVA, it is well known that the conventional F test of the equality of means is not robust to unequal variances, and numerous methods have been proposed for dealing with heteroscedasticity. On the basis of extensive empirical evidence of Type I error control and power performance, Welch's procedure is frequently recommended as the major alternative to the ANOVA F test...

The independence assumption, although reasonable when examining cross-sectional data using single-factor experimental designs, is seldom verified by investigators. A Monte Carlo type simulation experiment was designed to examine the relationship between true Types I and II error probabilities in six multiple comparison procedures. Various aspects, such as patterns of means, types of hypotheses,...

A key issue in various applications of analysis of variance is testing for interaction and the interpretation of resulting analysis of variance tables. In this note is demonstrated that for a two-way ANOVA, incorporating interactions or not may have a dramatic influence when considering the usual statistical tests for normality of residuals. The effect of numerical rounding is also discussed.