Analysis of variance (ANOVA) is a statistical technique to analyze variation in a response variable (continuous random variable) measured under conditions defined by discrete factors (classification variables, often with nominal levels). Frequently, we use ANOVA to test equality among several means by comparing variance among groups relative to variance within groups (random error). Sir Ronald ...

Common ratio-based approaches for analyzing gene expression microarray data do not provide a framework for handling replication, although replication is clearly desirable for these noisy data. In contrast, replication fits naturally into analysis of variance (ANOVA) methods. We use ANOVA to analyze data from a microarray experiment to compare gene expression in drug-treated and control cells li...

ANOVA was developed by the English statistician, R.A. Fisher (1890-1962). Though initially dealing with agricultural data[1], this methodology has been applied to a vast array of other fields for data analysis. Despite its widespread use, some practitioners fail to recognize the need to check the validity of several key assumptions before applying an ANOVA to their data. It is the hope that thi...

Data from repeated measures experiments are usually analyzed with conventional ANOVA. Three well-known problems with ANOVA are the sphericity assumption, the design effect (sampling hierarchy), and the requirement for complete designs and data sets. This tutorial explains and demonstrates multi-level modeling (MLM) as an alternative analysis tool for repeated measures data. MLM allows us to est...

This paper compares empirical type I error and power of different tests that have been proposed to assess the homogeneity of within-group variances, prior to anova. The tests of homogeneity of variance (THV) compared in this study are: Bartlett's test, the Scheffé-Box log-anova test, Cochran’s C test and Box’s M test, in their parametric and permutational forms. The main questions addressed in ...

Statistical methods used to test the null hypothesis are termed tests of significance. Selection of an appropriate test of significance is dependent on the type of data to be analyzed and the number of groups to be compared. Parametric tests of significance are based on the parameters, mean, standard deviation, and variance, and thus are used appropriately when interval or ratio data are analyz...

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.