ABSTRACT
This chapter introduces a classic and commonly used method for comparing means, called the analysis of variance or ANOVA F test, which assumes both normality and homoscedasticity. It describes numerous methods that have been proposed for improving on the ANOVA F test. They include heteroscedastic techniques based on robust measures of location as well as rank-based or nonparametric techniques. The chapter describes the most commonly used method for testing, the hypothesis of equal means. It provides a conceptual overview of the strategy behind the ANOVA F test. A popular way of approaching and describing the ANOVA F test is in the context of what is called the general linear model, which is a framework for describing a large class of methods that contains least squares regression as a special case. The Kruskall-Wallis test performs relatively well when the null hypothesis of identical distributions is true, but concerns arise when the null hypothesis is false, particularly in terms of power.
