independently sampled populations?
The ANOVA model assumes that all populations (at each level of X) are approximately normally distributed. There are several plots and tests that can be used to assess normality, including the Q-Q plot, the boxplot, and the non-parametric chi-square test of distributions (see Chapter 6), and the Kolmogorov-Smirnoff test. The statistical tests underlying the ANOVA methodology are robust, and so moderate departures from normality can be ignored (Glenberg, 1996). For severe departures from normality, a Kruskal-Wallis H test procedure should be used to compare sample means. Because the Kruskal-Wallis H test is not as powerful as ANOVA, it should only be used when the requisite ANOVA assumptions are not met.
