Nonparametric Methods for Two Samples

• In the independent two-sample t-test, we assume normality, independence, and equal variances. • This t-test is robust against nonnormality, but is sensitive to dependence. • If n1 is close to n2, then the test is moderately robust against unequal variance (σ 1 6= σ 2). But if n1 and n2 are quite different (e.g. differ by a ratio of 3 or more), then the test is much less robust. • How to determine whether the equal variance assumption is appropriate? • Under normality, we can compare σ 1 and σ 2 using S 1 and S 2 , but such tests are very sensitive to nonnormality. Thus we avoid using them. • Instead we consider a nonparametric test called Levene’s test for comparing two variances, which does not assume normality while still assuming independence. • Later on we will also consider nonparametric tests for comparing two means.