SUPERVISORS

ii It is common that two populations are to be compared, and one objective is to test the null hypothesis that the two populations have the same response distributions against the alternative that the response distributions are different. Three classes of tests are provided for this situation, depending on the type of alternative hypothesis. One class of tests has good power against shift alternatives (i.e., changes in the location), a second against dispersion alternatives (i.e., changes in the scale), and a third against general alternatives. In this research, the main focus will be the two-sample test for location problem, especially when the data are under nonnormality and heteroscedasticity, since the classical test are based on either of this two assumptions. For example, Welch t test (Welch, 1947) improves the simple t test (“Student”, 1908) when data are heterogeneous, but it works less efficiently than Wilcoxon Rank Sum test (Wilcoxon, 1945) when the data are skewed. Wilcoxon test is powerful under nonnormality but it behaves poorly under heteroscedasticity. In fact, without the parametric assumption of the underlying distribution of the data, th