ABSTRACT
There are four general approaches when comparing two groups, each group has its own strengths and weaknesses. This chapter explains what each approach is trying to accomplish and provides a general sense of their relative merits. The four approaches are compare measures of location; compare measures of variation; focus on the probability that a randomly sampled observation from the first group is smaller than a randomly sampled observation from the second group; and simultaneously compare all of the quantiles to get a global sense of where the distributions differ and by how much. The chapter describes the classic and commonly used method for comparing two independent groups: Student's T test. A way of testing the hypothesis that two independent groups have identical distributions is with the Kolmogorov-Smirnov test. Although the most common approach to comparing two independent groups is to use some measure of location, situations arise where there is interest in comparing variances or some other measure of scale.
