CHAPTER 5 Comparing Two Groups A natural and reasonable approach to comparing two distributions is to compare robust measures of location and scale, but first attention is focused on global comparisons of two distributions. The motivation for global comparisons is that if two distributions differ, they might do so in complicated and interesting ways that are not revealed by differences between single measures of location or scale. For example, if one or both distributions are skewed, the difference between the means might be large compared with the difference between the trimmed means, or any other measure of location that might be used. As is evident, the reverse can happen when the difference between the trimmed means is large and the difference between the means is not. Of course, two or more measures of location might be compared, but this might miss interesting differences and trends among subpopulations of participants. To elaborate, it helps first to consider a simple but unrealistic situation. Consider two normal distributions that have means µ 1 = µ 2 . Then any test of the hypothesis H 0 : µ 1 = µ 2 should