ABSTRACT
Consider again the null hypothesis that two independent samples are drawn from identical populations, but now suppose that we are interested in detecting differences in variability or dispersion. Some of the tests presented in Chapters 6 and 8, namely, the median, Mann–Whitney, Wilcoxon rank-sum, Terry, van der Waerden, and percentile-modified rank tests, were noted to be particularly sensitive to differences in location when the populations are identical otherwise, a situation described by the relation F Y (x) = F X (x – θ). These tests cannot be expected to perform especially well against other alternatives. The general two-sample tests of Chapter 6, like the Wald–Wolfowitz runs or Kolmogorov–Smirnov tests, are affected by any type of difference in the populations and therefore cannot be expected to be very efficient for detecting differences in variability. Some other nonparametric tests are needed for this dispersion problem.
