ABSTRACT
Consider again the situation of Chapter 8, where the null hypothesis is that two independent samples are drawn from identical populations; however, now suppose that we are interested in detecting differences in variability or dispersion instead of location. Some of the tests presented in Chapters 6 and 8, namely, the median, Mann-Whitney, Wilcoxon rank-sum, Terry, van der Waerden, and Ts − Br tests, were noted to be particularly sensitive to differences in location when the populations are identical otherwise, a situation described by the relation Fy (x) = FX (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 test or Kolmogorov-Smirnov tests, are affected by any type of difference in the populations and therefore cannot be relied upon as efficient for detecting differences in variability. Some other nonparametric tests are needed for the dispersion problem.
