Comparing K Populations With Linear Rank Statistics
Abstract There are many nonparametric tests available for the analysis of k independent samples. For example, the Kruskal—Wallis test (Wilcoxon rank sum test when k = 2) is widely used for detecting location differences, and Mood or Ansari—Bradley or Sigel—Tukey rank statistics are often suggested for detecting scale differences. If more general alternatives are of interest, then one can use omnibus tests such as the generalized Kolmogorov—Smirnov and Cramer—von Mises statistics [see Conover (1980, secs. 6.3 and 6.4) or Kiefer (1959)]. Unfortunately, “significant” results from these omnibus tests are hard to interpret. Instead, I would like to propose some new tests based on a 4×k table of linear rank statistics that are simple to interpret because the four rows of the table are aimed at specific alternatives: location, scale, skewness, and kurtosis. Row summary statistics consist of weighted sums of squares of the individual entries. The first two of these are the Kruskal—Wallis statistic and Mood's k-sa...