There are many nonparametric tests available for the analysis ofkindependent samples. For example, the Kruskal—Wallis test (Wilcoxon rank sum test whenk= 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 Cramér—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×ktable 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'sk-sample statistic for testing scale differences, and the last two are newk-sample test statistics relating to skewness and kurtosis alternatives. An overall omnibus statistic GLOBE is then formed by adding all four of these row summary statistics. GLOBE is also a weighted sum of column summary statistics that are computed by taking the sum of squares of each column of the 4×ktable.