ABSTRACT
The idea of decomposing a test into orthogonal contrasts, as in the analysis of variance, has long been appreciated by statisticians as a way of making hypothesis tests more informative. We have done this in our smooth goodness of fit work (see Rayner and Best, 1989a), and now, over the next several chapters, we do this in a variety of settings relevant to nonparametric testing. We use components. The definitions change with the setting, but all have the properties previously mentioned. These are that they are at least asymptotically mutually independent, they have convenient distributions, they reconstitute the original omnibus statistic, and they have immediate and useful interpretations. They therefore provide powerful directional tests and permit a convenient and informative scrutiny of the data. In addition, in each setting, the first one or two components of our omnibus statistic are familiar nonparametric test statistics, such as the Kruskal-Wallis, Friedman, and Spearman’s rho statistics. The remaining components can be viewed as extensions of these familiar statistics.
