ABSTRACT
A procedure commonly used in support of mean comparisons is a randomization test in which the scores from different groups are pooled and then reassigned to groups a large number of times, with the mean difference. The original mean difference or t is then compared to the resulting distribution of mean differences. The data of LeVay will be used to illustrate application of the independent groups direct methods to real data. LeVay measured the areas of two hypothalamic nuclei, INAH-2 and INAH-3, in two groups of cadavers. The issue with respect to possible scale transformation is substantive invariance of conclusions under transformation when they are based on what are really ordinal or nominal scales, not the statistical sampling behavior of such scales. Several statisticians have suggested various forms of what amounts to the ANCOVA of ranks as an alternative to ordinary ANCOVA. Several papers have examined the properties of such processes, using theoretical analysis or Monte Carlo studies.
