Approximate Small-Sample Distributions for Multivariate Two-Sample Nonparametric Tests

The multivariate, two-sample, nonparametric, location problem is considered. Emphasis is on approximate significance tests, important in applications since generally useful tables are precluded because of inherent correlations between variates. Multivariate randomization, ranksum and normal scores tests are considered. The first four moments for each test statistic, conditional on observed samples, are obtained under an hypothesis implying interchangeability of observation vectors between the two samples. Approximate sampling distributions for the test statistics are fitted yielding the approximate test procedures. While there is no way to evaluate the goodness of these approximations generally, a specific example is studied where Monte Carlo results are used to check the approximate methods. (Author)