Abstract
In medical science and biology, there often exist situations for some data where the number of characteristics is about equal to or greater than the one of individuals. In this paper we discuss the hypothesis testing in that case, i.e., the situation where the degrees of freedom of error are so small that usual test procedures in MANOVA can not be applied for given data. We propose a test procedure with a single test statistic. The test statistic is a multiplication of the sequence of test statistics based on principal component analysis proposed by Dempster (1963a, 1963b). We also propose an influential measure of each individual for the result of the test, and a criterion of how many principal components should be incorporated in the test when the degree of hypothesis is only one. The test procedure for multivariate two sample problem is demonstrated with some data sets appeared in literature.
