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This paper is motivated by the analysis of gene expression sets, especiallyby finding differentially expressed gene sets between two phenotypes. Gene$\log_2$ expression levels are highly correlated and, very likely, haveapproximately normal distribution. Therefore, it seems reasonable to usetwo-sample Hotelling's test for such data. We discover some unexpectedproperties of the test making it different from the majority of testspreviously used for such data. It appears that the Hotelling's test does notalways reach maximal power when all marginal distributions are differentiallyexpressed. For highly correlated data its maximal power is attained when abouta half of marginal distributions are essentially different. For the case whenthe correlation coefficient is greater than 0.5 this test is more powerful ifonly one marginal distribution is shifted, omparing to the case when allmarginal distributions are equally shifted. Moreover, when the correlationcoefficient increases the power of Hotelling's test increases as well.

Hotelling's test for highly correlated data