ONE-SAMPLE ONE-SIDED STUDENT T-TEST UNDER CONTAMINANTS

A paradoxical behavior of the t-test under epsilon-contamination is pr esented. The paradox consists in that under a fixed distribution of co ntaminants an increasing of the probability of the appearance of a con taminant may decrease the violation of the size of the test! A simple explanation of the phenomenon is given. It is revealed which contamina nts make the test conservative and which make it liberal: it appears t hat, in spite of the established opinion, conservatism or liberalism o f the test depends not so much on the tails of the contaminating distr ibution as on where its support is located.