One-Sample One-Sided Student T-Test Under Contaminants

A paradoxical behavior of the t-test under ε-contamination is presented. The paradox consists in that under a fixed distribution of contaminants an increasing of the probability of the appearance of a contaminant may decrease the violation of the size of the test! A simple explanation of the phenomenon is given. It is revealed which contaminants make the test conservative and which make it liberal: it appears that, in spite of the established opinion, conservatism or liberalism of the test depends not so much on the tails of the contaminating distribution as on where its support is located.