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This paper presents an investigation of the behavior of the levels of significance of the two-sample t and its related tests and the Mann-Whitney test when the samples are randomly drawn from mixtures of two normal populations (compound normals) and when the sample sizes are small (combined sample sizes ⩽ 15). The use of the compound normal allows for investigation when the underlying populations are unequal, nonnormal, heterogeneous in variances, unimodal or bimodal, possessing smaller than normal kurtosis or containing contamination. The exact distribution of the t and its related tests are given. However, they are not readily amenable to calculations. Most of the numerical results presented were obtained by simulations
Lee et al. (Thu,) studied this question.