If the variances of two treatment groups are heterogeneous and, at the same time, sample sizes are unequal, the Type I error probabilities of the pooledvariances Student t test are modified extensively. It is known that the separate-variances tests introduced by Welch and others overcome this problem in many cases and restore the probability to the nominal significance level. In practice, however, it is not always apparent from sample data whether or not the homogeneity assumption is valid at the population level, and this uncertainty complicates the choice of an appropriate significance test. The present study quantifies the extent to which correct and incorrect decisions occur under various conditions. Furthermore, in using statistical packages, such as SPSS, in which both pooled-variances and separate-variances t tests are available, there is a temptation to perform both versions and to reject H0 if either of the two test statistics exceeds its critical value. The present simulations reveal that this procedure leads to incorrect statistical decisions with high probability.