There are two well-known versions of the t-test for comparing means from unpaired data: Student's t-test and Welch's t-test. While Welch's t-test does not assume homoscedasticity (i.e., equal variances), it involves approximations. A classical textbook recommendation would be to use Student's t-test if either the two sample sizes are similar or the two sample variances are similar, and to use Welch's t-test only when both of the above conditions are violated. However, a more recent recommendation seems to be to use Welch's t-test unconditionally. Using past data from both TREC and NTCIR, the present study demonstrates that the latter advice should not be followed blindly in the context of IR system evaluation. More specifically, our results suggest that if the sample sizes differ substantially and if the larger sample has a substantially larger variance, Welch's t-test may not be reliable.