Type I error rates were estimated for three tests that compare means by using data from two independent samples: the independent samples t test, Welch's approximate degrees of freedom test, and James's second order test. Type I error rates were estimated for skewed distributions, equal and unequal variances, equal and unequal sample sizes, and a range of total sample sizes. Welch's test and James's test have very similar Type I error rates and tend to control the Type I error rate as well or better than the independent samples t test does. The results provide guidance about the total sample sizes required for controlling Type I error rates. Nine tables are included. (Contains 16 references.) (Author)