The procedures of Scheffé [4] and Welch [5] for testing equality of means of two normal populations are compared according to the expected lengths of the confidence intervals they yield, and a criterion is developed for deciding which of the two methods is better in any given situation. An expression for the expected length of the confidence interval for the Scheffé procedure was developed by Scheffé. Because of the asymptotic series nature of the Welch procedure, in this case, the analogous expression is more involved. It is developed below. A numerical computation was carried out for the case of a two-sided 90 per cent confidence interval. The results are presented in graphical form. Finally, it is shown that in large samples, the two procedures are equivalent.