Unequal Division of Type I Risk in Statistical Inferences

Introductory statistics texts give extensive coverage to two-sided inferences in hypothesis testing, interval estimation, and one-sided hypothesis tests. Very few discuss the possibility of one-sided interval estimation at all. Even fewer do so in any detail. Two of the business statistics texts we reviewed mentioned the possibility of dividing the risk of a type I error unequally between the tails for a two-sided confidence interval. None of the textbooks that were reviewed even considered the possibility of unequal tails for two-sided hypothesis tests. In this paper, we propose that statistics courses and texts should cover both one-sided tests and confidence intervals. Furthermore, we propose that coverage, at least in two semesters and advanced courses, should also be given to unequal division of the nominal risk of a type I error for both tests and confidence intervals. Examples are provided for both situations.