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.