Introductory statistics texts have given extensive coverage to two-sided inferences. All texts that were surveyed give significant coverage to one-sided hypothesis tests. Very few discussed the possibility of one-sided interval estimation at all. Even fewer mentioned so in any detail 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 suggest that all statistics courses and texts should cover both one-sided tests and confidence intervals. Furthermore, coverage should also be given to unequal division of the nominal risk of a type I error for both hypothesis tests and confidence intervals. Examples are provided for both situations.
"Z and t Distributions in Hypothesis Testing: Unequal Division of Type I Risk,"
Journal of Modern Applied Statistical Methods: Vol. 15
, Article 24.
Available at: http://digitalcommons.wayne.edu/jmasm/vol15/iss1/24