Two-tailed versus one-tailed tests: In inference that investigates whether there is a difference between two groups, there are two approaches to formulating the alternative hypothesis. Either you know the direction of the difference in advance of doing the study or you do not. A one-tailed test specifies the direction of the difference in advance. A two-tailed test does not specify the direction of the difference. For sample size estimation stick to two-tailed alternative hypotheses! For example, when comparing a new therapy to a standard therapy one might be convinced that the new therapy could only be better! But, examples abound where a new therapy under study was actually worse. Think about the case when Coca Cola introduced “New Coke” expecting it to improve sales. The huge negative public outcry was completely unexpected by Coca Cola.
