A Note on Information Seldom Reported via the P Value

The P value, or significance of a statistical test, is often reported when said value is small—that is, less than .05, and is used to reject the null hypothesis. What appears to be less well-known or perhaps less often used, certainly within the realm of clinical trials and perhaps in other areas as well, however, is that the P value also carries information about particular alternative hypotheses since the distribution of the P value under an alternative hypothesis can be found easily. By way of a simple example, this additional piece of information is used to make inference concerning the alternative hypothesis when the null hypothesis is not rejected. Suggestions for decision making and reporting are then given.