Why scientists value p values

Abstract

According to almost any approach to statistical inference, attained significance levels, or p values, have little value. Despite this consensus among statistical experts, p values are usually reported extensively in research articles in a manner that invites misinterpretation. In the present article, I suggest that the reason p values are so heavily used is because they provide information concerning the strength of the evidence provided by the experiment. In some typical hypothesis testing situations, researchers may be interested in the relative adequacy of two different theoretical accounts: one that predicts no difference across conditions, and another that predicts some difference. The appropriate statistic for this kind of comparison is the likelihood ratio, P(D|M0)/P(D|M1), where M0 and M1 are the two theoretical accounts. Large values of the likelihood ratio provide evidence that M0 is a better account, whereas small values indicate that M1 is better. I demonstrate that, under some circumstances, the p value can be interpreted in the same manner as the likelihood ratio. In particular, for Z, t, and sign tests, the likelihood ratio is an approximately linear function of the p value, with a slope between 2 and 3. Thus, researchers may report p values in scientific communications because they are a proxy for the likelihood ratio and provide the readers with information about the strength of the evidence that is not otherwise available.