Abstract
According to almost any approach to statistical inference, attained significance levels, orp 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 reasonp 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|M 0)/P(D|M 1), whereM 0 andM 1 are the two theoretical accounts. Large values of the likelihood ratio provide evidence thatM 0 is a better account, whereas small values indicate thatM1 is better. I demonstrate that, under some circumstances, thep value can be interpreted in the same manner as the likelihood ratio. In particular, forZ,t, and sign tests, the likelihood ratio is an approximately linear function of thep value, with a slope between 2 and 3. Thus, researchers may reportp 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.
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