WHY SCIENTISTS VALUE P-VALUES

According to almost any approach to statistical inference, attained si gnificance levels, or p values, have little value. Despite this consen sus among statistical experts, p values are usually reported extensive ly in research articles in a manner that invites misinterpretation. In the present article, I suggest that the reason p values are so heavil y used is because they provide information concerning the strength of the evidence provided by the experiment. In some typical hypothesis te sting situations, researchers may be interested in the relative adequa cy of two different theoretical accounts: one that predicts no differe nce across conditions, and another that predicts some difference. The appropriate statistic for this kind of comparison is the likelihood ra tio, P(D/M-0)/P(D/M-1), where M-0 and M-1 are the two theoretical acco unts. Large values of the likelihood ratio provide evidence that M-0 i s a better account, whereas small values indicate that M-1 is better. I demonstrate that, under some circumstances, the p value can be inter preted in the same manner as the likelihood ratio. Ln 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, researche rs may report p values in scientific communications because they are a proxy for the likelihood ratio and provide the readers with informati on about the strength of the evidence that is not otherwise available.