The journal of Basic and Applied Social Pychology banned the p-value in 2015, after Trafimow (2014) had explained in an editorial a year earlier that inferential statistics were no longer required. In the 2014 editorial, Trafimow notes how: “The null hypothesis significance procedure has been shown to be logically invalid and to provide little information about the actual likelihood of either the null or experimental hypothesis (see Trafimow, 2003; Trafimow & Rice, 2009)”. The goal of this blog post is to explain why the arguments put forward in Trafimow & Rice (2009) are incorrect. Their simulations illustrate how meaningless questions provide meaningless answers, but they do not reveal a problem with p-values. Editors can do with their journal as they like – even ban p-values. But if the simulations upon which such a ban is based are meaningless, the ban itself becomes meaningless.
To calculate the probability that the null-hypothesis is true, given some data we have collected, we need to use Bayes’ formula. Cohen (1994) shows how the posterior probability of the null-hypothesis, given a statistically significant result (the data), can be calculated based on a formula that is a poor man’s Bayesian updating function. Instead of creating distributions around parameters, his approach simply uses the p-value of a test (which is related to the observed data), the power of the study, and the prior probability the null-hypothesis is true, to calculate the posterior probability H0 is true, given the observed data. Before we look at the formula, some definitions:
P(H0) is the prior probability (P) the null hypothesis (H0) is true.
P(H1) is the probability (P) the alternative hypothesis (H1) is true. Since I’ll be considering only a single alternative hypothesis here, either the null hypothesis or the alternative hypothesis
Source:: r-bloggers.com
