Some supporters of the null hypothesis significance testing procedure recognize that the logic on which it depends is invalid because it only produces the probability of the data if given the null hypothesis and not the probability of the null hypothesis if given the data (e.g., J. Krueger, 2001). However, the supporters argue that the procedure is good enough because they believe that the probability of the data if given the null hypothesis correlates with the probability of the null hypothesis if given the data. The present authors' main goal was to test the size of the alleged correlation. To date, no other researchers have done so. The present findings indicate that the correlation is unimpressive and fails to provide a compelling justification for computing p values. Furthermore, as the significance rule becomes more stringent (e.g., .01, .001), the correlation decreases.
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