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Schneider's (2015) article is contemporary work addressing the shortcomings of null hypothesis significance testing (NHST). It summarizes previous work on the topic and provides original examples illustrating NHST-induced confusions in scientometrics. Among the confusions cited are those associated with the interpretation of p-values, old misinterpretations already investigated by Oakes (1986), Falk and Greenbaum (1995); Haller and Krauss (2000), and Perezgonzalez (2014a), and discussed in, for example, Carver (1978); Nickerson (2000), Hubbard and Bayarri (2003); Kline (2004), and Goodman (2008). That they are still relevant in recent times testifies to the fact that the lessons of the past have not been learnt.  As the title anticipates, there is a twist to this saga, a pedagogical one: p-values are typically taught and presented as probabilities, and this may be the cause behind the confusions. A change in the heuristic we use for teaching and interpreting the meaning of p-values may be all we need to start working the path toward clarification and understanding.  In this article I will illustrate the differences in interpretation that a percentile heuristic and a probability one make. As guiding example, I will use a one-tailed p-value in a normal distribution—z = −1.75, p = 0.04; Figure ​Figure1).1). The default testing approach will be Fisher's tests of significance, but Neyman–Pearson's tests of acceptance approach will be assumed when discussing Type I errors and alternative hypotheses (for more information about those approaches see Perezgonzalez, 2014b, 2015). The scenario is the scoring of a sample of suspected schizophrenics on a validated psychological normality scale. The hypothesis tested (Fisher's H0, Neyman–Pearson's HM) is that the mean score of the sample on the normality scale does not differ from that of the normal population (no H0 = the sample does not score as normal; HA = the sample scores as schizophrenic, assuming previous knowledge that schizophrenics score low on the scale, by a given effect size). Neither a level of significance nor a rejection region is needed for the discussion.    Figure 1  Location of an observed z-score and its corresponding p-value in the frequency distribution of the hypothesis under test. The accompanying scales are for the theoretical z-scores and percentiles, respectively.

frontiers in psychology

P-values as percentiles. Commentary on: â€œNull hypothesis significance tests. A mixâ€“up of two different theories: the basis for widespread confusion and numerous misinterpretationsâ€

P-values as percentiles. Commentary on: â€œNull hypothesis significance tests. A mixâ€“up of two different theories: the basis for widespread confusion and numerous misinterpretationsâ€

P-values as percentiles. Commentary on: â€œNull hypothesis significance tests. A mixâ€“up of two different theories: the basis for widespread confusion and numerous misinterpretationsâ€