A Primer on p-Value Thresholds and α-Levels – Two Different Kettles of Fish

It has often been noted that the “null-hypothesis-significance-testing” (NHST) framework is an incon-sistent hybrid of Neyman-Pearson’s “hypothesis test-ing” and Fisher’s “significance testing” that almost inevitably causes misinterpretations. To facilitate a realistic assessment of the potential and the limits of statistical inference, we briefly recall widespread inferential errors and outline the two original ap-proaches of these famous statisticians. Based on the understanding of their irreconcilable perspectives, we propose “going back to the roots” and using the ini-tial evidence in the data in terms of the size and the uncertainty of the estimate for the purpose of statisti-cal inference. Finally, we make six propositions that hopefully contribute to improving the quality of infer-ences in future research.