## Mindless statistics

17 Jun, 2022 at 09:13 | Posted in Statistics & Econometrics | 1 Comment

Knowing the contents of a toolbox, of course, requires statistical thinking, that is, the art of choosing a proper tool for a given problem. Instead, one single procedure that I call the “null ritual” tends to be featured in texts and practiced by researchers. Its essence can be summarized in a few lines:

The null ritual:
1. Set up a statistical null hypothesis of “no mean difference” or “zero correlation.” Don’t specify the predictions of your research hypothesis or of any alternative substantive hypotheses.
2. Use 5% as a convention for rejecting the null. If signiﬁcant, accept your research hypothesis. Report the result as p < 0.05, p < 0.01, or p < 0.001 (whichever comes next to the obtained p-value).
3. Always perform this procedure …

The routine reliance on the null ritual discourages not only statistical thinking but also theoretical thinking. One does not need to specify one’s hypothesis, nor any challenging alternative hypothesis … The sole requirement is to reject a null that is identiﬁed with “chance.” Statistical theories such as Neyman–Pearson theory and Wald’s theory, in contrast, begin with two or more statistical hypotheses …

We know but often forget that the problem of inductive inference has no single solution. There is no uniformly most powerful test, that is, no method that is best for every problem. Statistical theory has provided us with a toolbox with effective instruments, which require judgment about when it is right to use them … Judgment is part of the art of statistics.

To stop the ritual, we also need more guts and nerves. We need some pounds of courage to cease playing along in this embarrassing game. This may cause friction with editors and colleagues, but it will in the end help them to enter the dawn of statistical thinking.