JEP, p-values and tests of statistical significance

The Summer 2021 issue of the Journal of Economic Perspectives came out recently:

I have been the Managing Editor of the Journal of Economic Perspectives since the first issue in Summer 1987. The JEP is published by the American Economic Association, which decided about a decade ago–to my delight–that the journal would be freely available on-line, from the current issue all the way back to the first issue. You can download individual articles or the entire issue, and it is available in various e-reader formats, too. Here, I’ll start with the Table of Contents for the just-released Summer 2021 issue, which in the Taylor household is known as issue #137.

(JEP is a great journal to read as a student. If you’re looking for a good place to start, may I recommend the Anomalies column?)

Of particular interest this time around is the section on statistical significance. This paper, in particular, was an enjoyable read.

And reading that paper reminded of a really old blogpost written by an ex-colleague of mine:

The author starts off by emphasizing the importance of developing a statistical toolbox. Indeed statistics is a rich subject that can be enjoyed by thinking through a given problem and applying the right kind of tools to get a deeper understanding of the problem. One should approach statistics with a bike mechanic mindset. A bike mechanic is not addicted to one tool. He constantly keeps shuffling his tool box by adding new tools or cleaning up old tools or throwing away useless tools etc. Far from this mindset, the statistics education system imparts a formula oriented thinking amongst many students. Instead of developing a statistical or probabilistic thinking in a student, most of the courses focus on a few formulae and teach them null hypothesis testing.

If you are a student of statistics, and think that you “get” statistics, please read the post in its entirety. Don’t worry if you get confused – that is, in a way, the point of that post. It challenges you by asking a very simple question: do you really “get” statistics? And the answer is almost always in the negative (and that goes for me too!)

And my final recommendations du jour is this (extremely passionately) written tirade:

We want to persuade you of one claim: that William Sealy Gosset (1876-1937)—aka “Student” of “Student’s” t-test—was right, and that his difficult friend, Ronald A. Fisher (1890-1962), though a genius, was wrong. Fit is not the same thing as importance. Statistical significance is not the same thing as scientific importance or economic sense. But the mistaken equation is made, we find, in 8 or 9 of every 10 articles appearing in the leading journals of science, economics to medicine. The history of this “standard error” of science involves varied characters and plot twists, but especially R. A. Fisher’s canonical translation of “Student’s” t. William S. Gosset aka “Student,” who was for most of his life Head Experimental Brewer at Guinness, took an economic approach to the logic of uncertainty. Against Gosset’s wishes his friend Fisher erased the consciously economic element, Gosset’s “real error.” We want to bring it back.

Although it might help by reading this review first:

However, thanks to an arbitrary threshold set by statistics pioneer R.A. Fisher, the term ‘significance’ is typically reserved for P values smaller than 0.05. Ziliak and McCloskey, both economists, promote a cost-benefit approach instead, arguing that decision thresholds should be set by considering the consequences of wrong decisions. A finding with a large P value might be worth acting upon if the effect would be genuinely clinically important and if the consequences of failing to act could be serious.

Statistics is a surprisingly, delightfully conceptual subject, and I’m still peeling away at the layers. Every year I think I understand it a little bit more, and every year I discover that there is much more to learn. The symposium on statistical significance in this summer’s issue of the JEP, RK’s blogpost and Deirdre McCloskey’s paper are good places to get started on unlearning what you’ve been taught in stats.