abandoned, one year ago…

Deirdre McCloskey dans Le Monde

retire statistical significance [follow-up]

[Here is a brief update sent by my coauthors Valentin, Sander, and Blake on events following the Nature comment “Retire Statistical Significance“.]

In the eight months since publication of the comment and of the special issue of The American Statistician, we are glad to see a rich discussion on internet blogs and in scholarly publications and popular media.Nature

One important indication of change is that since March numerous scientific journals have published editorials or revised their author guidelines. We have selected eight editorials that not only discuss statistics reform but give concrete new guidelines to authors. As you will see, the journals differ in how far they want to go with the reform (all but one of the following links are open access).

1) The New England Journal of Medicine, “New Guidelines for Statistical Reporting in the Journal”

2) Pediatric Anesthesia, “Embracing uncertainty: The days of statistical significance are numbered”

3) Journal of Obstetric, Gynecologic & Neonatal Nursing, “The Push to Move Health Care Science Beyond p < .05“

4) Brain and Neuroscience Advances, “Promoting and supporting credibility in neuroscience”

5) Journal of Wildlife Management, “Vexing Vocabulary in Submissions to the Journal of Wildlife Management”

6) Demographic Research, “P-values, theory, replicability, and rigour”

7) Journal of Bone and Mineral Research, “New Guidelines for Data Reporting and Statistical Analysis: Helping Authors With Transparency and Rigor in Research“

8) Significance, “The S word … and what to do about it”

Further, some of you took part in a survey by Tom Hardwicke and John Ioannidis that was published in the European Journal of Clinical Investigation along with editorials by Andrew Gelman and Deborah Mayo.

We replied with a short commentary in that journal, “Statistical Significance Gives Bias a Free Pass“

And finally, joining with the American Statistical Association (ASA), the National Institute of Statistical Sciences (NISS) in the United States has also taken up the reform issue.

p-values, Bayes factors, and sufficiency

Among the many papers published in this special issue of TAS on statistical significance or lack thereof, there is a paper I had already read before (besides ours!), namely the paper by Jonty Rougier (U of Bristol, hence the picture) on connecting p-values, likelihood ratio, and Bayes factors. Jonty starts from the notion that the p-value is induced by a transform, summary, statistic of the sample, t(x), the larger this t(x), the less likely the null hypothesis, with density f⁰(x), to create an embedding model by exponential tilting, namely the exponential family with dominating measure f⁰, and natural statistic, t(x), and a positive parameter θ. In this embedding model, a Bayes factor can be derived from any prior on θ and the p-value satisfies an interesting double inequality, namely that it is less than the likelihood ratio, itself lower than any (other) Bayes factor. One novel aspect from my perspective is that I had thought up to now that this inequality only holds for one-dimensional problems, but there is no constraint here on the dimension of the data x. A remark I presumably made to Jonty on the first version of the paper is that the p-value itself remains invariant under a bijective increasing transform of the summary t(.). This means that there exists an infinity of such embedding families and that the bound remains true over all such families, although the value of this minimum is beyond my reach (could it be the p-value itself?!). This point is also clear in the justification of the analysis thanks to the Pitman-Koopman lemma. Another remark is that the perspective can be inverted in a more realistic setting when a genuine alternative model M¹ is considered and a genuine likelihood ratio is available. In that case the Bayes factor remains smaller than the likelihood ratio, itself larger than the p-value induced by the likelihood ratio statistic. Or its log. The induced embedded exponential tilting is then a geometric mixture of the null and of the locally optimal member of the alternative. I wonder if there is a parameterisation of this likelihood ratio into a p-value that would turn it into a uniform variate (under the null). Presumably not. While the approach remains firmly entrenched within the realm of p-values and Bayes factors, this exploration of a natural embedding of the original p-value is definitely worth mentioning in a class on the topic! (One typo though, namely that the Bayes factor is mentioned to be lower than one, which is incorrect.)

aftermaths of retiring significance

Beyond mentions in the general press of the retire significance paper, as in Retraction Watch, Bloomberg, The Guardian, Vox, and NPR, not to mention the large number of comments on Andrew’s blog, and Deborah Mayo’s tribune on a ban on free speech (!), Nature of “the week after” contained three letters from Ioannidis, calling for more stringent thresholds, Johnson, essentially if unclearly stating the same, and my friends from Amsterdam, Alexander Ly and E.J. Wagenmakers, along with Julia Haaf, getting back to the Great Old Ones, to defend the usefulness of testing versus estimation.