The Waves and the Sigmas (To Say Nothing of the 750 GeV Mirage)

Abstract

This paper shows how p-values do not only create, as well known, wrong expectations in the case of flukes, but they might also dramatically diminish the `significance' of most likely genuine signals. As real life examples, the 2015 first detections of gravitational waves are discussed. The March 2016 statement of the American Statistical Association, warning scientists about interpretation and misuse of p-values, is also reminded and commented. (The paper is complemented with some remarks on past, recent and future claims of discoveries based on sigmas from Particles Physics.)

arXiv comment28 pages, 6 figures, based on on the invited talk "Claims of discoveries based on sigmas" at MaxEnt 2016 (Ghent, Belgium, 15 July 2016) and on seminars and courses to PhD students in the first half of 2016. (the R script and the Hugin Bayesian network mentioned in the text, as well as related links, can be found in http://www.roma1.infn.it/~dagos/prob+stat.html#waves-sigmas)

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