ইতিহাস এবং উত্স
রবার্ট ডি কাজিন্স 1 এবং টমাসো ডরিগো 2 এর মতে , 5 σ প্রান্তিক উত্সটির উত্স 60 এর দশকের প্রথম দিকের কণা পদার্থবিজ্ঞানের কাজের মধ্যে রয়েছে যখন ছড়িয়ে ছিটিয়ে থাকা অসংখ্য হিস্টোগ্রাম পরীক্ষাগুলি অনুসন্ধান এবং অনুসন্ধান করা হয়েছিল যেগুলি কিছু নতুন আবিষ্কৃত কণাকে নির্দেশ করতে পারে । প্রান্তিক হ'ল একাধিক তুলনা যা তৈরি করা হচ্ছে তার জন্য অ্যাকাউন্ট করার মোটামুটি নিয়ম।125σ
উভয় লেখক Rosenfeld থেকে 1968 নিবন্ধটি উল্লেখ 3 হোক বা না হোক সেখানে আউট গবেষণার মাধ্যমে মেসনের এবং বেরিয়নের পর্যন্ত, যা বিভিন্ন জন্য, যা প্রশ্নের সঙ্গে মোকাবিলা 4 σ প্রভাব যেখানে মাপা। নিবন্ধটি প্রশ্নের জবাবে নেতিবাচক যুক্তি দিয়ে উত্তর দিয়েছে যে প্রকাশিত দাবির সংখ্যা পরিসংখ্যানগতভাবে প্রত্যাশিত ওঠানামার সংখ্যার সাথে মিলে যায়। বিভিন্ন এই যুক্তি প্রবন্ধের ব্যবহার উন্নীত সমর্থনকারী গণনার সাথে সাথে 5 σ স্তর:34σ5σ
(Kππ)3/2,(πρ)−−3σ>4σ
এবং পরে কাগজে (জোর আমার)
Rosenfeld: "Then to repeat my warning at the beginning of this section; we are generating at least 100 000 potential bumps per year, and should expect several 4σ and hundreds of 3σ fluctuations. What are the implications? To the theoretician or phenomenologist the moral is simple; wait for 5σ effects."
Tommaso seems to be careful in stating that it started with the Rosenfeld article
Tommaso: "However, we should note that the article was written in 1968, but the strict criterion of five standard deviations for discovery claims was not adopted in the seventies and eighties. For instance, no such thing as a five-sigma criterion was used for the discovery of the W and Z bosons, which earned Rubbia and Van der Meer the Nobel Prize in physics in 1984."
But in the 80s the use of 5σ was spread out. For instance, the astronomer Steve Schneider4 mentions in 1989 that it is something being taught (emphasize mine in the quote below):
Schneider: "Frequently, 'levels of confidence' of 95% or 99% are quoted for apparently discrepant data, but this amounts to only two or three statistical sigmas. I was taught not to believe anything less than five sigma, which if you think about it is an absurdly stringent requirement --- something like a 99.9999% confidence level. But of course, such a limit is used because the actual size of sigma is almost never known. There are just too many free variables in astronomy that we can't control or don't know about."
Yet, in the field of particle physics many publications where still based on 4σ discrepancies up till the late 90s. This only changed into 5σ at the beginnning of the 21th century. It is probably prescribed as a guidline for publications around 2003 (see the prologue in Franklin's book Shifting Standards5)
Franklin: By 2003 the 5-standard-deviation criterion for "observation of" seems to have been in effect
...
A member of the BaBar collaboration recalls that about this time the 5-sigma criterion was issued as a guideline by the editors of the Physical Review Letters
Modern use
Currently, the 5σ threshold is a textbook standard. For instance, it occurs as a standard article on physics.org6 or in some of Glen Cowan's works, such as the statistics section of the Review of Particle Physics from the particle data group7 (albeit with several critical sidenotes)
Glen Cowan: Often in HEP, the level of significance where an effect is said to qualify as a discovery is Z=5, i.e., a 5σ effect, corresponding to a p-value of 2.87×10−7 . One’s actual degree of belief that a new process is present, however, will depend in general on other factors as well, such as the plausibility of the new signal hypothesis and the degree to which it can describe the data, one’s confidence in the model that led to the observed p-value, and possible corrections for multiple observations out of which one focuses on the smallest p-value obtained (the “look-elsewhere effect”).
The use of the 5σ level is now ascribed to 4 reasons:
History based on practice one found that 5σ is a good threshold. (exotic stuff seems to happen randomly, even between 3σ to 4σ, like recently the 750 GeV diphoton excess)
The look elsewhere effect (or the multiple comparisons). Either because multiple hypotheses are tested, or because experiments are performed many times, people adjust for this (very roughly) by adjusting the bound to 5σ. This relates to the history argument.
Systematic effects and uncertainty in σ often the uncertainty of the experiment outcome is not well known. The σ is derived, but the derivation includes weak assumptions such as the absence of systematic effects, or the possibility to ignore them. Increasing the threshold seems to be a way to sort of a protect against these events. (This is a bit strange though. The computed σ has no relation to the size of systematic effects and the logic breaks down, an example is the "discovery" of superluminal neutrino's which was reported to be having a 6σ significance.)
Extraordinary claims require extraordinary evidence Scientific results are reported in a frequentist way, for instance using confidence intervals or p-values. But, they are often interpreted in a Bayesian way. The 5σ level is claimed to account for this.
Currently several criticisms have been written about the 5σ threshold by Louis Lyons8,9, and also the earlier mentioned articles by Robert D Cousins1 and Tommaso Dorigo2 provide critique.
Other Fields
It is interesting to note that many other scientific fields do not have similar thresholds or do not, somehow, deal with the issue. I imagine this makes a bit sense in the case of experiments with humans where it is very costly (or impossible) to extend an experiment that gave a .05 or .01 significance.
The result of not taking these effects into account is that over half of the published results may be wrong or at least are not reproducible (This has been argued for the case of psychology by Monya Baker 10, and I believe there are many others that made similar arguments. I personaly think that the situation may be even worse in nutritional science). And now, people from other fields than physics are thinking about how they should deal with this issue (the case of medicine/pharmacology11).
Cousins, R. D. (2017). The Jeffreys–Lindley paradox and discovery criteria in high energy physics. Synthese, 194(2), 395-432. arxiv link
Dorigo, T. (2013) Demystifying The Five-Sigma Criterion, from science20.com 2019-03-07
Rosenfeld, A. H. (1968). Are there any far-out mesons or baryons? web-source: escholarship
Burbidge, G., Roberts, M., Schneider, S., Sharp, N., & Tifft, W. (1990, November). Panel discussion: Redshift related problems. In NASA Conference Publication (Vol. 3098, p. 462). link to photocopy on harvard.edu
Franklin, A. (2013). Shifting standards: Experiments in particle physics in the twentieth century. University of Pittsburgh Press.
What does the 5 sigma mean? from physics.org 2019-03-07
Beringer, J., Arguin, J. F., Barnett, R. M., Copic, K., Dahl, O., Groom, D. E., ... & Yao, W. M. (2012). Review of particle physics. Physical Review D-Particles, Fields, Gravitation and Cosmology, 86(1), 010001. (section 36.2.2. Significance tests, page 394, link aps.org )
Lyons, L. (2013). Discovering the Significance of 5 sigma. arXiv preprint arXiv:1310.1284. arxiv link
Lyons, L. (2014). Statistical Issues in Searches for New Physics. arXiv preprint arxiv link
Baker, M. (2015). Over half of psychology studies fail reproducibility test. Nature News. from nature.com 2019-03-07
Horton, R. (2015). Offline: what is medicine's 5 sigma?. The Lancet, 385(9976), 1380. from thelancet.com 2019-03-07