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When the W boson was discovered in the 1980s, nobody spoke of sigmas. How many sigmas was it at that time?

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Standard deviations of significance (i.e. "sigmas") were part of the process and the literature long before 1980. I wasn't around then, but @anna might be able to say a few words about when the consensus that five sigma were needed to claim discovery came to be. –  dmckee Jul 2 '12 at 15:59
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Look at figure 1.3 in this lecture.

The number of Z bosons, about 22, over an extrapolated background of 0, makes it a five sigma.

The W is more complicated, since it is detected by the Jacobean peak (search for Jacobean) of the seen electron, fig. 1.4, but still it is well over 5 sigma.

Actually when a phenomenon is way out of the possible background, even one event is significant beyond the statistics of one. Take the lambda baryon. Even if you see only one, there is not doubt of its existence. A pair production of a proton and a negative pion is not something that can be swept under the rug of statistics (except if it is a measurement error, which is a different story).

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Thank you. But isn't a number of 22 over a zero background almost an infinite number of sigmas? –  Clara Jul 3 '12 at 4:50
Well, the statistical error of 22 is the square root of 22 divided by 22, by construction, and that is the standard deviation. The reason it was not quoted is because it was irrelevant, models were predicting 0 at that part of phase space, and, as I said in the lamda example, statistical estimates are irrelevant and the observation is valid regardless (unless there is a conceptual or systematic or..error). –  anna v Jul 3 '12 at 7:37
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