3 ms·
The issue lies in the way the signal was actually measured. The first observation was in the digamma decay channel, where it basically amounted to an excess pho
by sigmoid10 4y ago
The issue lies in the way the signal was actually measured. The first observation was in the digamma decay channel, where it basically amounted to an excess photon count over the background at a specific energy (i.e. invariant mass). So the idea of a simple "null" hypothesis was not really well defined here, because the excess could have also been at other energies. But the five sigma value was given only for the bump over background at ~125 GeV. In that specific sense, Krauss' statement is very much correct, but the overall hypothesis of whether H0 exists - yes or no - given arbitrary data is a bit more complicated when doing the statistics rigorously. That's also why you really want 5 sigmas, because as you widen the parameter space you're searching in, even 3 sigma results (= less than half a percent chance of statistical error) at specific energies regularly turn out to be flukes.
- ncmncm 4y agoI seem to recall that they didn't declare victory until it hit 6 sigma. It always tickles me that a hedge fund is called Two Sigma. Who would want that on their CV?
- d0mine 4y agoFor reference, 6 sigma is one-in-a-billion case (one-tail): print(f"{1 - statistics.NormalDist().cdf(6):.1g}") # 1e-09 and 2 sigma is two-in-a-hundred (~2%). ~5% for two-tail case.
- evanb 4y agoFor those curious, this is often described as the look-elsewhere effect. https://en.wikipedia.org/wiki/Look-elsewhere_effect https://en.wikipedia.org/wiki/Look-elsewhere_effect