Everyone was excited when the Higgs boson results were reported on July 4, 2012 indicating evidence for a Higgs-like particle based on a “5 sigma observed effect”. The observed effect refers to the number of excess events of a given type that are “observed” in comparison to the number (or proportion) that would be expected from background alone, and not due to a Higgs particle. This continues my earlier post. This, too, is a rough outsider’s angle on one small aspect of the statistical inferences involved. (Doubtless there will be corrections.) But that, apart from being fascinated by it, is precisely why I have chosen to discuss it: we should be able to employ a general philosophy of inference to get an understanding of what is true about the controversial concepts we purport to illuminate, e.g., significance levels.
Following an official report from ATLAS, researchers define a “global signal strength” parameter “such that μ = 0 corresponds to the background only hypothesis and μ = 1 corresponds to the SM Higgs boson signal in addition to the background” (where SM is the Standard Model). The statistical test may be framed as a one-sided test, where the test statistic (which is actually a ratio) records differences in the positive direction, in standard deviation (sigma) units. Reports such as: Read more
