We all know by now that CERN announced the discovery of the long-sought Higgs particle (or the so called God particle) last Wednesday. This is a discovery about nothing – that is it describes what is occurring in the vacuum. This achievement is huge considering it culminates literally decades of effort by thousands of physicists and engineers spending billions of euros to build the Large Hadron Collider. But the media’s reporting of 5-sigma as a measure of “certainty” was also remarkable.
First the vacuum - A vacuum is a space entirely devoid of matter and so represents a least possible energy state. Peter Higgs, and others realized that the state with least energy needn’t be empty - it can instead be filled with a physical quantity that slows down [electron] and gives mass to everything we know.
As mentioned some media outlets associated 5-sigma as a measure of certainty for the discovery of the Higgs boson. The gold standard for a discovery is a "5-sigma" bump, where sigma is a measure of bumpiness or standard deviation. A bump that high means that the odds are less than 1 in 3.5 million that it was produced by chance.
For instance, the science editor at the Swedish news paper Dagens Nyheter reported that a sigma of 4.9 equals a certainty of 99.99994%, which obviously isn’t true, simply because p(D|H0 ) is not the same as p(H0|D) meaning p-value represents the conditional probability of getting the data given that the null hypothesis is true. Nothing more, and it surely doesn’t give the probability for the alternative hypothesis being true, Ala the “certainty” that something has been found that’s not a random fluctuation.