# What do “local” and “global” mean when talking about standard deviations in experimental particle physics?

I found the following sentence:

The excess is most compatible with a SM Higgs hypothesis in the vicinity of 124 GeV and below, but the statistical significance (2.6σ local and 1.9σ global after correcting for the LEE in the low mass region) is not large enough to say anything conclusive.

I am familiar with sigma, but not familiar with local and global. What do they mean?

## 2 Answers

The local significance in $\sigma$ is the deviation from the expectation divided by the standard deviation. This is what jumps at you when looking at a plot and the data doesn't match up with the expectation.

The global significance takes into account that you're looking at a whole range of places for such a deviation. The probability that you see such a deviation at any mass in the range you're looking (115-600 GeV or so) is larger than the probability to see it at just one place. This is called the Look-Elsewhere effect, as you quoted.

So to sum up global means over the entire mass range and local in this context means at the specific mass where the deviation was observed.

For a detailed explanation look at Dorigo's blog here: http://www.science20.com/quantum_diaries_survivor/inverse_lookelsewhere_effect-75341

The "local" means the garden variety of computing standard deviations, i.e.statistical, from the number of events in the resonance peak, plus systematic error, which is now added in quadrature.

"Global" is a way of trying to estimate the Look Elsewhere Effect ( LEE). The words say it, when one is scanning a large phase space for something unusual it is not only the statistics of the specific mass region where a fluctuation has been observed that gives the significance but possibly the statistics of the whole region where one has been blindly searching.

If the higgs really exists at a specific mass then necessarily once enough statistics is accumulated there, there should be the given local significance. Since one does not know if and where the higgs is, it is inevitable that a statistical fluctuation might simulate a real signal, if one looks elsewhere in enough phase space.