Look-elsewhere effect

The look-elsewhere effect is a phenomenon in the statistical analysis of scientific experiments, particularly in complex particle physics experiments, where an apparently statistically significant observation may have actually arisen by chance because of the size of the parameter space to be searched.

Once the possibility of look-elsewhere error in an analysis is acknowledged, it can be compensated for by careful application of standard mathematical techniques.

More generally known in statistics as the problem of multiple comparisons, the term gained some media attention in 2011, in the context of the search for the Higgs boson at the Large Hadron Collider.

Many statistical tests deliver a p-value, the probability that a given result could be obtained, assuming random coincidence. When asking “does X affect Y?”, it is common to vary X and see if there is significant variation in Y as a result. If this p-value is less than some predetermined statistical significance threshold α, one considers the result "significant".

However, if one is performing multiple tests (“looking elsewhere” if the first test fails) then obviously a p value of 1/n is likely to occur after n tests. For example, an event with p < 0.05 will probably be seen after 20 tests, even if there is no effect whatsoever. In order to compensate for this, you must divide your threshold α by the number of tests n, so a result is significant when p < α/n. Or, equivalently, multiply the observed p value by the number of tests (significant when np < α).

This is a simplified case; the number n is actually the number of degrees of freedom in the tests, or the number of effectively independent tests. If they are not fully independent, the number may be lower than the number of tests.

The look-elsewhere effect is a frequent cause of "significance inflation" when the number of independent tests n is underestimated because failed tests are not published. One paper may fail to mention alternative hypotheses considered, or a paper producing no result may simply not be published at all, leading to journals dominated by statistical outliers.

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