If, in a series of measurements, some estimates of the parameter of interest (e.g. a cross-section) are significantly different from the average, is it sensible to exclude them?
When an experiment makes several/many measurements xi ± ei of some quantity, the distribution of (xi – xtrue)/ei should be normally distributed with mean zero and unit variance. Similarly yi = (xi – xmean)/ei should be normal with variance (N-1)/N (for the case of all ei equal). Thus large |yi| are unlikely, and it may well be a good idea to reject them. It is even more sensible to try to establish why these measurements gave anomalous values, because it may conceal a more important problem which is affecting the other measurements. We recommend that this be done (even though it is an a posteriori procedure), with the realisation that it could result in the rejection of other measurements which gave `acceptable’ yi. The rejection of outliers is also used for distributions which are known to have (genuine) long tails, where the measurements in the tails are not incorrect. For example, the rate of energy loss (dE/dx) of a charged particle as it passes through a detector follows the Landa
