Rejection of Outliers

If one reading is a long way from the rest in a series of replicate determinations, or if in a least-squares analysis one reading is found to have a much greater residual than the others, there is temptation to reject it as spurious. Numerous criteria for the rejection of outliers have been proposed and discussed during the past 100 years. They seem always to have been regarded as something like significance tests, and attention has been focussed on rejection rates. It is suggested that rejection rules are not significance tests but insurance policies, and attention would be better focussed on error variance. A detailed study is made of the effect of routine application of rejection criteria to replicate determinations of a single value. Determinations in triplicate and quadruplicate are especially considered. Complex patterns of observations are also considered, especially factorial arrangements with high symmetry, and there is a study of the correlations between residuals. Attention is focussed mainly on rejection rules appropriate when the population variance is known, but some consideration is also given to Studentieed rules.