ESTIMATION OF VARIATION AFTER OUTLIER REJECTION

Outliers are common in many sources of data used for estimation of variation; for example, they are a constant problem in data used to determine the precision of analytical methods. Ordinary analysis of unaltered data is often undesirable because the value of an estimate of variation can be essentially determined by only a few points. This paper shows that outlier rejection followed by an ordinary analysis of the remaining data is not an acceptable method either - when any data are actually rejected, the variance of the remaining points is badly biased down, even when the distribution from which the data are generated is outlier-prone. By comparison, the robust method of Rocke (1983) performs well. Maximum likelihood for mixtures of normals is promising, but requires further development before its use is practical in small samples.