Analysis of Data Containing Outliers

A strategy for accommodating outlying observations, as well as non-representative, suspect, missing, or otherwise troubling observations, is described. Each unusual observation is decomposed into the sum of two components. One component is the value implied by the trusted observations in the data set. The other component is the unusual part. In this way, the fitting of the data set can then proceed, and, additionally, a numerical value can be ascribed to the unusual part. The method offers not only an antidote for observations with irregular numerical values, which often have the power to contaminate and alter analyses, but also a measure of the magnitudes of the unusual components of those observations. Univariate data and ordered pairs in least-squares fitting are presented as examples.