Part X

Tests on Outliers

Outliers are a phenomenon which inevitably occurs in the analysis of statistical data. Although there is no generally accepted unique definition of the term outlier they are commonly understood as observations which somehow do not fit into the data set. In Barnett and Lewis (1994, p. 7) we read ‘We shall define an outlier in a set of data to be an observation (or subset of observations) which appears to be inconsistent with the remainder of that set of data’. The same authors further proceed by putting emphasis on the fact that outliers are to be described as observations which are extreme as well as surprising for the observer. Whether an extreme value should be declared as an outlier depends on what we think about the main population from which we sample. Here a distinction has to be made from contaminants in the sense of observations originating from some other population, which might or might not be extreme with respect to the remaining observations and hence may or may not be outliers. How we generally decide to deal with the question of handling outliers is beyond the scope of this book, whether it is better to accommodate them by using robust methods, to detect them as they are of interest in themselves or just an undue influence on the applied analysis. Here we just present some well known discordancy tests from the toolkit of statistical methods to handle outliers. In tests of discordancy we aim at a decision on whether or not an extreme observation is to be seen as belonging to the main population or not. The main population is usually characterized by assuming some statistical distribution, which defines the null hypothesis. This assumption is sufficient to set up a statistical test. However, the choice of a reasonable test statistic as well as the assurance of desirable properties of the test depends on the existence of a meaningful alternative model. Often such models are formulated as an outlier-generating model (Barnett and Lewis 1994, p. 43).