Statistical Hypothesis Testing with SAS and R

Chapter 15

Tests on outliers

In this chapter we present so-called discordancy tests (Barnett and Lewis 1994) for univariate samples. We consider outlier situations, where the basic sample follows some null distribution with a continuous distribution function. The general alternative hypothesis of this kind of test is that one (or more) observations are sampled from a different, maybe just shifted, distribution. Considering the ordered sample determines the extremes. Whether or not they are judged as outliers depends on their relation to the assumed null model. It is therefore common to use some spread/range test statistics which compare the extreme values with the center of the dataset or other extreme. In the tests introduced in this chapter the question usually is, if the lowest and/or highest value of the ordered sample is an outlier. However, if for instance the second highest value is an extreme as well a test might not detect the outlier as this value is masked by the other outlier. Most tests are prone to masking, which needs to be kept in mind. In Section 15.1 the null distribution is assumed to be a Gaussian distribution and in the Section 15.2 we deal with exponential and uniform distributions.

15.1 Outliers tests for Gaussian null distribution

In this section the assumed null distribution for the main population is the Gaussian distribution with unknown parameters. Most of the discussed tests can also be formulated for known parameters; please refer to Barnett and Lewis ...