A single outlier in normal samples

Abstract

In view of the central position which the normal distribution occupies in parametric statistics, it is not surprising to find that the question of outliers from normal samples has received both the earliest and the most concentrated study in outlier theory. This chapter will discuss a very particular class of problems — those in which the data are assumed, under the null hypothesis, to be both normal and independent, and identically distributed. A later chapter will relax this assumption of identical distribution by assuming that the data are generated by a homoscedastic general linear model. It will also be assumed that, if the null hypothesis is false, at most a single outlier is present. This assumption will also be relaxed in a later chapter.