INTRODUCTION

The topic of this text is the problem of testing whether a sample of observations comes from a normal distribution. Normality is one of the most common assumptions made in the development and use of statistical procedures. The problem has not suffered from lack of attention. In our review of the literature we found more tests than we ever imagined existed. This text, for instance, considers about forty formal testing procedures that have been proposed to test specifically for normality, as well as plotting methods, outlier tests, general goodness of fit tests and other tests that are useful in detecting non-normality in specialized situations. Further, the list is probably not exhaustive. For example, while the sample moment skewness and kurtosis statistics are commonly used as tests of normality, many such moment tests could be considered (Chapter 3). Geary (1947)

2 Chap. 1

considered the larger class of absolute moment tests and developed quite general results concerning their power. Thode (1985) used Geary's calculations to further refine the evaluation of these absolute moment tests and found that some of these tests had modestly better power under certain circumstances than the kurtosis test or Geary's test.