The Normal Curve and Outlier Detection

Abstract

No doubt the reader is well aware that the normal curve plays an integral role in applied research. Properties of this curve, that are routinely described in every introductory statistics course, make it extremely important and useful. Yet, in recent years, it has become clear that this curve can be a potential source for misleading and even erroneous conclusions in our quest to under- stand data. This chapter summarizes some basic properties of the normal curve that play an integral role in conventional inferential methods. But this chapter also lays the groundwork for understanding how the normal curve can mislead. A specific example covered here is how the normal curve suggests a frequently employed method for detecting outliers that can be highly misleading in a variety of commonly occurring situations. This chapter also describes the central limit theorem, which is frequently invoked in an attempt to deal with nonnormal probability curves. Often the central limit theorem is taken to imply that with about 25 observations, practical problems due to nonnormality become negligible. There are several reasons why this view is erroneous, one of which is given here. The illustrations in this chapter provide a glimpse of additional problems to be covered.