Introduction

If we measure the worth of an equation by how many disciplines use it, few can rival the equation for the normal curve. It plays a fundamental role in physics and astronomy as well as in manufacturing, economics, meteorology, medicine, biology, agriculture, sociology, geodesy, anthropology, communications, accounting, education, and psychology. The normal curve suggests a strategy toward a host of applied problems of great importance, and it even influences how many of us view the world in which we live. We have all encountered, for example, the notion that IQ scores follow a normal curve, or that this curve should be used to assign grades in school. The utility of the equation is not in doubt—it provides a useful solution to a wide range of problems. But our understanding of this curve—how it might mislead us in our attempts to model reality—has grown tremendously during the last forty years. As pointed out in hundreds of journal articles, for many applied problems the use of the normal curve can be disastrous. Even under arbitrarily small departures from normality, important discoveries are lost by assuming that observations follow a normal curve. These lost discoveries include both the detection of differences between groups of subjects and important associations among variables of interest. Even if differences are detected, the magnitude of these differences can also be grossly underestimated using a commonly employed strategy based on the normal curve, and the characterization of differences can be highly misleading. Associations among variables can also be grossly misunderstood. Moreover, some commonly recommended methods for dealing with nonnormality have been found to be completely useless. In some cases the normal curve even leads to the wrong answer no matter how many observations we might have.