A Statistical mystery resolved

Abstract

Everybody dealing with data will, at one time or another, employ regression analysis. This very unusual case happened during the exploratory phase of the data of a sex-discrimination lawsuit.1 The 32 librarians,16 male and 16 equally qualified female librarians of that government agency, appeared to be ideally suited to initiate discovery of the claimed discrimination in that professional workforce. Simple linear regressions of salary and length of employment, computed separately for the male and the female librarians, was a first approach to reveal the supposed existence and nature of sex-discrimination. Though expecting differences between these two regressions, the author was unprepared to make sense of the women’s regression and incredulous. The fundamental insight gained by resolving this statistical puzzle should be of general interest.