Nonparametric tests in small unbalanced samples: Application in employment-discrimination cases

Abstract

Unbalanced-size samples arise naturally in equal-employment cases, as the minority fraction of all employees or applicants are invariably less than one half. Motivated by an actual case in which the median test with no power to detect disparate treatment was accepted in court, we develop a symmetrized form of the control median test having the same asymptotic properties as the median test. Since the actual case concerned the relative merits of the median and Wilcoxon test, a Monte Carlo study of the power of the new test and other nonparametric tests is reported. The results show that the new procedure is more powerful than the ordinary median test in small unbalanced samples. When the data come from a normal or double-exponential law, the Wilcoxon test is however usually superior to either of the others. When the data come from a Cauchy distribution, on the other hand, the powers of the procedures typically are reversed.

Statistical Reasoning in the Legal Setting

“…The trial judge accepted the median test even though the defendant's expert admitted under cross-examination that the median test would not "find discrimination" if the difference in time to promotion were a million years. Because this data has been discussed by Hollander and Proschan (1979), Gastwirth and Wang (1987), and Finkelstein and Levin (1990), we will not reproduce it here. Another point, however, is worth noting.…”

“…Although the Supreme Court will not review the case, the A/S ratio studies (Behrens 1977, Gastwirth 1982 conducted in the past by the Census Bureau would have clarified matters. The latest data (1982) for Cook County showed a median A/S ratio of 19.4%.…”

“…Because workers who accept benefits under special compensation laws often forego the right to sue for larger amounts, and as these laws are of a humanitarian nature [see O'Keefe v. Smith Associates (1965) at 3621, the amount of evidence required to show "causation" is less than in a tort case. As several worker compensation cases are discussed elsewhere (Gastwirth 1988, sec. 14.2), we just note that epidemiologic data showing that a condition at work, usually exposure to a chemical, increased one's chances of contracting the disease is sufficient to establish a worker's eligibility for compensation.…”

“…46, N o . I tained by word of mouth from a virtually all majority work force), a comparison group is constructed using Census data on persons residing in the labor market area who possess the skills required for the position [see Gastwirth (1981) and Baldus and Cole (1987) for further discussion]. Data on all employees includes those hired before the legally relevant time frame, fails to incorporate the fact that firemen must have at least a year's experience to be eligible for promotion, and confounds the hiring and promotion issues and ignores the voluntary quits.…”

Wage Discrimination Measurement: In Defense of a Simple but Informative Statistical Tool

“…Indeed, the total hours of work for white woman is about 15 percent less of total amount for men. 16 Table A2 looks at occupation di¤erences by gender. We distinguish three occupational categories that regroupe those of 2000 Census of Population and Housing: managers and professionals (executive, administrators, and managers; professional specialties); white collars (technical, sales, clerical workers, precision production, craft, and repair workers); blue collars (operators, fabricators, laborers, and service workers).…”