Law, Probability and Risk Advance Access originally published online on July 6, 2009
Law, Probability and Risk 2009 8(2):171-191; doi:10.1093/lpr/mgp017
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© The Author [2009]. Published by Oxford University Press. All rights reserved.
Formal statistical analysis of the data in disparate impact cases provides sounder inferences than the U. S. government's ‘four-fifths’ rule: an examination of the statistical evidence in Ricci v. DeStefano
Department of Statistics, George Washington University, Washington, DC 20052, USA
Department of Mathematics, Haverford College, Haverford, PA 19041, USA
* Email: jlgast{at}gwu.edu
Received on 24 April 2009. Revised on 22 May 2009. Accepted on 4 June 2009.
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Abstract |
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Many countries have fair employment laws to protect racial, gender, religious or ethnic minorities from discrimination and courts in the USA can order remedies such as one out of every three new hires should be a member of a protected group after finding an employer discriminated. What steps can an employer undertake to ensure its employment practices do not disadvantage minorities when it does not need to comply with a court order? This issue arose in Ricci v. DeStefano, a ‘reverse discrimination’ case under review by the U.S. Supreme Court. Seventeen Whites and 1 Hispanic who achieved sufficiently high scores qualifying them for promotion to lieutenant or captain of the New Haven Fire Department sued the city because it cancelled the examinations after seeing that no African American could be appointed to an existing vacancy. The City of New Haven justified its action on the basis that both examinations had a disparate impact on African Americans and Hispanics because the ratios of their pass rates to that of Whites were less than 80%, contrary to a ‘rule of thumb’ in the government's Uniform Guidelines. The city did not conduct statistical tests, which are referred to in the guidelines.
The lower courts accepted New Haven's explanation and granted summary judgement to it. A statistical study of the various criteria considered by the city and lower courts in their review of the data demonstrates that nearly 70% of the time a fair non-discriminatory test for either position will fail the government's ‘80% rule’ and at least 60% of the time both fair tests would fail this ‘four-fifths rule’. Since the city created a new criterion after seeing the results, it is difficult to formulate precisely the other ‘rare’ or ‘unusual’ outcomes that would lead to cancellation of the examination. Would New Haven reject a list with no Hispanics or no Whites eligible for an immediate promotion? Would it require that all three groups be represented in the pool eligible for advancement to each position? From the viewpoint of statistical theory, the hypothesis being tested and the definition of pass or selection rates that will be compared should be decided before examining the data. Formal statistical tests on several relevant pass rates show that the lieutenant examination had a disparate impact on minority applicants, but the differences in the pass rates on the captain examination were not close to statistical significance. Furthermore, when the city cancelled both examinations, it only focused on the demographic mix of the high scorers who could receive an immediate promotion and ignored the 2-year life cycle of the list. Neither likely retirements nor job turnover during the 2-year life cycle of the results were considered. If this had been done, the city might have realized that three African Americans were likely to be appointed lieutenants along with two Hispanic captains.
Keywords: disparate impact; equal employment; ‘four-fifths’; rule; numerical disparity; reverse discrimination; tests of statistical significance