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Statistical Lessons of Ricci v. De Stefano
The first part of this article about the Supreme Court's ruling Ricci v. De Stefano discussed what statisticians really have to say about disparate impact. The conclusion herein addresses the results of, and lessons to be learned from, the Ricci case. But first a quick review: The City of New Haven, CT, hired a company to develop a promotional test for firefighters. The lieutenant's test was given to 43 white firefighters and 19 black firefighters, producing the following results: 25 whites passed (58%) and six blacks passed (32%). The New Haven procedure for promotion involved a second phase and the results of that phase meant that 10 whites (40% of those passing the test) and no blacks (0%) would actually receive promotions. The City was sued.
A Quick Look at the Ricci Results
Suppose we make the common assumption that all lieutenant candidates, black and white, were equally well qualified. When we calculate the probabilities under the Fisher Exact Test, the results may be somewhat surprising. First, the probability that, given entirely equal ex ante qualification, results equally unusual or more unusual than 25 of the 31 passing scores coming from white candidates would be expected 10% of the time. This is substantially in excess of the standard statistical rule of thumb and thus is not “statistically significant” as that term is normally used. It is important to note that that does not mean the disparity is not legally meaningful, but a result such as this would not normally pass muster in a refereed journal as a reliable index of statistical inference.
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