When comparing the success rates of two groups, statisticians often stratify the data into subgroups of individuals with similar levels of other factors related to the response of interest. In the clinical trial context, one might create subgroups according to the number and strength of risk factors the subjects have, while in the equal employment context, one might form strata based on the type of position and seniority. Sometimes the data are naturally stratified, e.g. applicants for different jobs requiring different skills. However, plaintiffs may pool all the data into one large 2 × 2 table, making it easier to find that the pass rates are statistically significantly different. In contrast, defendants may argue that only when statistical significance is reached in many, e.g. at least one-half of the strata, should a court find that the data supports a prima facie case of discrimination. These issues arose in Kerner v. Denver, a case concerning the disparate impact of a pre-employment exam on minority applicants. The statistical presentations of both parties are reviewed and potential issues with them are noted. After demonstrating that the disparities in pass rates in the various jobs are sufficiently similar, the Mantel–Haenszel test is used to combine the data in each stratum into one overall test. Our analysis shows that there is a statistically significant disparity in the odds minority and majority applicants pass the test. Furthermore, the associated estimator of the common odds ratio of the pass rates is 0.40 indicating that the odds a minority applicant had of passing the test were less than one-half those of a Caucasian.

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