Statistical Procedures for Assessing the Need for an Affirmative Action Plan: A Reanalysis of Shea v. Kerry

Abstract In the 1980s, reports from Congress and the Government Accountability Office (GAO) presented statistical evidence showing that employees in the Foreign Service were overwhelmingly White male, especially in the higher positions. To remedy this historical discrimination, the State Department instituted an affirmative action plan during 1990–1992 that allowed females and race-ethnic minorities to apply directly for mid-level positions. A White male employee claimed that he had been disadvantaged by the plan. The appellate court unanimously held that the manifest statistical imbalance supported the Department’s instituting the plan. One judge identified two statistical issues in the analysis of the data that neither party brought up. This article provides an empirical guideline for sample size and a one-sided Hotelling’s T2 test to answer these problems. First, an approximate rule is developed for the minimum number of expected minority appointments needed for a meaningful statistical analysis of under-representation. To avoid the multiple comparison issue when several protected groups are involved, a modification of Hotelling’s T2 test is developed for testing the null hypothesis of fair representation against a one-sided alternative of under-representation in at least one minority group. The test yields p-values less than 1 in 10,000 indicating that minorities were substantially under-represented. Excluding secretarial and clerical jobs led to even larger disparities. Supplemental materials for this article are available online.