One-Sided T2 Test for Assessing the Need for an Affirmative Action Plan: A Reanalysis of Shea v. Kerry

• Activity Number: 34 - Social Justice and Statistical Science
• Type: Invited
• Date/Time: Sunday, August 8, 2021 : 3:30 PM to 5:20 PM
• Sponsor: Statistics and Public Policy
• Author(s): Qing Pan* and Joseph L. Gastwirth and Weiwen Miao
• Companies: George Washington University and George Washington University and Haverford University
• Keywords: Affirmative Action plan; Employment discrimination; Under-representation of minority groups; One-sided Hotelling’s T2 test; Mixed Chi-square distribution; Required sample size

Abstract

In the 1980's, GAO reports presented statistical evidence showing that employees in the Foreign Service were overwhelmingly White male, especially in the higher positions. 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. This paper 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. Second, 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< .0001 indicating that minorities were substantially under-represented. Excluding secretarial and clerical jobs led to even larger disparities.