The Annals of Applied Statistics

The problem of infra-marginality in outcome tests for discrimination

Camelia Simoiu, Sam Corbett-Davies, and Sharad Goel

Full-text: Open access

Abstract

Outcome tests are a popular method for detecting bias in lending, hiring, and policing decisions. These tests operate by comparing the success rate of decisions across groups. For example, if loans made to minority applicants are observed to be repaid more often than loans made to whites, it suggests that only exceptionally qualified minorities are granted loans, indicating discrimination. Outcome tests, however, are known to suffer from the problem of infra-marginality: even absent discrimination, the repayment rates for minority and white loan recipients might differ if the two groups have different risk distributions. Thus, at least in theory, outcome tests can fail to accurately detect discrimination. We develop a new statistical test of discrimination—the threshold test—that mitigates the problem of infra-marginality by jointly estimating decision thresholds and risk distributions. Applying our test to a dataset of 4.5 million police stops in North Carolina, we find that the problem of infra-marginality is more than a theoretical possibility, and can cause the outcome test to yield misleading results in practice.

Article information

Source
Ann. Appl. Stat., Volume 11, Number 3 (2017), 1193-1216.

Dates
Received: January 2017
Revised: April 2017
First available in Project Euclid: 5 October 2017

Permanent link to this document
https://projecteuclid.org/euclid.aoas/1507168827

Digital Object Identifier
doi:10.1214/17-AOAS1058

Mathematical Reviews number (MathSciNet)
MR3709557

Zentralblatt MATH identifier
1380.62270

Keywords
Tests for discrimination outcome test benchmark test infra-marginality traffic stops policing

Citation

Simoiu, Camelia; Corbett-Davies, Sam; Goel, Sharad. The problem of infra-marginality in outcome tests for discrimination. Ann. Appl. Stat. 11 (2017), no. 3, 1193--1216. doi:10.1214/17-AOAS1058. https://projecteuclid.org/euclid.aoas/1507168827


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