Evaluating Disparate (Adverse) Impact Using Z-Difference-Test & Z-Impact-Ratio-Test in R

This tutorial demonstrates how to evaluate whether their is prima facie evidence of disparate impact (adverse impact) by using the Z-test (i.e., Z-difference-test, "2 standard deviation rule") and the Z-impact-ratio-test. For the Z-impact-ratio_test, I also demonstrate how to compute a 95% confidence interval on the same scale/metric as the impact ratio using the formulas presented by Morris and Lobsenz (2000), which provides a more direct glimpse into the sampling error and a better indication of the precision of our estimated impact ratio.
Other approaches for evaluating disparate impact that are not covered in this tutorial include the 4/5ths Rule, chi-square test of independence (with and without Yates continuity correction), and the Fisher exact test, and these are covered in the following tutorial: • Evaluating Disparate A... .
When sample sizes are small, selection ratios are low, and/or there is a small proportion of individuals from the focal group, then a one-tailed Z_IR test may help to avoid false negatives (Morris, 2001; Morris & Lobsenz, 2000). Given that the 4/5ths Rule has a tendency to result in large proportion of false positives (even in large samples), it is advisable to pair the 4/5ths test with a statistical test like the chi-square test of independence, Fisher exact test, or the Z_IR test (Roth, Bobko, & Switzer, 2006).
The following topics appear at the timestamps noted in brackets: (a) a list of recommended readings and their references [0:27]; (b) Z-difference-test (Z-test-test; "two standard deviations rule") [7:15]; Z-impact-ratio-test [43:02]; and constructing confidence interval around impact ratio [53:56].
If you would like to learn how to visualize evidence (or the lack thereof) of disparate (adverse) impact, check out this video: • Visualizing Disparate ... .
Other videos from my "R Tutorials" playlist can be found here: • R Tutorials .
The data file(s) referenced in this R tutorial (and other R tutorials on this playlist) can be downloaded as a compressed (zipped) folder by visiting the following link: github.com/dav.... Click "Clone or Download" followed by "Download ZIP".