Some of the OFCCP’s decisions on whether a contractor has discriminated in its hiring decision making process are driven by the result of the gross calculation of hiring rates, availabilities, and impact ratio analyses that OFCCP conducts during the Desk Audit review period. Below, using a simple example, I show why gross calculations on aggregate data sometimes provide misleading results and conclusions. I will also discuss how contractors can evaluate and respond to a potentially misleading result.

In probability and statistics, the fact that sometimes a gross calculation may result in a misleading result is a very well known phenomenon called Simpson’s Paradox 1. One of the best practical and real life examples of Simpson’s Paradox occurred in a sex bias case against the University of California, Berkeley in 1973. The gross analysis of graduate admission data t