The 80% Rule, Part II 

 In my last post, I introduced the so-called 80% rule in employment discrimination cases.  In this post, I discuss some of the reasons why it stinks.  For the sake of illustration, pretend I’m interested in knowing whether a company discriminates against women in hiring, and recall that the 80% rule says that I should see whether the hiring rate for women is less than 80% of the hiring rate for men. 


 The first issue with the 80% rule is that it means different things depending on the hiring rate for men.  Suppose 90% of men that apply for a job are hired.  80% of 90% is 72%, so the difference between men and women is 18%; that might seem like something worth investigating.  But suppose the company at issue is very exclusive, so it only hires 5% of men who apply; 80% of 5% is 4%.  Is this 1% difference something to worry about?  Perhaps it is, perhaps it isn’t, but it sure is different from the 18% difference in the previous example. 

 A second issue with the 80% rule is that it varies depending on whether we’re talking about success rates or failure rates ("success" means getting hired here, "failure" means not getting hired).  In one of my hypotheticals above, a company hired 90% of the men who applied.  So the success rate is 90%, and the failure rate is 10%.  If we apply the 80% rule to the success rate, we should worry if the hiring rate for women is below 72%.  But what happens if we apply the reasoning of the rule to the failure rate for men?  By analogy to the 80% rule’s reasoning, it seems like we should worry if the failure rate for women is greater than, say, 120% (100% + 20%), or perhaps 125% (1/.8 = 1.25), of the failure rate for men.  Take the 125% for the sake of argument, and return to our hypothetical in which the failure rate for men was 10%.  125% of 10% is 12.5%, so we should worry if the failure rate for women is greater than 12.5%.  But a failure rate for women of greater than 12.5% corresponds to a success rate for woment of less than 87.5%, and we just said that we’re supposed to worry if the success rate was less than 72%.  So which is it, 87.5% or 72%? 

 A final criticism (for the purposes of this post; I could go on and on here):  is any of this significant in the statistical sense?  P-values, anyone?  Significance tests?  Posterior intervals?  Anything at all? 

 Next time you hear someone applying the 80% rule in an employment discrimination case, invite the speaker join us on this planet.