Judge Alito & Statistics 

 Social science statistics is everywhere.  So is law.  And both are tangled up with each other.  I was forcefully reminded of these facts when my wife pointed out an  article on Salon.com  about an  opinion Samuel Alito (as of yesterday, a nominee to the Supreme Court) wrote  while a judge on the United States Court of Appeals for the Third Circuit in a case called Riley v. Taylor.  The facts of the specific case, which concerned the potential use of race in preemptory challenges in a death penalty trial, are less important than Judge Alito's approach to statistics and the burden of proof. 

 Schematically, the facts of the case follow this pattern:  Party A has the burden of proof on an issue concerning race.  Party A produces some numbers that look funny, meaning  instinctively unlikely in a race-neutral world, but conducts no significance test or other formal statistical analysis.  The opposing side, Party B, doesn't respond at all, or if it does respond, it simply points out that a million different factors could explain the funny-looking numbers.  Party B does not attempt to show that such innocent factors actually do explain the observed numbers, just that they could, and that Party A has failed to eliminate all such alternative explanations. 

 Such cases occur over and over again in cases involving employment discrimination, housing discrimination, preemptory challenges, and racial profiling, just to name a few.  When discussing them, judges inevitably lament the fact that one side or the other did not conduct a multiple regression analysis, as if that technique would provide all the answers (Judge Alito's Riley opinion is no exception here). 

 The point is, of course, that how a judge views such cases has almost nothing to do with the facts at bar and everything to do with a judge's priors on the role of race in modern society.  For judges who believe that race has little relevance in the thought processes of modern decision makers (employers, landlords, prosecutors, cops), Party A in the above situation must eliminate all potential explanatory factors via (alas) multiple regression in order to meet its burden of production.  For judges who believe that race still matters, Party B must respond in the above situation or lose the case.  Judge Alito's Riley opinion demonstrates where he stands here. 

 Is there a middle way?  Perhaps.  In the above situation, what about requiring some sort of significance test from Party A, but not one that eliminates alternative explanations?  In the specific facts of Riley, the number-crunching necessary for "some sort of significance test" is the statistical equivalent of riding a tricycle:  a two-by-two hypergeometric with row totals of 71 whites and 8 blacks, column totals of 31 strikes and 48 non-strikes, and an observed value of 8 black strikes yields a p-value of 0.