James P. Scanlan, Attorney at Law

(October 16, 2009)

The Measuring Health Disparities page (MHD) and the Scanlan’s Rule page of this site discuss the statistical pattern whereby the rarer the outcome the greater tends to be the relative difference in experiencing it and the smaller tends to be the relative difference in avoiding it, as well as the way the failure to understand this pattern has led to the misinterpretations of data on group differences in the law the social and medical sciences.  Those pages and the materials they reference also explain why no standard measure of group differences in outcome rates can effectively indicate meaningful differences in susceptibilities to an outcome because all such measures are affected by the overall prevalence of an outcome.  The Solutions sub-page of MHD describes an approach for appraising the size of group differences in susceptibilities to an outcome that is unaffected by the overall prevalence of the outcome and the Solutions Database sub-page provides a downloadable database with which to implement that approach.  To apply the approach, however, it is necessary to know the actual rates of the affected groups, not simply the rate ratios.   Section A.6 of the Scanlan’s Rule page and Issue 3 of the Case Study sub-page of MHD address this issue with regard to the efforts to appraise the size of group differences when all that is known is each group’s representation among those potentially experiencing some outcome and among those actually experiencing the outcome.  These pages or their references explain that, while the information just mentioned will allow one to calculate relative differences or rate ratios, such information is insufficient to effectively appraise the size of the differences in the settings being compared.

In light of the above, consider attention given in October 2009 to the Palm Center’s release of figures showing that women comprised higher proportions of persons  discharged from military service for violation of sexual orientation policies than they comprised of persons subject to such policies.  The information below is from an October 9, 2009 Associated Press article by Lisa Leff styled “Women More Likely to be Expelled under ‘Don’t Ask.’”  The article provided, for all services combined and for each branch, the female representation of personnel and the female representation of those discharged for violation of the “don’t ask – don’t tell” policy in 2008.  The article highlighted as particularly striking the disparity in the Air Force, where women comprised 20 percent of personnel but 61 percent of those discharged, which was contrasted with overall figures showing that women comprised 15 percent of all military personnel but more than a third of those terminated.  The table below shows the figures provided in the article (using 33.3% for the overall female representation among those terminated) along with the calculated ratio of the female termination rate to the male termination rate.[i]    

The rate ratio is highest in the Air Force by a considerable margin.  But without the underlying rates, it is impossible to determine whether, or the extent to which, the high Air Force figure is a function of more lenient application of the discharge policy in the Air Force.  Compare this issue with the discussion in Race and Mortality (Society 2000) and When Statistics Lie (Legal Times 1996) of the way that lenders most responsive to pressures to relax lending criteria because of the disparate impact of those criteria on minorities tend to show especially large relative differences in mortgage rejection rates, or the discussion in Getting it Straight When Statistics Can Lie (Legal Times1993) of the way that policies that reduce overall termination rates tend to increase relative differences in termination rates.  

The Leff article also noted that the female representation among those terminated increased from 36 percent in 2006 to 49 percent in 2007.  Unless there was decline in the female representation of those terminated in 2008 (something that seems inconsistent with the discussion in the article), these figures seem inconsistent with the overall female representation (“more than a third”) in 2008.  In any case, however, an important corollary to the statistical pattern described at the outset is that the rarer an outcome the greater will tend to be the proportion that the more susceptible group comprises of those experiencing the outcome.  See Sections A.5, B.1, and B.2 of the Scanlan’s Rule page and the discussion of the feminization of poverty in Race and Mortality.  Thus, if the policy was being applied more leniently in 2007 than 2006, one would expect the female representation among those terminated to increase.  And, if  the female representation among those terminated in fact declined in 2008, such decline would be consistent with a less lenient application in 2008 than 2007.  Again, however, one needs to see the underlying figures to make an informed appraisal of these patterns.

The above discussion applies regardless of whether the greater likelihood of female discharges arises from (a) greater rates of violations of the policy by female personnel or (b) biased application of the policy.  But it does not consider the extent to which (a) and (b) may vary across services.  In any case, in order to determine in which service the gender difference is largest in a meaningful sense, as, say, a basis for further investigation of (a) or (b), it would be necessary to know the underlying rates.