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August 30, 2006


A subject of great interest around the blogs these days is the low number of women clerks hired by Supreme Court justices this year.  It is the subject of a story by Linda Greenhouse in today's New York Times.  (See here)  Apparently, the number of female clerks hired this year fell by half from a year ago.  Out of 37 clerkships for the new term, only 7 are women.  Trying to downplay the significance of this fact, Justices Souter and Breyer, both with a history of hiring many female clerks, attributed the low number to "random variation."  This proposition, of course, is testable.  According to the story in the Times, 37 clerks were hired from a population of applicants that contained approximately 1/3 women.  (This 1/3 number is suspect, since more than half of all graduates today are women.  If the number is higher, then the expected number of clerks would be higher as well -- thus strengthening the basic conclusion I reach below.)  All things being equal, therefore, we would have expected the justices to hire approximately 12 female clerks.  They hired 7.  The question, therefore, is what is the likelihood that this departure from what is expected would happen by "random variation."  According to the Supreme Court's own precedent, Castaneda v. Partida, this can be derived by first determining the standard deviation for this binomial distribution (male/female).  The standard deviation here is the square root of the product of (1) the total size of the group (37), times (2) the percentage of women (1/3), times (3) the pecentage of men (2/3).  A little simple math gives us a standard deviation of 2.86.  The obtained number of women this year, therefore, is almost two standard deviations from the expected number.  According to the Court in Castaneda, "if the expected value and the observed number is greater than two or three standard deviations," chance fluctuations are an extremely unlikely explanation.  Certain caveats must be noted.  First, the sample is small here, which affects how confident we can be in drawing any conclusion.  Also, the departure was less than two standard deviations, so it does not quite meet the arbitrary standard created by the Court.  Finally, while the data suggest that chance is not a good explanation, they cannot tell us what alternative hypotheses might explain the disparity.  So, are Justices Souter and Bryer correct?  Is "random variation" a good explanation for the small number of female clerks?  My answer is, probably not.  But more research would be needed to say what is causing the  disparity observed.  I am sure the Justices will welcome further research on this question.
-- DLF

August 30, 2006 | Permalink


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Tracked on Sep 23, 2006 7:28:28 PM


Can this “test” of the “random variation” hypothesis pass muster under Daubert or Kumho Tire? It relies on a statistical procedure that may have been appropriate in a case like Castaneda, but I wonder if a competent statistician would use it in this situation.

First, are the two Justice saying that (i) the number this year is a random departure from the usual number of female clerks who are hired, or (ii) it is a random depature from the number expected if hiring were gender-blind? The "standard deviation analysis" here is confined to a single year and addresses (ii), not (i) for that year. The Times story indicates that the Justices were speaking of a fluctuation from the usual pattern. In fact, Ms. Greenhouse reported that "In interviews, two of the justices, David H. Souter and Stephen G. Breyer, suggested that the sharp drop in women among the clerkship ranks reflected a random variation in the applicant pool." With no data at all on how the applicant pool may have changed, the entire analysis is not responsive the the Justices' explanation. It addresses randomess in selecting from a given pool of applicants, which has nothing to do with the randomness in the composition of the pool itself.

Second, addressing a different source of variation than the Justices mentioned and looking to this single year in isolation, the analysis pretends that all the clerks were hired by a single Justice. In reality, each sitting Associatiate Justice only gets to hire four clerks, the Chief Justice gets five, and a retired Justice hires only one. The proportion of women applying could vary across Justices. (It might not, but a complete analysis would attend to this possibility.)

Third, the binomial model presupposes that each hire is independent of every other hire and that the probability of selecting a woman is the same for every hire. But how large is the pool of applicants that gets serious scrutiny by each Justice? Does taking one woman out of the pool (by hiring her) reduce the chance of hiring another woman? (This probably is not a serious problem in the analysis, but it deserves some thought.)

Fourth, while the mean and standard deviation of the number of women hired (given the above assumptions) is indeed np and sqrt[np(1-p)], the normal curve with these parameters is a poor approximation to the binomial distribution with parameters p and n when n is small. In Castaneda, n was large. The usual rule of thumb is to use the normal approximation — with a continuity correction (something else that has been overlooked here) — only if np>10 and np(1-p)>10. Here, np(1-p) = 37(1/3)(2/3) = 74/9 < 10.

In light of these unanswered questions and defects in the analysis, it is hard to conclude that “the data suggest that chance is not a good explanation.” Justices Souter and Breyer might be wrong in their surmise, but blindly applying the mathematics used in Castaneda simply fails to establish this. Can anyone provide a statistical assessment of the hypothesis that random variation in the applicant pool or the selection process, even putting points (2) and (3) to the side, that possesses the "intellectual rigor" mentioned in Kumho Tire?

Posted by: DH Kaye | Aug 31, 2006 10:55:03 PM

The issue of clerk selection has arisen before and the %law school grads is not the proper population to compare to. It is who applied & who had federal appelate clerkship experience.

Posted by: tjf | Sep 9, 2006 9:52:22 PM

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