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A “sharp drop in women” among the ranks of Supreme Court law clerks has become front-page news. It has been reported that only seven of the 37 law clerks hired this year were women (19%, compared with 16 out of 43 from the previous year, or 37%)-a decline of nearly 50%. These numbers have caused much consternation. Former Justice Sandra Day O’Connor expressed her “surprise,” and Justice Ruth Bader Ginsburg signaled her disappointment. One former clerk and law professor cited seven out of 37 as proof of the justices’ “insidious and pervasive unconscious discrimination.” Discrimination might explain why women do not constitute a larger share of the clerks, but it is hard to imagine that those justices who used to hire women but did not this year suddenly turned against women. The dramatic change calls for some other explanation. Justices David H. Souter and Stephen G. Breyer speculated that the drop reflects “a random variation in the applicant pool.” If we accept this statement as accurate-the court releases no official statistics on the applicants-then the change is explained. But let us assume that they are mistaken, and that the fraction of applicants who are women is identical from year to year. Some “random variation” still could be at work here. After all, who gets hired in a pool of immensely talented young men and women is inevitably somewhat arbitrary. Even if every prodigy has precisely the same chance of being hired, there will be some fluctuations Thus, statisticians would ask whether the change is “statistically significant.” Is it outside the range that would be expected if the justices’ hiring decisions are independent of the gender of the aspiring clerks? When attention is restricted to this one year’s change, it is on the borderline for significance, but when this year is viewed as but one of many opportunities for a sudden drop to occur at random, the change is not significant. A standard statistical test reveals that the probability of seeing a change from last year as large or even larger than this one is about 8.6%-this when the probability of a woman being hired actually is the same as that for a man. In most social science and biomedical research, such a difference is not regarded as statistically significant, although it is near the conventional borderline of 5%. It is some evidence that the justices are influenced by gender (or something correlated with gender) but hardly a slam-dunk case. We could lower the 8.6% figure and reach a significant result by comparing this year’s class of clerks not just to last year’s, but to those from the preceding six years. The chance that the proportion this year would be as low or lower if the proportion of women in the pool were constant and if men and women applying for the positions are equally qualified, then becomes 4%. It is tempting to infer that either the pool changed or that selection was not always independent of gender since the 2000-2001 term. There is a catch, however. People look at these figures every year. Sooner or later, a single year will exhibit a big drop even when the fluctuations are entirely random. The drop this year is thus much less surprising than has been assumed. This is the first year in the last six that a significant finding has been observed. The probability of one such aberrant year when six years are studied is closer to 30% than to the borderline of 5%. This year’s drop may just be random after all. In making this point, we are not arguing that the number of women clerks is comfortingly large. Neither do we assert that the statistics disprove the complaints of discrimination. We lack the necessary data on the applicant pool and the annual outcomes of the “clerkship lottery” to take sides. We can say, however, that for all the raised eyebrows, the numbers are not so dramatic as to establish that this year’s decline is anything other than the “random variation” asserted by Souter and Breyer. David H. Kaye is a professor at Arizona State University Sandra Day O’Connor College of Law. Joseph L. Gastwirth is a professor at George Washington University in the Department of Statistics.

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