History Jobs and Statistics

Over at Inside Higher Ed, they’ve posted a report on the job market in history, which finds that there are more jobs than new Ph.D.’s, but that American and European history are overrepresented in the candidate pool, relative to the number of jobs. It also includes this comment about the number of degreees awarded to women:

The decline for women — to 40.9 percent from 41.6 percent — is the third decline in the last 10 years, and comes a time that a majority of Ph.D.’s in the humanities are being awarded to women.

The other two declines, from their handy table, were from 40.3% to 40.0% in 2001-2, and from 39.6% to 38.3% in 1999-2000.

So, is this decline a sign of the regressiveness of history as a discipline? Actually, I don’t even think it’s a decline.

Well, OK, it’s a real decline in their sample, but I doubt very much that it’s at all significant. Look at it this way: the total number of Ph.D.’s awarded is somewhere in the neighborhood of 1000 (940 this past year, which was a “slight dip from the previous year”). If you assume that the relative numbers of men and women were completely random, you would expect a year-to-year fluctuation of something like the square root of the numbe rof people i the sample, and the square root of 1000 is about 31.

So, for a random distribution, you would expect the relative numbers of men and women to fluctuate by about 3%. Which means that an 0.7% drop in the number of degrees awarded to women is, well, pretty meaningless.

And, in fact, if you look at their table of data for the last ten years, what you see looks a lot like random fluctuations about a slowly increasing average. There are six increases in the fraction of degrees to women, and only three decreases (though the sample is way too small for that to be meaninful), and the average change is an increase of 0.4% per year. The worst you could say would be that the percentage has more or less leveled off.

But that doesn’t make much of a hook to get people interested in the data, so an insignificant fluctuation is cited as a decrease. And, presumably, the 1.4% increase a couple of years ago would be touted as a great step forward.

(Please note (this means you, “Uncle Al”) that this is not an argument about the actual distribution of the degrees. I’m really not interested in what the fraction “ought” to be, or whether it’s something we should care about at all. I’m just commenting on the slightly dodgy statistics, here.)