Mostly Male Meetings: what are the odds?

A story in the Atlantic talks about an ongoing problem in science (and tech, and science fiction): the large number of conferences where nearly all the high-profile speaking slots go to men.  This isn’t news, even to their readers; there was a story in the Atlantic two and a half years ago on the same point. You don’t see this to quite the same extent in statistics, but at least part of that is because we don’t do as many conferences with a lot of high-profile speaking slots. We tend to let everyone speak.

When this is raised, one of the main negative response (of the ones people are prepared to put their names to), has been that this is chance. That’s what the piece in the Atlantic talks about.

Working with a “conservative” assumption that 24 percent of Ph.D.s in mathematics have been granted to women over the last 25 years, he finds that it’s statistically impossible that a speakers’ lineup including one woman and 19 men could be random.

The  probability of getting 0 or 1 women in a random sample of 20 people from a population with 24% women is 3%.  You could argue that the speakers are likely to be academics, and will tend to be more senior and increase the probability a bit, but the story’s figure of “less than 5%” is not an outlandish estimate — especially as mathematicians make a point of claiming they do their best work young.

On the other hand, 5% (or 3%) isn’t that small a number. It certainly isn’t “statistically impossible” as in the quote or “astronomically small” as in the story’s headline. Considering this conference in isolation the evidence of bias would be positive, but hardly overwhelming.

The statistical aspect of this problem is a bit like the statistical aspect of the Bechdel test for movies (two female characters; who talk to each other; not only about a man). You’d expect some movies to fail the Bechdel test. Some movies should fail the Bechdel test. What’s notable is that about half of all movies do.

You’d expect some conferences to have substantially fewer women than the population average for a field — the women in, say, mathematics will not be spread out evenly, so some topics will have more and some will have fewer in a way that messes up the probability calculation.  Also, some conferences will be more worried about other forms of under-representation — it’s more obvious for women because they are a relatively large fraction of the target population and because you can tell someone’s gender fairly reliably from a name and photo.

There wouldn’t be anything noteworthy about the occasional conference having substantially fewer women than expected. Even with perfect homogeneity across topics and no bias, about one conference in thirty would have a one-in-thirty under-representation of women. In that scenario you could argue there wasn’t any need to do anything about it.

That is so not where we are.