# Baffling Demographic Math: Women in Computing

Somebody on Twitter linked this article about “brogrammers”, which is pretty much exactly as horrible as that godawful neologism suggests. In between descriptions of some fairly appalling behavior, though, they throw some stats at you, and that’s where it gets weird:

As it is, women remain acutely underrepresented in the coding and engineering professions. According to a Bureau of Labor Statistics study, in 2011 just 20 percent of all programmers were women. A smaller percentage of women are earning undergraduate computer science degrees today than they did in 1985, according to the National Center for Women in Technology, and between 2000 and 2011 the percentage of women in the computing workforce dropped 8 percent, while men’s share increased by 16 percent.

Specifically, that last sentence. How is that even possible? The only way I can see for that number to make sense is if at least 8% of the workforce in 2000 didn’t provide gender data, but if that’s the case, you can’t really say anything sensible about changes in those numbers. You could probably arrange some distribution in which those figures are percentages of percentages (that is, the fraction of women started at some value, and decreased to 92% of that original value), but it would require the initial fraction of women to be higher than the initial fraction of men (so that the same decrease in absolute terms is a larger percentage for men than women), which is obviously not the case.

Of course, being traditional journalists, they don’t make it easy to find the source. They sorta-kinda attribute it to the National Center for Women in Technology, whose scorecard makes a similar claim for 2000-2009, though the disparity is smaller (11% and 13%). They source it to the Bureau of Labor Statistics, but the relevant-seeming tables don’t break out men and women separately, so I can’t see how you would get a bizarre claim like the quoted bit. If you want to know the male participation in these industries from those BLS tables, the only thing you can do is subtract the women’s percentage from 100, which obviously cannot give you a different change in the fraction of men than the fraction of women. Unless they’re working from some more complete data set with more fine-grained demographic information, but if so, it’s not obvious where you would find that.

I have too much other stuff to do to keep trying to track this weirdness down, but this is going to bug me all day, so I’ll throw it out to my readership in hopes that one of you either knows how you would get such an obviously weird result, or can track down an explanation with superior Google-fu.

1. #1 Eric Suh
April 27, 2012

Maybe they’re percentages of two different populations? e.g. if by “percentage of women in the computing workforce” they mean something like (women in computing / women who work), and analogously for men. Then you can have the absolute number of women who are in computing be low compared to men, but have an even lower number of women who work compared to men, thus allowing a small “percentage” change to result in the same absolute change.

2. #2 John Armstrong
April 27, 2012

I think Eric has hit it.

Buried lede: even a physics professor doesn’t reflexively scream “percent OF WHAT?” whenever percentage statistics are quoted without reference in the news.

April 27, 2012

Maybe they’re percentages of two different populations? e.g. if by “percentage of women in the computing workforce” they mean something like (women in computing / women who work), and analogously for men.

If that’s what they mean, they’re as bad at writing as they are at math, because I have a hard time parsing the quoted sentence to mean that.

I thought briefly that it might be a garbled reference to an increase in the number of jobs in those fields– that is, the absolute number of jobs in computing held by men increased by 16% while the absolute number of jobs held by women decreased by 8%. But again, I can’t quite make the words they wrote mean that (and the phrase in the article is nearly identical to what was used in the NCWT “scorecard”).

Buried lede: even a physics professor doesn’t reflexively scream “percent OF WHAT?” whenever percentage statistics are quoted without reference in the news.

Oh, I do, but so many people have complained about that that it’s not interesting material for a blog post any more. This was a new one on me.

4. #4 Paul
April 27, 2012

Some other options:

1) Everything else we’ve heard is wrong, 2/3 of the CS workforce in 2000 was female.

2) In the last 10 years, the US gender ratio has skewed heavily female.

3) There are many Computer workers who consider themselves a non-standard gender (though fewer today than 10 years ago).

4) 2/3 of the CS workforce in 2000 was male. However, that workforce is actually negative in quantity (but we’re getting closer to positive employment!).

5) The numbers include robotic workers, who are replacing women at a much faster clip than men.

5. #5 history1861
April 27, 2012

I read that article earlier this morning and ended up in the same confused state. I’m not a statistician but it didn’t seem to make a whole lot of sense to me, either.

6. #6 AliceB
April 27, 2012

At first I thought Paul had it: the only way it worked was that 2/3 of the CS workforce had to be female.

But then I realized, if we construe the sentence to mean that the percentages we are talking about are the increase/decrease of a particular gender in workforce, in relation to that gender, it can make sense.

E.g., let’s assume (for argument’s sake only) that in 2000 the workforce was 200 men, 100 women, for a total of 300 workers.

By 2011, the number of men grew by 16%, i.e., 32 more. Total men: 232. The number of women decreased by 8%, i.e., 8 less. Total women: 92. Total workforce: 324. It works.

The problem may not be the numbers, but the sloppy writing.

7. #7 CCPhysicist
April 27, 2012

I think AliceB has solved it.

But it should have been self-evident that the writing was bad. You can probably trace all of it back to a press release that tried to make it flashy enough to get noticed.

April 27, 2012

But then I realized, if we construe the sentence to mean that the percentages we are talking about are the increase/decrease of a particular gender in workforce, in relation to that gender, it can make sense.

This is, in fact, what they meant. The folks at Mother Jones noticed this post, looked into it, and have now corrected the wording of the article.

Never let it be said that blogging never accomplished anything…

9. #9 Tasneem Raja
April 28, 2012

Thanks for bringing this up, everyone. We looked into it, and the sentence now reads:

A smaller percentage of women are earning undergraduate computer science degrees today than they did in 1985, according to the National Center for Women in Technology, and between 2000 and 2011 the number* of women in the computing workforce dropped 8 percent, while men’s share increased by 16 percent.

With an update at the bottom of the post:

Correction: The original version of this article relied on incorrect information from the National Center for Women in Technology stating that the percentage of women and men in the computing workforce changed between 2000 and 2011. Thanks to the blog Uncertain Principles for catching the error.