Sunday, January 25, 2015

Snarking At Leslie More Rigorously

What an awesome rejoinder to Leslie et al. (PDF):
This is the paper that concludes that “women are underrepresented in fields whose practitioners believe that raw, innate talent is the main requirement for success because women are stereotyped as not possessing that talent.” They find that some survey questions intended to capture whether people believe a field requires innate talent correlate with percent women in that field at a fairly impressive level of r = -0.60

The media, science blogosphere, et cetera has taken this result and run with it. A very small sample includes: National Science Foundation: Belief In Raw Brilliance May Decrease Diversity. Science Mag: the “misguided” belief that certain scientific fields require brilliance helps explain the underrepresentation of women in those fields. Reuters: Fields That Cherish Genius Shun Women. LearnU: Study Findings Point To Source Of Gender Gap In STEM. Scientific American: Hidden Hurdle Looms For Women In Science. Chronicle Of Higher Education: Disciplines That Expect Brilliance Tend To Punish Women. News Works: Academic Gender Gaps Tied To Stereotypes About Genius. Mathbabe: “The genius myth” keeps women out of science. Vocativ: Women Avoid Fields Full Of Self-Appointed Geniuses. And so on in that vein.

Okay. Imagine a study with the following methodology. You survey a bunch of people to get their perceptions of who is a smoker (“97% of his close friends agree Bob smokes”). Then you correlate those numbers with who gets lung cancer. Your statistics program lights up like a Christmas tree with a bunch of super-strong correlations. You conclude “Perception of being a smoker causes lung cancer”, and make up a theory about how negative stereotypes of smokers cause stress which depresses the immune system. The media reports that as “Smoking Doesn’t Cause Cancer, Stereotypes Do”.

This is the basic principle behind Leslie et al (2015).

The obvious counterargument is that people’s perceptions may be accurate, so your perception measure might be a proxy for a real thing. In the smoking study, we expect that people’s perception of smoking only correlates with lung cancer because it correlates with actual smoking which itself correlates with lung cancer. You would expect to find that perceived smoking correlates with lung cancer less than actual smoking, because the perceived smoking correlation is just the actual smoking correlation plus some noise resulting from misperceptions.
Alexander goes on to analytically dispose of this silly argument by looking at GRE Quantitative scores and finding — shockingly — "a correlation of r = -0.82 (p = 0.0003) between average GRE Quantitative score and percent women in a discipline". In other words, the better you score in those areas, the more likely you are to end up in a STEM career, and men typically are the ones on the right side of that graph (with higher scores). There's a lot more solid analysis there, including the observation that Leslie overweighted verbal and writing scores. It's well worth the read.

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