31 July 2008

Journalism in 2008

If you believe what you read in the news media then take a look at this Marginal Revolution post on the recent stories about a study on gender variations in mathematical ability.

For those of you who don't remember, Larry Summers had to leave Harvard because of what he said on this subject, essentially that the male and female distributions had the same mean but the male distribution had a higher standard deviation. Summers said this was a major factor in the high ratio of men to women in jobs requiring extremely high mathematical ability such as mathematics professors in elite colleges.

Summers' chain of reasoning was hard to argue with. If ability in a field of endeavor is approximately normally distributed and two groups have the same mean ability then the group with higher variation in that ability will be tend to be occupy more of the jobs that require extremely high levels of that ability. Therefore either Summers' conclusion was correct or the data he based it on was wrong. It appears that many journalists did not agree with Summers' conclusion so they were eager to report on the new study that showed that his data were questionable. The only problem was that the new study's data confirmed that variarition in mathematical ability is higher in males than females. From the Marginal Revolution post

  • If you do the same type of calculation as the authors but now look at the expected gender ratio at 4 standard deviations from the mean you find a ratio of more than 3:1, i.e. just over 75 men for every 25 women should be expected at say a top-25 math or physics department on the basis of math ability alone .
No-one who posts on this blog claims to be able to predict how the tail-ends of data sets that are expected to be normally distributed will behave in reality. However higher variation within a population usually leads to more people at the top and more at the bottom.


Peter Williams said...

Aleks from "Statistical Modeling, Causal Inference, and Social Science" has graphed some related data

Peter Williams said...

http://freakonomics.blogs.nytimes.com/2008/08/04/how-healthy-is-the-economy-it-depends-where-you-get-your-news/ is a nice illustration of hard it is not to do this.

Peter Williams said...

See also http://norvig.com/reporters-and-parrots.html