Simpson's paradox

While doing some advanced preparation for an upcoming unit on statistics in my news writing class, I learned something new today (from Wikipedia).  When coming across a statistic that looks like slam-dunk evidence of bias or wrongdoing, an activist will have a motivation to present that data to journalists in order to advance a particular perspective. The problem comes when the well-meaning activist does not really understand statistics, and so presents an inaccurate interpretation to a journalist. It’s the journalist’s obligation to check out any statistic he or she uses in a story, often by contacting an expert who is not directly connected with whatever research is being cited, so that the expert can offer an independent interpretation of the data.

One of the best known real life examples of Simpson’s paradox occurred when the University of California, Berkeley was sued for bias against women applying to graduate school. The admission figures for fall 1973 showed that men applying were more likely than women to be admitted, and the difference was so large that it was unlikely to be due to chance.^[16][3]

	Applicants	% admitted
Men	8442	44%
Women	4321	35%

However when examining the individual departments, it was found that no department was significantly biased against women; in fact, most departments had a small bias against men.

Major	Men		Women
	Applicants	% admitted	Applicants	% admitted
A	825	62%	108	82%
B	560	63%	25	68%
C	325	37%	593	34%
D	417	33%	375	35%
E	191	28%	393	24%
F	272	6%	341	7%

The explanation turned out to be that women tended to apply to departments with low rates of admission, while men tended to apply to departments with high rates of admission. The conditions under which department-specific frequency data constitute a proper defense against charges of discrimination are formulated in Pearl (2000).