Simpson's paradox

The Simpsons paradox is when a statistic can be misinterpreted and not understood correctly.  I randomly read about it today and it reminded me of something I've always heard that didn't make sense. Which I think would be an example of the Simpson Paradox. 

You know how "they" always say that more than 50% of all car accidents happen 5 miles from your home - as a reason to always wear you seat belt? (#'s might be off)  The assumption might be that it's most dangerous to drive around your home - as compared to further away. But if you think about it - the reason there are more accidents around a drivers individual home - isn't that it's more dangerous - but that they are driving in that area more. 

So it's not that it's more dangerous - it's that it's more common. 
The more you drive - the more likely you are to have an accident. 
The more you drive in a certain area - the more likely you are to have an accident in that area. 
You drive around your home - most often. 

But you should still wear your seatbelt regardless!

I don't know if that is really a Simpson's paradox, but it seems like it! ?



This is about the Simpson's Paradox from wikepedia:



"In probability and statisticsSimpson's paradox (or the Yule-Simpson effect) is an apparent paradox in which a correlation (trend) present in different groups is reversed when the groups are combined. This result is often encountered in social-science and medical-science statistics,[1] and it occurs when frequency data are hastily given causal interpretations.[2] Simpson's Paradox disappears when any causal relations are derived systematically – i.e. through formal analysis."



Berkeley sex bias case

One of the best known real life examples of Simpson's paradox occurred when the University of California at Berkeley was sued for bias against women who had applied for admission to graduate schoolsthere. The admission figures for the fall of 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.[3][14]
Applicants % admitted
Men844244%
Women432135%
However when examining the individual departments, it was found that no department was significantly biased against women. In fact, most departments had a "small but statistically significant bias in favor of women"[14].

DepartmentMenWomen
Applicants % admittedApplicants % admitted
A82562%10882%
B56063%2568%
C32537%59334%
D41733%37535%
E19128%39324%
F2726%3417%
The research paper by Bickel, et al.[14] concluded that women tended to apply to competitive departments with low rates of admission even among qualified applicants (such as in the English Department), whereas men tended to apply to less-competitive departments with high rates of admission among the qualified applicants (such as in engineering and chemistry). The conditions under which the admissions' frequency data from specific departments constitute a proper defense against charges of discrimination are formulated in the research paper by Pearl (2000)"
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