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# simpson's paradox

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• Suppose we want to compare two treatments, A and B, for a particular disease. 160 patients are given A - 60 recover; 230 patients receive B and 65 recover.

Clearly, treatment A, with a cure rate of 60/160 = 38%, is preferable to treatment B, with cure rate 65/230 = 28%. Right?

Maybe not. What if we are also given the recovery rates by sex, as follows:

men : A 20/100 (20%) B 50/210 (24%)

women: A 40/60 (67%) B 15/20 (75%)

overall: A 60/160 (38%) B 65/230 (28%)

Thus, even though A appears better overall, clearly treatment B is better both for men and for women. This contradiction is known as Simpson's paradox.

October 16, 2007