Simpson's paradox

Simpson's paradox (or the Yule-Simpson effect) is a statistical paradox described by E. H. Simpson in 1951 and G. U. Yule in 1903, in which the successes of several groups seem to be reversed when the groups are combined. This seemingly impossible result is encountered surprisingly often in social science and medical statistics.

The batting average paradox

The most common example of the paradox in America involves batting averages in baseball. It is possible — and in rare occasions it has actually happened — for one player to hit for a higher batting average than another player during the first half of the year, and to do so again during the second half, but to have a lower batting average for the entire year, as shown in this example:

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First Half Second Half Total season

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Player A 4/10 (.400) 25/100 (.250) 29/110 (.264)

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Player B 35/100 (.350) 2/10 (.200) 37/110 (.336)

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