Thursday, February 4, 2010

Simpson's Paradox......Doh!

Professor Neo Klassikle asked his research assistant to find out if the average wage of women rose or fell over a ten-year period. The following morning, the assistant returned and said, "I wasn't able to find anything on women, but I found out that the average wage for all workers fell during that period while the average wage for men rose. It must, therefore, be true that the average wage for women fell." "Not necessarily," said the professor. "It's possible that the average wage for women rose during that period, too." How could that happen? Use a numerical example to support your answer.

Congratulations to Yuan Tao for correctly explaining the seemingly odd set of facts described above. The problem presents an application of Simpson's Paradox.

1 comment:

Yuan Tao said...

Ten years ago:
Male population---5
Female population---5
Male total wages----7
Female total wages----3
Average male wage—1.4
Average female wage—0.6
Overall average wage---- 1.0

Ten years later:
Male population---2
Female population---8
Male total wages----4
Female total wages----5
Average male wage—2↑
Average female wage—0.625↑
Overall average wage----0.9 ↓

PS: The change of sex ratio and total wages may lead such a result. Both men and women have higher average wage among each gender respectively while the overall average wage decreases.

submitted by Yuan Tao