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.