Simpson's Paradox Obscures Reality in the Current Recession, Baseball

December 11, 2009

Simpson's Paradox is a common but misleading statistical phenomenon where aggregated data can appear to reverse important trends in the numbers being combined. In a recent article in The Wall Street Journal, Cari Tuna uses the paradox in her comparison between unemployment rates by education during recessions in the 1980s and today.  

During the 1982 recession, the unemployment rate peaked at 10.8%. Comparatively, the current unemployment rate of 10.2% seems less severe. However, when Tuna looks at the data another way she finds the opposite is true. The unemployment rate among college graduates is higher today than in the 1980s. This is also true for some high school graduates and high school dropouts.

The reason, or "anomaly" as Tuna describes it, is a direct result of Simpson's Paradox. The article cites Xiao-Li Meng, chairman of Harvard University's statistics department, saying, "Simpson's paradox is responsible for a vast quantity of misinformation. You can easily be fooled."

"The jobless rates for each educational subgroup are higher today, but the overall rate is lower because workers are more educated," she wrote. "There are more college graduates, who have the lowest unemployment rate. And there are fewer high-school dropouts, who have the highest unemployment rate."

Elsewhere in our society, Simpson's Paradox, or the Yule-Simpson effect in probability and statistics, skews baseball statistics as well. Tuna used the batting averages of David Justice and Derek Jeter as an example. In both 1995 and 1996, Atlanta's David Justice had a higher batting average than Yankee superstar Derek Jeter. However, when the two years are combined, Jeter shows a better average.

In 1995 Jeter had only 48 at-bats with a .250 average while Justice had more at-bats (411) with a .253 average. Tuna. The next year, Jeter had 582 at-bats with a .314 average while Justice had only 140 at-bats with a higher average of .321, pushing the two-year average in Jeter's favor.

This phenomenon often occurs among pairings of formidable ball players, observed former MAA President Ken Ross (University of Oregon) in "A Mathematician at the Ballpark: Odds and Probabilities for Baseball Fans" (2004).

Tuna also cited examples of the paradox in modern medical studies and air transportation delays. The real question is how do you develop effective methods of analysis that are safe from Simpson's Paradox?

Source: The Wall Street Journal (December 2, 2009)