Social Science Statistics Blog

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19 October 2006

Simpson’s Paradox

Jim Greiner

As a lawyer, I have to be interested not just in what quantitative principles are true, but also in how to present “truth” to people without quantitative training. To that end, HELP! One of the maddening things about statistics is Simpson’s paradox. The quantitative concept, undoubtedly well-known to most readers of this blog, is that the correlation between two variables can change sign and magnitude, depending on what is conditioned on. That is, Corr(A, B | C) might be positive, while Corr(A, B | C, D) might be negative, while Corr (A, B | C, D, E) might be positive again. At bottom, this is what’s going on when regression coefficients become (or cease to be) significant as one adds additional variables to the right-hand side. Because regression currently enjoys a stranglehold on expert witness analyses in court cases (I’ll be ranting on that in the future), communicating Simpson's Paradox a matter of real concern for someone like me who cares about what juries see, hear, and think. Any ideas on how to get this concept across?

Posted by James Greiner at 11:13 AM