Social Science Statistics Blog

James,

In class, I use the Jeter vs. Justice batting average example from _A Mathematician at the Ballpark_ by Ken Ross (2004), pp. 12-14.

It might not go over so well with Red Sox fans.

Another good one is the Berkeley graduate school admissions example from Freedman et al's _Statistics_, pp. 17-20, 3rd edition.

For the latter, it's easier to explain the lack of controls driving the results.

Eric

Of course, Simpson's Paradox is an example of Stigler's Law of Eponymy ("no scientific discovery is ever named after its original discoverer"), having been identified as early as 1899 (and possibly earlier). This website has lots of fun facts about the earliest use of various terms in mathematics and statistics.

For categorical data, the circumstances under which collapsing won't reverse the directions is given in Agresti (Categorical Data Analysis), in sections 5.3.2 and 5.5.4.2. I hope that will be of some help.

James,

Is that the correct definition of Simpson's Paradox? The site mentioned by Mike claims that:

SIMPSON'S PARADOX is the name given to a result in conditional probability by C. R. Blyth: "The paradox is the possibility of P{A | B}

At the very least, I think that it is possible to have regression coefficients change with the addition of more variables (the situation which worries you) even if the data is not an example of Simpson's Paradox as defined above.

Or perhaps I am missing something? Simpson's Paradox has always confused me . . .

I would definitely use a concrete example to explain it - as simple an example as you can find. Nancy Cartwright has some discussion of the Berkeley grad school case in her famous paper "Causal Laws and Effective Strategies" which you might find useful. I think it's pretty understandable.

Whatever way you think will be the easiest to explain it, why don't you try explaining it to a child that way and see if they get it.

As far as an example of Simpson's paradox goes, I took the example (with explanation) from my math book and put it up on a webpage. See http://people.hmdc.harvard.edu/~jgill/simpson/node1.html