“Three Statistical Paradoxes in the Interpretation of Group Differences: Illustrated With Medical School Admission and Licensing Data”, 2006 (; backlinks; similar):
Interpreting group differences observed in aggregated data is a practice that must be done with enormous care. Often the truth underlying such data is quite different than a naïve first look would indicate. The confusions that can arise are so perplexing that some of the more frequently occurring ones have been dubbed paradoxes. In this chapter we describe 3 of the best known of these paradoxes—Simpson’s Paradox, Kelley’s Paradox, and Lord’s Paradox—and illustrate them in a single data set.
The data set contains the score distributions, separated by race, on the biological sciences component of the Medical College Admission Test (MCAT) and Step 1 of the United States Medical Licensing Examination™ (USMLE). Our goal in examining these data was to move toward a greater understanding of race differences in admissions policies in medical schools. As we demonstrate, the path toward this goal is hindered by differences in the score distributions which gives rise to these 3 paradoxes.
The ease with which we were able to illustrate all of these paradoxes within a single data set is indicative of how wide spread they are likely to be in practice.