A case for the case-control method 

 In his  opinion piece in this weekend's New York Times , Henry Louis Gates presents a taste of the research behind his forthcoming book,  In Search of Our Roots : 

 I have been studying the family trees of 20 successful African-Americans, people in fields ranging from entertainment and sports (Oprah Winfrey, the track star Jackie Joyner-Kersee) to space travel and medicine (the astronaut Mae Jemison and Ben Carson, a pediatric neurosurgeon). And I’ve seen an astonishing pattern: 15 of the 20 descend from at least one line of former slaves who managed to obtain property by 1920 — a time when only 25 percent of all African-American families owned property. 

 The question is, how astonishing is the pattern Gates points out?  


 Whether we should be impressed that 15 of 20 successful African-Americans had landowning ancestors depends a lot on what we assume about patterns of intermarriage among landowning and non-landowning African-Americans. Let's consider two extreme possibilities. First, assume that landowners never married non-landowners. In that case, one's grandparents would have been either all landowners or all non-landowners (more precisely, all from landowning families or all from non-landowning families). Given that 25% of all African-American families were landowners in 1920, 25% of African Americans of Oprah's generation would have had landowning grandparents (assuming that landowners and non-landowners had equally sized families, and also assuming that African-Americans had only African-American grandparents). The fact that 75% of Gates's successful African-Americans had landowning grandparents would indeed be remarkable, supporting his claim that having landowning ancestors helped them succeed.  

 At the other extreme, assume that landowners intermarried perfectly freely with non-landowners. In that case, there is an almost 70% chance that a randomly-selected person of Oprah's generation would have at least one landowning grandparent. (To see this: given that 3/4 of all grandparents were not landowners, the probability that a randomly selected person would have no landowning grandparents is (3/4)^4 = 31.6%.) If that were true, we would be quite likely to see as many as 15 people with landowning ancestors in Gates's sample even if landowning had nothing to do with success (p-value = .19). The pattern he observes would thus provide only very weak evidence for his argument about the importance of landowning.  

 Gates's book appears typical of a genre of case study that focuses on remarkable people (or companies, or countries) in order to determine how they became that way. The problem with these studies (as pointed out in  KKV , among many other places) is that they assume too much about the characteristics of unremarkable people (or companies, or countries). In the above example, Gates implicitly assumes that far fewer than 75% of unsuccessful African-Americans had a landowning ancestor in 1920. Instead of relying on this (possibly erroneous) assumption, he could have explicitly compared the family histories of his sample of remarkable African-Americans with those of another sample of unremarkable African-Americans. (This research design is known as "case-control" in epidemiology.) I doubt it would help with book sales to include a few chapters about thoroughly unfamous people, but it would make his arguments more convincing.