Several research papers and a book have been published by Satoshi Kanazawa raising interesting questions and trying to answer them from an evolutionary biology perspective. For other such questions read this article in Psychology Today. Our question of the day concerns beautiful parents and their offspring. Based on his research Kanazawa asserts that beautiful parents have more daughters. Rather than debate the evolutionary basis of such a claim, the Columbia University statistician and blogger Andrew Gelman decided to look at the statistical basis of the claim. What he found has larger implication for general analysis of data.
Kanazawa's claim is primarily based on a study with multiple waves and about 3000 respondents. Attractiveness of parents is measured on a 5 point scale by an interviewer. But, as Gelman states, Kanazawa selectively compares those rated a 5 (very attractive) to those in categories 1-4 and finds that 44% of the former have boys compared to 52% of the latter. With the large sample size, this is shown to be statistically significant leading to the generalized claim that beautiful people have more daughters.
Gelman has several statistical critiques of the analysis that have been published in the journal (Journal of Theoretical Biology) where Kanazawa's articles were published. One of them is with the selective comparison of categories 1-4 with category 5. Further it appears that while three attractiveness ratings were made over multiple years, only one was used. Gelman's question is why the other scale point comparisons (1 against 2-5, 1-2 against 3-5 etc) have not been reported on. There are a total of 20 such combinations possible and it is no surprise, he says, that one of them is statistically significant, especially at this sample size. He argues that to hang such a controversial claim on a single result is not good statistics.
Gelman also suggests that in these situations it would be better to run a regression of attractiveness and proportion of girl births, which he does in this article. He and his coauthor (David Weakliem) find that the effect size is only about as large as the standard error, meaning that it is not statistically significant. Why use a regression instead of splitting the scale and looking at proportions on the second variable? Because scale splitting is arbitrary and the regression is using the entire scale, any effect found through the regression analysis is likely to be closer to the truth.
Gelman and Weakliem also go a step beyond in a rather novel manner to see if there is an anything to the idea that beautiful people have more daughters. They use the universal definition of beauty - People Magazine's list of the 50 most beautiful people! Given their celebrity it is easy to track down the sex of their children. Looking at five years of data Gelman and Weakliem find no evidence for more daughters than sons.
A larger point being made by Gelman and Weakliem is about effect sizes and statistical significance. With small samples it is possible that large effects can occur due to chance. Understanding the effects in context can avoid misleading conclusions. Use of additional data or related examples can be useful. For example, most of the recent Presidential elections have been won by taller candidates, yet this result has not been shown to hold for other offices. Given the small number of recent Presidential elections we don't want to state that taller candidates will always win Presidential elections. On the other hand, impact of facial appearance on election outcomes seems to have at least directional support in different levels of elections, thus providing more confidence in the general conclusion.
There are other claims made by Kanazawa including ones such as violent men have more sons, big and tall parents have more sons, engineers have more sons and nurses have more daughters. I'm not aware of any work like Gelman's that has examined the statistical claims of these assertions, but based on what we've seen here that may be a worthwhile effort.