During his now widely read and scrutinized remarks at the NBER conference held in January 2005, Harvard President Larry Summers made a “very crude calculation” for estimating gender ratios in “top” groups, consisting of those who score very highly on certain tests. From a conservative estimate of 2:1 male-to-female ratio in the top 5% group, Summers concluded that a conservative estimate of the ratio in “very top” groups would be 5:1. The purpose of this lecture is to carry out a careful examination of Summers? arguments, as well as to provide a more refined estimate, ultimately showing that Summers? 5:1 estimate is indeed very conservative under his assumptions. Although this is a relatively simple estimation problem, it has all the fundamental ingredients underlying statistical inference, from model formulation to uncertainty assessment to sensitivity analysis. It also reminds us of the danger of mixing association with causation. It therefore provides an excellent case study to introduce newcomers to the wonderful, and sometimes mysterious, world of Statistics, a fundamental discipline for all modern quantitative scientific investigations.
Groupe d’études et de recherche en analyse des décisions