Chapter 10. Approximate Bayesian Computation
The Variability Hypothesis
I have a soft spot for crank science. Recently I visited Norumbega Tower, which is an enduring monument to the crackpot theories of Eben Norton Horsford, inventor of double-acting baking powder and fake history. But thatâs not what this chapter is about.
This chapter is about the Variability Hypothesis, which
âoriginated in the early nineteenth century with Johann Meckel, who argued that males have a greater range of ability than females, especially in intelligence. In other words, he believed that most geniuses and most mentally retarded people are men. Because he considered males to be the âsuperior animal,â Meckel concluded that femalesâ lack of variation was a sign of inferiority.â
I particularly like that last part, because I suspect that if it turns out that women are actually more variable, Meckel would take that as a sign of inferiority, too. Anyway, you will not be surprised to hear that the evidence for the Variability Hypothesis is weak.
Nevertheless, it came up in my class recently when we looked at data from the CDCâs Behavioral Risk Factor Surveillance System (BRFSS), specifically the self-reported heights of adult American men and women. The dataset includes responses from 154407 men and 254722 women. Hereâs what we found:
The average height for men is 178 cm; the average height for women is 163 cm. So men are taller, on average. ...