Thursday, January 20, 2005

The Bell Curve

If you have an even passing familiarity with statistics, then you know that a bell curve is the graphical representation of a normal distribution. The peak of the curve represents the average value of the population, and the left tail are the low values while the right tail are the high values. There are usually equal numbers of people on the left and right of the curve.

You may also know that The Bell Curve is the title of a book published in 1994 by Richard Herrnstein and Charles Murray. The book is about how intelligence appears to play a central role in predicting how successful individuals fare in modern America. It describes the strong correlation between low intelligence and measures of social failure (welfare recipients, criminals, illegitimacy rates, and so forth). It became controversial (indeed, notorious) because it suggests that intelligence was largely immutable, and that there are differences in the distribution intelligence among various racial groups. These two points are important in formulating social policy and in understanding racial differences that exist within society, respectively. They are not, however, relevant in terms of understanding the most important point that the book attempts to make: Namely, that intelligence is fundamental to success in modern America. Those with more intelligence will normally be more successful, those with less intelligence are, on average, less successful. If we substitute the word “education” for “intelligence” then the above sentence is transformed into a common truism that hardly anybody would dispute. The key difference, of course, is that intelligence is a quality of the individual, while education is an external process albeit one that presumably has the power to transform the individual. However, it is quite likely that education is a proxy for intelligence. How many would dispute that the average person with a PhD degree is more intelligent than the average high school drop-out? Years of education has not made that so. Rather, those who are inherently more intelligent will tend excel within the educational system and proceed farther than those with lower intelligence.

Humans are biologic organisms, and as such we are subject to biologic variation. It is this variation that gives rise to natural selection and evolution. Variation is hard-wired into our genes. Take, for example, height. Some people are taller than others. If you took a large sample of adults and measured them all you would find a normal distribution of heights. You might also notice that certain subpopulations, say Filipinos, are, on average, shorter than normal, and other subpopulations, say the Tutsi of Central Africa, that are taller than average. So, what about variation of intelligence? Currently, the SAT is the most widely administered an intelligence test. As expected, the distribution of SAT scores follows a normal distribution (figures below)

How surprising is to learn that there are subpopulations that have, on average, intelligence that is higher or lower than normal? Based upon what we know about variation of biologic variables, it should not be very surprising at all. And this is, in fact, precisely what the SAT finds (figure below).

It is against this backdrop that we learn of the comments of Larry Summers, President of Harvard University, who on January 14, 2005 stated that “innate sex differences” are one possible reason why there are fewer women on science and engineering faculties at elite universities. What innate differences was he referring to? He may have been referring to differences in IQ. Some believe that men, on average, have about a 4 point higher IQ than women. Others report that men and women have the same average intelligence, but that men have a larger spread, with more men at the extreme high and extreme low ends of the distribution. Looking again at SAT scores, we find that men score higher in both the math and verbal portions (figure below). Whether there is an average difference, or a greater spread, one might expect to find more men than women at the higher extremes of the intelligence distribution.

The controversy surrounding the book and Mr. Lawrence Summer’s comments stems not from the science, which is rather straightforward, but from the politics of equality. Any scientific evidence that one group is inherently different from another can expect to be roundly criticized and summarily rejected out of hand as biased, racist, and unworthy of serious consideration. The reason for this is clear: history is full of examples of one group of people claiming superiority over another group. Such claims are often followed by state-sponsored persecution of the allegedly inferior group. There is indeed considerable risk that the state will use its power to persecute it’s own citizens. It is this power that we should fear, not the science. Our government is founded on the principle that all men are created equal, not that all men are equal. While we must all remain equal in the eyes of the Law, this is not grounds to reject the possibility that we are in fact different.

SAT data is drawn from the 2004 College-Bound Seniors Report and The College Board Research Report 2002-11

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