Is "race realism" realistic? - by Arnold Kling
Yesterday’s post on race and high achievement produced some pushback from commenters who defended “race realism.” I want to engage further.
Let’s stipulate that in order to perform at the highest levels in some realms, such as chess or economics, one needs an IQ of 145 or higher, which is three standard deviations above normal for the white population (normal mean is 100, each standard deviation is 15). And assume that the mean IQ in the black population is 85, so that for blacks to achieve at the highest level, one must be four standard deviations above normal. Taking into account that there are roughly 6 times as many whites as blacks in the U.S. population, what will we expect the ratio of whites to blacks performing at the highest levels in these realms?
Consider two ways to make this calculation.
(a) Survey very large numbers of blacks and whites to arrive at estimates of the numbers in each racial category that has an IQ of 145 or higher.
(b) Assume that the formula for the normal distribution applies 3 and 4 standard deviations out, and use that to estimate the ratio of whites to blacks with an IQ of 145 or higher.
I would regard method (a) as reliable, as long as the samples were large enough. Method (b) instead is making a very risky assumption, which is that distributions that seem to follow the normal formula near the mean also follow the normal formula near the extremes.
Method (b) is often erroneous. In finance, Nassim Taleb and many others have pointed out the poor performance of calculations based on using the formula for the normal distribution at the extremes. Events that should occur less than once in a thousand years have occurred often in our lifetime. The problem is that approximating probabilities using the normal distribution tends to break down at the extremes. Phenomena that appear to be normally distributed close to the mean are not actually normally distributed across the full range.
Self-described “race realists” are relying on method (b) to estimate the ratio of whites to blacks with an IQ of 145 or higher. But we do not know whether the normal formula truly applies when we are that many standard deviations from the mean.
Relying on the normal formula gives .0013 as the probability of being above 3 standard deviations. At the moment, I cannot even find a calculator that will give me an answer other than “0” for the probability of being above 4 standard deviations. But I think that the ratio of the portion within 3 standard deviations to the portion within 4 standard deviations is about 42. Please correct me if you find a more accurate calculation.
With 6 times as many whites as blacks, method (b) would predict 42x6 = 250 times as many ultra-high achieving whites as blacks in the United States.
When I look around the economics profession, I do not see 250 whites for every ultra-high achieving black. As I pointed out in the previous post, there are 2 black winners of the Clark medal. There are fewer than 100 white winners, not 500.
On the other side, consider the Jewish American population. If Jews and non-Jews were equal in numbers and Jews have an average IQ one standard deviation higher, then there would be about 42 Jews for every non-Jew in an ultra-high achievement category. But since Jews are only 2.5 percent of the population, there should be about one Jew for every non-Jew in an ultra-high achievement category. In fact, I think that the number is much lower. For example, Jews are only 8 percent of American billionaires.
If these examples are representative, then it appears that “race realism” over-predicts racial differences in the proportion of very high achievers. If so, this could be because IQ does not continue to follow the normal distribution at the extremes. And it could be because factors other than IQ are important for very high achievement.
If you want to assume that the normal distribution applies to IQ at the extremes, you can do that. And if you want to assume that IQ determines outcome in some realm, you can do that. But you are using a model to arrive at your conclusions, and people are entitled to question the assumptions in your model. In describing your analysis, I would come up with some term less self-assured than “realism.”
UPDATE: A commenter points to this analysis, by Taleb. Worth looking at. I worry that Taleb’s rhetoric goes too far, making it sound like IQ should be ignored altogether. I would say that the Gaussian assumptions about IQ and its relationship to outcomes are a map, not the territory. It is better to rely on observed data, not on assumptions.
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