The Logic of Bell Curve Leftism #3

My last post on this topic will not include quotes from Andrew Sullivan’s article. Of course, income and IQ are partly correlated, but not near as much as argued by Sullivan and DeBoers.

This article shows a graph of lifetime income based on AFQT (Armed Forces Qualifying Test) score. Note the degree of dispersion above and below the gray line. The article includes the following.

But a lot of other things also predict income. So, what’s the unique contribution of AFQT scores? More precisely, how much of the variability in income can they explain? Statisticians often answer this question by reporting a statistic called r-squared that varies from zero to one. In this analysis, zero means AFQT has no predictive power, while one would mean that someone’s income can be perfectly predicted by knowing their AFQT score. An r-squared of 0.5 would mean that half of the variation in income could be explained by knowing someone’s AFQT scores (or, less scientifically, half the time you can predict someone’s income by knowing how they did on the AFQT).

The data show that AFQT scores explain 21% of the variation in income between survey respondents. That translates to a correlation coefficient of 0.46.

Is that a large correlation? It depends upon your perspective. If your cup is half full, you can correctly point out that 0.46 rivals the largest observed correlations in social psychology, sociology, and other relevant fields. But if your cup is half empty, you’ll say that many things determine how much money people make, and smarts is only one of them.

In fact, the true contribution of AFQT to income is probably smaller. That’s because AFQT is serving as a proxy for other attributes correlated with earnings. People with high AFQT scores probably stayed in school longer, and most likely had more successful parents. These and other correlates of intelligence factor into the aforementioned 21 percent.

A reader might wonder how the 0.46 and 0.21 are related. Two statistical metrics are the correlation coefficient, r, and the coefficient of determination, r^2 (link).  The range of r is [-1, +1] while the range of r^2 is [0, 1]. 0.46^2 = 0 .2116.

Two other oft-used statistical metrics of dispersion, standard deviation σ and variance σ^2, are similarly related.

Related: 10 Jobs Where Employees Tend to Have the Highest IQs