Great post on the messy reality hidden by smooth statistics (Pacific Standard)

How Well Do Teen Test Scores Predict Adult Income?
// Miller-McCune Online

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If someone told you that the test scores people get in their late teens were highly correlated with their incomes later in life, you probably wouldn't be surprised. If I said the correlation was -.35, on a scale of 0 to 1, that would seem like a strong relationship. And it is. That's what I got using the National Longitudinal Survey of Youth. I compared the Armed Forces Qualifying Test scores, taken in 1999, when the respondents were aged 15-19 with their household income in 2011, when they were 27-31.

Here is the linear fit between between these two measures, with the 95 percent confidence interval shaded, showing just how confident we can be in this incredibly strong relationship:

That's definitely enough for a screaming headline, "How Your Kids' Test Scores Tell You Whether They Will Be Rich or Poor." And it is a very strong relationship—that correlation of 0.35 means AFQT explains 12 percent of the variation in household income.

But take heart, ye parents in the age of uncertainty: 12 percent of the variation leaves a lot left over. This variable can't account for how creative your children are, how sociable, how attractive, how driven, how entitled, how connected, or how white they may be. To get a sense of all the other things that matter, here is the same data, with the same regression line, but now with all 5,248 individual points plotted as well (which means we have to rescale the y-axis):

Each dot is a person's life—or two aspects of it, anyway—with the virtually infinite sources of variability that make up the wonder of social existence. All of a sudden that strong relationship doesn't feel like something you can bank on with any given individual. Yes, there are very few people from the bottom of the test-score distribution who are now in the richest households (those clipped by the survey's topcode and pegged at three on my scale), and hardly anyone from the top of the test-score distribution who is now completely broke. . . 

This post originally appeared on Sociological Images, a Pacific Standard partner site, as "How Well Do Teen Test Scores Predict Adult Income?"

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How Well Do Teen Test Scores Predict Adult Income? was first posted on May 20, 2014 at 2:00 pm.