{"id":37315,"date":"2011-07-08T10:00:44","date_gmt":"2011-07-08T15:00:44","guid":{"rendered":"http:\/\/thesocietypages.org\/socimages\/?p=37315"},"modified":"2011-11-02T20:18:06","modified_gmt":"2011-11-03T01:18:06","slug":"sats-gpas-and-bias","status":"publish","type":"post","link":"https:\/\/thesocietypages.org\/socimages\/2011\/07\/08\/sats-gpas-and-bias\/","title":{"rendered":"SATs, GPAs, and Bias"},"content":{"rendered":"

Cross-posted at Montclair SocioBlog<\/a>.<\/em><\/p>\n

Is the SAT biased?\u00a0 If so, against who is it biased?<\/p>\n

It has long been part of the leftist creed that the SAT and other standardized tests are biased against the culturally disadvantaged \u2013 racial minorities, the poor, etc.\u00a0 Those kids may be just as academically capable as more privileged kids, but the tests don\u2019t show it.<\/p>\n

But maybe SATs are biased against privileged kids.\u00a0 That\u2019s the implication in a blog post by Greg Mankiw.\u00a0 Mankiw is not a liberal.\u00a0 In the Bush-Cheney first term, he was the head of the Council of Economic Advisors.\u00a0 He is also a Harvard professor and the author of a best-selling economics text book.\u00a0 Back in May he had a blog post called \u201cA Regression I\u2019d Like to See.\u201d<\/a> If tests are biased in the way liberals say they are, says Mankiw, let\u2019s regress GPA on SAT scores and family income.\u00a0 The correlation with family income should be negative.<\/p>\n

…a lower-income student should do better in college, holding reported SAT score constant, because he managed to get that SAT score without all those extra benefits.<\/p><\/blockquote>\n

In fact, the regression had been done, and Mankiw added this update:<\/p>\n

Todd Stinebrickner, an economist at The University of Western Ontario, emails me this comment:<\/p>\n

\u201cRegardless, within the income groups we examine, students from higher income backgrounds have significantly higher grades throughout college conditional on college entrance exam . . . scores<\/strong>.\u201d [Mankiw added the boldface]<\/p>\n

What this means is that if you are a college admissions officer trying to identify the students who will do best in college, as measured by grades, you would give positive rather than negative weight on family income.<\/p><\/blockquote>\n

Not to give positive weight to income, therefore, is bias against those with higher incomes.<\/p>\n

To see what Mankiw means, look at some made-up data on two groups.\u00a0 To keep things civil, I\u2019m just going to call them Group One and Group Two.\u00a0 (You might imagine them as White and Black, Richer and Poorer, or whatever your preferred categories of injustice are.\u00a0 I\u2019m sticking with One and Two.)\u00a0 Following Mankiw, we regress GPA on SAT scores.\u00a0 That is, we use SAT scores as our predictor and we measure how well they predict students\u2019 performance in college (their GPA).<\/p>\n

\"\"<\/a><\/p>\n

In both groups, the higher the SAT, the higher the GPA.\u00a0 As the regression line shows, the test is a good predictor of performance.\u00a0 But you can also see that the Group One students are higher on both.\u00a0 If we put the two groups together we get this.<\/p>\n

\"\"<\/a><\/p>\n

Just as Mankiw says, if you\u2019re a college admissions director and you want the students who do best, at any level of SAT score, you should give preference to Group One.\u00a0 For example, look at all the students who scored 500 on the SAT (i.e., holding SAT constant at 500).\u00a0 The Group One kids got better grades than did the Group Two kids.\u00a0 So just using the SATs, without taking the Group factor (e..g., income ) into account, biases things against Group One.\u00a0 The Group One students can complain: \u201cthe SAT underestimates<\/em> our abilities, so the SAT is biased against us.\u201d<\/p>\n

Case closed?\u00a0 Not yet.\u00a0 I hesitate to go up against an academic superstar like Mankiw, and I don\u2019t want to insult him (I\u2019ll leave that to Paul Krugman<\/a>).\u00a0 But there are two ways to regress the data.\u00a0 So there\u2019s another regression, maybe one that Mankiw does not want to see.<\/p>\n

What happens if we take the same data and regress SAT scores on GPA?\u00a0 Now GPA is our predictor variable.\u00a0 In effect, we\u2019re using it as an indicator of how smart the student really is, the same way we used the SAT in the first graph.<\/p>\n

\"\"<\/a><\/p>\n

Let\u2019s hold GPA constant at 3.0.\u00a0 The Group One students at that GPA have, on average, higher SAT scores.\u00a0 So the Group Two students can legitimately say, \u201cWe\u2019re just as smart as the Group One kids; we have the same GPA.\u00a0 But the SAT gives the impression that we\u2019re less smart.\u00a0 So the SAT is biased against us.\u201d<\/p>\n

So where are we?<\/p>\n