Sunday, March 6, 2011

Educational Attainment and Simpson's Paradox

Here's Paul Krugman on the educational performance of Texas schools:

But here’s the thing: While low spending may sound good in the abstract, what it amounts to in practice is low spending on children, who account directly or indirectly for a large part of government outlays at the state and local level.

And in low-tax, low-spending Texas, the kids are not all right. The high school graduation rate, at just 61.3 percent, puts Texas 43rd out of 50 in state rankings. Nationally, the state ranks fifth in child poverty; it leads in the percentage of children without health insurance. And only 78 percent of Texas children are in excellent or very good health, significantly below the national average.

I came to this post from a link from Cafe Hayek to a thorough post by someone named iowahawk, who had an interesting response to Krugman:
Perhaps because a state's "average ACT/SAT" is, for all intents and purposes, a proxy for the percent of white people who live there. In fact, the lion's share of state-to-state variance in test scores is accounted for by differences in ethnic composition. Minority students - regardless of state residence - tend to score lower than white students on standardized test, and the higher the proportion of minority students in a state the lower its overall test scores tend to be.

Please note: this has nothing to do with innate ability or aptitude. Quite to the contrary, I believe the test gap between minority students and white students can be attributed to differences in socioeconomic status. And poverty. And yes, racism. And yes, family structure. Whatever combination of reasons, the gap exists, and it's mathematical sophistry to compare the combined average test scores in a state like Wisconsin (4% black, 4% Hispanic) with a state like Texas (12% black, 30% Hispanic).

The post by iowahawk goes on to compare tests scores by race between Wisconsin and Texas for a whole suite of comparisons of educational performance between the two states (broken down by race). Of the 18 comparisons (race-grade-specific test score by state), 17 of them favor Texas.

This reversal of trend is a phenomenon known as Simpson's paradox:

In probability and statistics, Simpson's paradox (or the Yule-Simpson effect) is a paradox in which a correlation (trend) present in different groups is reversed when the groups are combined. This result is often encountered in social-science and medical-science statistics, and it occurs when frequency data are hastily given causal interpretations. Simpson's Paradox disappears when causal relations are brought into consideration (see Implications to decision making).

The picture from Wikipedia is nice too:

To draw the analogy to the picture, Krugman was reporting along the downward-sloping dotted black line; iowabuck was reporting along the colored (red and blue) upward-sloping lines.

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