Tuesday, March 08, 2011

Bikini statistics: Simpson's Paradox edition

Statistics are like a bikini. What they present is suggestive, but what they conceal is vital.--Aaron Levenstein
Paul Krugman seemingly makes a great point, that Wisconsin students perform better than Texas students, so maybe collective bargaining is a great thing, since Texas doesn't have it. Iowahawk discovers that something is amiss. It turns out that Texas achieves far better educational outcomes. Excerpts and links below, via Eric Falkenstein.
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. 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--Paul Krugman

..., 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). So how to compare educational achievement between two states with such dissimilar populations? In data analysis this is usually done by treating ethnicity as a "covariate." A very simple way to do this is by comparing educational achievement between states within the same ethnic group. In other words, do black students perform better in Wisconsin than Texas? Do Hispanic students perform better in Wisconsin or Texas? White students? If Wisconsin's kids consistently beat their Texas counterparts, after controlling for ethnicity, then there's a strong case that maybe Texas schools ought to become a union shop. ... white students in Texas perform better than white students in Wisconsin, black students in Texas perform better than black students in Wisconsin, Hispanic students in Texas perform better than Hispanic students in Wisconsin. In 18 separate ethnicity-controlled comparisons, the only one where Wisconsin students performed better than their peers in Texas was 4th grade science for Hispanic students (statistically insignificant), and this was reversed by 8th grade. Further, Texas students exceeded the national average for their ethnic cohort in all 18 comparisons; Wisconsinites were below the national average in 8, above average in 8. Perhaps the most striking thing in these numbers is the within-state gap between white and minority students. Not only did white Texas students outperform white Wisconsin students, the gap between white students and minority students in Texas was much less than the gap between white and minority students in Wisconsin. In other words, students are better off in Texas schools than in Wisconsin schools - especially minority students. Conclusion: instead of chanting slogans in Madison, maybe it's time for Wisconsin teachers to take refresher lessons from their non-union counterparts in the Lone Star State.--Iowahawk

Previous BS installment here.  Photo link here. Elsewhere, Eric throws up his hands:
That an economist like Krugman would see such monopolies as a good thing highlights the fact that economics does not constrain or guide one's thinking, merely provides another way to frame arguments. That the inefficiency of union monopolies is still disputed is one reason I don't take economics so seriously anymore. You can always find some convoluted reason why some partial equilibrium result generalizes, and so basic economic insights like the inefficiency of monopolies, trade restrictions, or taxes that favor debt over equity. It makes me think, what's the point of economics if these easy issues are still debatable?

UPDATE: Steve Landsburg, too:
So to encourage innovation, you want to strengthen the unions? To encourage innovation, you want to reduce the relative reward to innovation, by insuring that everyone gets the same health care regardless of their social contributions?

Now, you might suppose that Krugman was thinking something along the following lines: Large swaths of American workers are being rendered unproductive by computers. Somehow or another, we have to support those people even though they’re not producing much. Unions and universal health care will keep them afloat.

But that can’t be what Krugman was thinking. I’m sure of this, because I happen to know that Krugman has a Ph.D. in economics. Therefore he must surely be aware that you can’t divorce incomes from productivity. Sure, you can redistribute, but you can’t redistribute more than what gets produced. If the problem is that our old skills are no longer productive, then our incomes must fall unless and until we acquire different — and less computer-replaceable — skills.

UPDATE: Scott Sumner, too:
No need to read Marginal Revolution, Becker/Posner, Econlog, John Taylor, Greg Mankiw, Robin Hanson, Steven Landsburg, etc, etc. Nothing of interest, just move right along folks. I’m always amazed when someone so brilliant can be so clueless about life. How someone can reach middle age and still live in a kindergartener’s world of good guys and bad guys.

Perhaps if Krugman would get out a bit more he might make fewer embarrassing errors, like this one, where he forgot the fallacy of composition, something taught in EC101. I guess none of his liberal friends have the nerve to point out these sorts of silly errors. So it’s still there, uncorrected after two weeks. A monument to his pride at being ignorant of the views of those with whom he disagrees.

You might ask whether I’m being a bit harsh calling him “ignorant.” Actually, he’s the one who proudly flaunts his ignorance of conservative thought.

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