New York could dramatically improve its chances of winning up to $700 million in federal Race to the Top dollars by eliminating its cap on the number of charter schools allowed to operate in the state. But the United Federation of Teachers would rather forgo those much-needed funds than let Gotham’s (typically) non-unionized charter-school sector expand. The UFT is making a desperate effort to confuse the state legislature into inaction, so that the deadline to compete for Race to the Top—now less than two weeks away—passes, hoping that the pressure to remove the cap will then subside. Hence the UFT’s new report, in which it charges that charter schools only seem to be more effective than traditional public schools. “No one should be surprised,” the UFT report said, “that some researchers find that charter schools have higher test scores, given that charters enroll students who are, on average, less poor, less disabled, and more likely to speak English.” The success of New York’s charter schools, then, becomes a mirage.

But take a closer look, and you’ll see how groundless the UFT’s charge is. Though the UFT didn’t identify the “researchers” in question, it’s surely referring to Stanford economist Caroline Hoxby and her recent, high-profile study of New York City’s charter schools. According to that study, the positive impact of attending a Gotham charter school rather than a public school is so large that five years of charter-school attendance nearly closes the proficiency gap between students in Harlem and those in upper-class Scarsdale.

Despite the UFT’s claims, Hoxby’s findings are absolutely valid. True, charter schools have smaller enrollments of special-education and ELL (English Language Learner) students than non-charter public schools. But Hoxby’s study takes this into account. Her study works like a medical trial. All students who apply for seats in an oversubscribed charter school—which describes nearly every charter in New York City—must enter a lottery for admission. Hoxby’s study compares the achievement of lottery winners and lottery losers. If the pool of applicants is big enough—as is the case in New York City—the laws of probability ensure that the group of students randomly selected to attend a charter school is essentially identical to the group that lost the lottery. The Hoxby study doesn’t compare all charter students with all non-charter students; in essence, it compares the performance of a charter student with his nearly identical colleague who was sent back to a traditional public school.

Of course, Hoxby’s study relies on the randomness of the lottery results. In its report, the UFT complains that the lower percentage of special-education and ELL students in charter schools proves that the lotteries are rigged. But the fact is that when disabled and ELL students enter a charter-school lottery, they are just as likely as other students to win a seat and to enroll in the charter school. Examination of the lottery results reveals no differences between lottery winners and losers in any observed characteristic, including disabilities and ELL. (The higher percentage of disabled and ELL students in non-charter schools results mainly from differences in who applies to charters, as well as the fact that charters are less willing than non-charters to diagnose marginal students as disabled.)

Granted, the Hoxby study was designed to test whether students who want to attend a charter school actually benefit from a charter-school education. It has nothing to tell us about students who don’t choose to apply to charters—for example, whether those students would benefit from somehow being forced to attend one, which would be wholly inconsistent with the entire idea of charter schools as schools of choice. But that’s inconsequential for our purposes. What matters is that the study results are in no way contaminated by differences between the lottery’s winners and losers.

The UFT may not like it, but it’s simply true: students who attend New York City’s charter schools do much better than if they had remained in their previous public schools. Claiming otherwise without offering any plausible supporting evidence, as the UFT did this week, only obscures that important reality.

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