As school choice sweeps across the country, opponents are getting more desperate in their attempts to stem the tide. Like those who spring October surprises in presidential campaigns, aiming to derail candidates with false but confidently expressed last-minute accusations, opponents of school choice seek to undermine it with a falsehood just as state legislatures gather to vote on choice proposals.

The misleading falsehood is the claim that universal school choice programs wouldn’t expand opportunity because the vast majority of the beneficiaries would be students who already are enrolled in private schools.

The claim is that choice programs do little more than give taxpayer money to families whose kids already attend or would have attended private schools anyway at their own expense. This may provide financial relief to those families, but they are assumed to be advantaged and therefore undeserving of assistance.

Let’s leave aside the fact that all families pay taxes and so all deserve greater control over how those resources are used to educate their own children. As education freedom advocate Corey DeAngelis reminds us, we should fund students, not systems.

And let’s also ignore the insulting assumption that parents who struggle to pay private school tuition, even as they pay taxes for a public school they don’t use, are somehow unworthy of relief from this double financial burden. The assertion that the vast majority of students who use school choice already were enrolled in private schools is completely untrue.

The main promoter of this false claim is Josh Cowen, a professor at Michigan State University who founded and directed its Education Policy Innovation Collaborative. Cowen, however, ceased being affiliated with that center for reasons that haven’t been disclosed, and, around the same time, became a full-throated advocate against school choice.

Cowen writes in a Network for Public Education blog post: “Despite supporter rhetoric that voucher schemes are about new opportunities, the reality is 70-80 percent of kids in states like Arizona, Missouri, and Wisconsin were already in private school before taxpayers picked up the tab.”

He also has widely circulated on social media an infographic by the National Coalition for Public Education that answers the question “Who benefits from school vouchers?” by asserting: “The majority of voucher users in these states have never attended a public school. Vouchers subsidize tuition for students who already attend pricey private schools.”

The coalition’s infographic claims that 80% of choice students in Arizona, 89% of choice students in New Hampshire, and 75% of those in Wisconsin were “already in private school.”

The true rates of choice students who were “already in private school” (or would have enrolled in one anyway) are less than half as large as Cowen claims in those states. Cowen arrives at his inflated figures only by using outdated information and wrongly assuming that all students without a record of prior enrollment in a public school in the state must have been in private school previously.

The largest number of school choice students enter those programs in kindergarten or first grade. Cowen falsely asserts that all those students were “already in private school,” when in fact most weren’t enrolled in regular school at all. They would show no record of having previously been enrolled in public school, but that doesn’t mean that they were “already in private school.”

Arizona: 37% Already in Private School, Not 80%

For Arizona statistics, for example, Cowen relies upon a newspaper article published a month after the state expanded eligibility for its school choice program offering education savings accounts.

In the article, a state official says, “So far, nearly 80% of universal eligibility applicants do not have a record of prior public school enrollment.”  But that snapshot was premature, because private school families signed up for the expanded program right away while public school families waited for breaks in schooling before switching.

After winter break, the Arizona Department of Education now reports that 51% of choice students lack a record of prior public school enrollment. That figure likely will drop further following the first summer break of the expanded program as more public school families sign up.

In addition to using the outdated figure of 80%, Cowen wrongly assumes that all students beginning the program in preschool, kindergarten, or first grade who lacked record of prior public enrollment must have been “already in private school” or would have enrolled in private school anyway absent the choice program.

Past experience with school choice programs suggests that about 26% of students in those “entering grades” would have enrolled in private school anyway without a choice program. If we assume that the large number of students in the choice program in preschool, kindergarten, or first grade would have enrolled in private schools at that rate without that program, then only 37% of all students with education savings accounts in Arizona were “already in private school” or would have been in the absence of a choice program. (See below for more details regarding how we reached this figure.)

Cowen wrongly asserts that 80% of Arizona’s choice students were “already in private school,” when the true rate is less than half that.

New Hampshire: 44% Already in Private School, Not 89%

Cowen makes the same two errors when claiming that 89% of New Hampshire’s school choice students were “already in private school.”

Shortly after passage of the program, the state’s Department of Education reported that “just 204 of the 1,800 students that were enrolled in the program this school year had attended a public school the prior year.”

That works out to 89% of students without a record of prior enrollment in public school. But less than half a year later, that rate already had dropped significantly so that “58 percent of student recipients had never attended public school before entering the program.” Again, Cowen uses an outdated and inflated figure.

But even 58% is too high, because not all students who showed no record of previously attending a public school in the state came from private schools, given the large number of students who enroll in choice programs in kindergarten or first grade and were not previously enrolled in any kind of regular school.

If we assume that 26% of the choice students entering kindergarten or first grade would have enrolled in a private school anyway, then only 44% of New Hampshire’s choice students already were enrolled in a private school or would have been anyway in the absence of the program.

Asserting that 89% of choice students in New Hampshire were “already in private school” is more than twice the true rate.

Wisconsin: 13% Already in Private School, Not 75%

The misleading nature of Cowen’s figure for Wisconsin is even more egregious.

In Wisconsin, all students already enrolled in the school choice program must reapply each year. The only way Cowen arrives at his claim that 75% of Wisconsin choice students “were already in private school” is by counting all students continuing in the choice program as private school students, even if they previously had been enrolled in public school prior to participating in school choice.

According to official data, only 1,076 of the 17,079 students (or 6.3%) in the school choice program previously had been enrolled in a private school. If we assume that 26% of the 2,181 students in preschool, kindergarten, or first grade would have been in private school absent the program, then only 13% of all choice students in Wisconsin already were enrolled in a private school or would have been anyway in the absence of the choice program.

Asserting that 74% of choice students in Wisconsin were “already in private school” is more than five times the true rate.

Calculating Rate of Choice Students Already in Private School

To calculate the percentage of school choice students who were enrolled or would have enrolled in private schools anyway in each of the states in question—Arizona, New Hampshire, and Wisconsin—first we found the total number of students participating in the choice program.

Next, we either found the reported total number of students who hadn’t been enrolled previously in a public school (for Wisconsin) or calculated that figure using the reported rate for such students (for Arizona and New Hampshire).

Next, for each state, we multiplied the total number of choice students in the “entering grades” (preschool, kindergarten, and  first grade) by the take-up rate of existing private school students who became eligible for a school choice policy. For that latter rate, we looked to data from the Indiana Choice Scholarship Program, which had a year one take-up rate of 11% and a year two take-up rate of 26%.

We used the rate from the second year of the program to arrive at a more cautious estimate. Multiplying the number of students in entering grades by the take-up rate among existing private school students produces the number of students who likely would have enrolled in a private school anyway. Adding that figure to the number of students in grades 2 through 12 who had not been enrolled previously in a public school produces a conservative estimate for the number of students who already were in private school or would have enrolled in private school anyway, in the absence of a school choice program.

We say this is a conservative estimate because it doesn’t factor in students who moved from out of state and had attended or otherwise would have attended a public school, as well as students who might have switched from a private school to a public school, if it weren’t for the school choice program.

Finally, dividing that figure by the total number of choice students produces the rate of choice students who had been enrolled in a private school or would have enrolled in one anyway, in the absence of a school choice program.

As shown in the table below, 37% of choice students in Arizona, 44% in New Hampshire, and 13% in Wisconsin already were enrolled in a private school or likely would have enrolled in one anyway. Those figures are far below the unreasonable estimates provided by Cowen and the National Coalition for Public Education.

Put another way, the majority of students enrolled in a private school choice program—63% in Arizona, 56% in New Hampshire, and 87% in Wisconsin—otherwise would have been enrolled in a public school.

Conclusion: School Choice Expands Education Opportunity

Readers should be able to detect a pattern here. Despite impressive academic credentials, Cowen and the National Coalition for Public Education repeatedly use outdated information and make the unreasonable assumption that all students not previously enrolled in public school are really private school students.

That’s how they arrive at the ridiculously inflated claim that between 75% and 89% of school choice students across multiple states were “already enrolled in private school.”

As with October surprises, Cowen may think he can undermine political momentum with a last-minute charge that is confidently asserted, but false. But in this case, it doesn’t take very long to realize that his numbers are seriously distorted.

The reality is that most of the families who benefit from school choice policies otherwise would not have enrolled their children in a private school. School choice policies significantly expand education opportunity.

This piece originally appeared in The Daily Signal