Lest doubt linger in respect of the value of school choice, a new report released today by a Harvard professor will settle the question. It responds to a recent study performed by the Department of Education that found public schools outperforming private institutions. The author of the response, Paul Peterson of Harvard’s Program on Education Policy and Governance, has used the same data to reach a conclusion opposite that reached by the Education Department. Though Mr. Peterson’s analysis is more credible than the research he rebuts, the real lesson from this duel is that policy wonks will never be able to tell with certainty whether schools are offering a good education. The right way to decide these things is to give parents, who can tell whether their children can read and add, the choices they need to manage their youngsters’ education.

Private schools have long out-scored public schools in student achievement. The question has been why — do they do a better job teaching or just attract smarter students? The Department of Education analysis released last month tried to answer this question by using statistical techniques to separate out the effects of parental income and education and similar factors. After doing so, the analysis found that public schools were better at the actual teaching, while private schools presumably were just better at attracting those students who would succeed whatever school they attended.

Mr. Peterson has concluded that the earlier report used a faulty method for sorting out these other factors. For example, when measuring family poverty, which tends to have a significant impact on educational results, the Department of Education relied on statistics on participation in Title I, a federal program for disadvantaged students. However, Title I money is more widely available to public schools. If at least 40% of a public school’s students qualify for free or reduced school lunch, the entire school can get Title I money. Even the regular students in such a school were counted as “disadvantaged” in the earlier study, effectively giving such a public school a pass if it failed to educate its better-off students.

Private schools, meantime, face more hurdles to receiving Title I aid and many don’t, or receive much less than the public schools. Those schools didn’t receive the same benefit of the doubt as public schools in the earlier report. After using different measures of how disadvantaged students were available in the same data-set, Mr. Peterson concluded that private schools in fact do a better job educating students in reading and math at almost every grade level. He’s cautious about interpreting his own results. “The results should not be understood as showing that private schools outperform public schools,” he warns, because at the end of the day the data aren’t necessarily suited to proving a causal relationship of any kind.

Then again, that’s the problem. The data used in both of these studies were compiled as part of the ongoing National Assessment of Educational Progress. Despite its grand name, even what sounds like a comprehensive study of education turns out to be open to conflicting interpretations.Mr. Peterson makes a case that the earlier study got it wrong, but we doubt his latest report will be the last word on the debate. That debate won’t do a thing to help those low-income parents who can see, plain as day, that their local public schools are not teaching their children to read. Whatever conclusions one draws from Mr. Peterson’s report, he has performed a valuable service in reminding everyone that statisticians will never agree on the meaning of test scores. Only vouchers can free individual children from the tyranny of dueling data.