Thanks to a new federal report comparing public and private schools, there’s no doubt that public schools have one huge advantage: the leaders of their unions are unrivaled masters of spin.

They didn’t merely celebrate the report’s release on Friday, they complained that the Bush administration tried to bury it by releasing it for the weekend. They spun so well that the report was treated as a public-school triumph that “casts doubt on the value of voucher programs,” as The Wall Street Journal described it.

But if anything, the report from the Education Department did just the opposite. It concluded, after compensating for socioeconomic differences and other factors, that public-school students score slightly better on tests in fourth grade, while private-school students score slightly better in eighth grade. Given a choice, would you rather be ahead in the fourth inning or later in the game?

But even if you ignore that trend, even if you focus on the overall similarity of the scores in both types of school, that’s still bad news for public schools. Their students ought to be scoring higher if you believe in the unions’ favorite prescription for improving education: more money.

Most private schools are not places like Exeter or Dalton. They’re Catholic parochial schools and others on lean budgets. According to federal surveys, the typical private school’s tuition is only about half what a public school spends per pupil.

The public schools are spending more even if you exclude their expenses for special education, buses, lunch programs and central administration, as William Howell and Paul Peterson found in a study of New York elementary schools. The political scientists calculated that the public schools were still spending twice as much per pupil as were the Catholic schools in New York.

General Motors would not celebrate the news that its $40,000 Cadillac performed almost as well as a $20,000 Honda. It would not have its dealers put up signs reading: “Why Pay Less? Our Cars Are Nearly As Good.” But that’s the logic of the teachers’ union leaders who want to prevent students from getting vouchers and taxpayers from saving money.

For fans of public schools, about the only bright spot in this new study is that it’s not as damning as previous comparisons, but that’s because it’s a much less rigorous study. Its authors caution that it’s of “modest utility,” and other scholars think that’s too kind. Some critics fault its methodology and say it understates the advantages of private schools, and some don’t think this kind of comparison can prove anything.

The best way to compare schools is not to simply look at test scores one year, because it’s impossible to account for the students’ intrinsic advantages and disadvantages, and their varying motivations for choosing one type of school over another. Researchers can try to control for factors like family income and ethnicity or race, but these are crude measures.

Why, for instance, do some poor parents switch to a private school while their equally poor next-door neighbors are content with public school? Are the private-school parents more motivated because they put more value on education? Or are they just more desperate for a change because their children were doing much worse in public school than the children next door?

The most scientific way to compare schools is with the kind of randomized experiment that has been conducted in New York, Dayton and Washington. In these cities, students from low-income families were given a chance to apply for school vouchers. After the vouchers were awarded by lottery, researchers tracked the voucher students in private schools and compared them with a control group: the losers of the lottery who remained in public school.

After three years, the white and Hispanic voucher students were doing as well as their counterparts in public school, and the African-American voucher students were testing a full grade level higher than the blacks in the control group. The parents of all the voucher students — white, Hispanic and African-American — reported that there was much less fighting, cheating, vandalism and absenteeism in their schools than did the public-school parents.

Even though the private schools spent less money per pupil than the public schools, the parents were much more satisfied with them. Happier parents, better students, lower costs — those are the clear advantages of private schools and voucher programs. No wonder the teachers’ unions are so busy spinning.