WASHINGTON — For more than a decade, House Republicans led by the former Speaker John A. Boehner have used school children in the nation’s capital as an experiment for school choice, funding a far-reaching voucher program to send poor children to private schools over the opposition of local teachers and unions.

Now, with Betsy DeVos, one of the country’s fiercest advocates of school choice, installed as education secretary, that experiment is poised to go national. But Ms. DeVos’s own department this week rendered judgment on the Washington school choice program: It has not improved student achievement, and it may have worsened it.

The examination of the D.C. Opportunity Scholarship Program, the only federally funded voucher program in the country, by the department’s Institute of Education Sciences, found that students who attended a private school through the program performed worse on standardized tests than their public school counterparts who did not use the vouchers.

Among students who attended poor-performing public schools — the targets of this and other voucher programs — there was no significant effect on achievement.