WASHINGTON -- The Department of Education has acknowledged using flawed data in a study on the impact of race on student loan repayment rates, having omitted black students from its calculation. The analysis was conducted during the debate over gainful employment regulations, in response to complaints that the rules would hurt colleges that enroll relatively high percentages of minority students.

Department officials disclosed the error in a December court filing, which is part of the ongoing legal challenge to gainful employment by the Association of Private Sector Colleges and Universities, the primary for-profit trade group. That lawsuit appears to have led to the mistake’s discovery.

The Obama administration designed the federal rules in an attempt to ensure that most programs at for-profit colleges and certificate and vocational programs at nonprofit institutions prepare students for "gainful employment." For programs to be eligible for federal financial aid, they must adhere to benchmarks related to student loan repayment and debt-to-income ratios.

The original analysis was included in the introduction section of the final rules, which were issued last June. It asserted that the “percentage of the students that are members of a minority group explains 1 percent of the total variance in repayment rates” at for-profit institutions. The low figure, the department concluded at the time, meant the racial composition of students was not a statistically significant contributor to how an institution stacks up on loan repayments. The percentage of lower-income students an institution enrolled was a better measure.

But by failing to count black students, the study understated the impact of race: the actual variance is 20 percent over all, the department said in the December filing.

Eduardo Ochoa, the department’s assistant secretary for postsecondary education, described the mistake in that filing, but said accurate figures would have had no impact on the final regulations.

A subsequently corrected analysis “does not justify altering the regulations,” Ochoa said, because “factors other than student demographics account for the success or failure of institutional repayment rates.”

The for-profit association, however, said in a January court filing that the mistake is fundamental and validates concerns aired by scores of public commenters that for-profits were unfairly targeted by gainful employment regulations.

“The department’s error demolishes its decision to reject commenters’ concerns about the relationship between its regulations and race and educational opportunity,” the association said. “This error, by itself, requires that the regulations be vacated.”

Monday's Federal Register contained the department’s correction, which noted that the final regulations remain unchanged.

"We've known for a long time that race and poverty are linked," Justin Hamilton, a department spokesman, said in a written statement. "But the data shows that demography is not destiny and can't be used as a reliable indicator for predicting loan defaults, most especially at for-profit colleges."

The publicly acknowledged mistake is certain to fuel claims by for-profits and their advocates here that the sector is being picked on by lawmakers and politically motivated regulators. They point to what they see as a pattern of flawed data or other information being used by the department, the U.S. Senate Committee on Health, Education, Labor, & Pensions and, perhaps most notably, the Government Accountability Office.

Critics of for-profits, however, say the industry has pored over language in federal documents to look for procedural mistakes in an effort to undermine legitimate concerns about their practices.

Last April, the Education Department said it had made an error in tabulating draft loan default rates that reflected poorly on for-profits, having improperly included loans that defaulted up to three months after the three-year period that was being measured.

Ochoa, in his statement, said Pell recipient rates remain more significant in the corrected analysis. Pell rates explain 23 percent of the variance while minority enrollment accounts for 20 percent, he said.

However, the association said in its filing that the department’s revised figures show that race is a significant predictor of loan repayment rates. “The public policy consequences of the department’s error are clear -- schools that enroll a higher percentage of minority students are more likely to fail the department’s repayment test.”

(Note: This article has been updated from an earlier version to correct erroneous references to statistics and to add a comment from the Department of Education.)