The Knowledge Is Power Program, a charter school network known for lifting the achievements of poor children through high standards and long hours of work, benefits from significant private funding and student attrition, a new study contends.

The study from researchers at Western Michigan University, to be released Thursday, estimated that KIPP schools receive more than $5,000 a year per pupil through private donations in addition to regular sources of public funding. It also found that about 15 percent of KIPP students leave the schools each year as they progress from sixth to eighth grades — and that those students often are not replaced.

Gary Miron, the study’s author, said KIPP schools in Washington and elsewhere often outperform regular public schools. “But they’re not doing it with the same students, and they’re not doing it with the same dollars,” he said.

KIPP officials said that the study was riddled with errors because of flaws in the data that were analyzed.

“The questions they ask are the right ones,” said KIPP spokesman Steve Mancini. “We reject their conclusions.”

With 99 schools serving about 27,000 students, mostly from middle schools, KIPP is one of the nation’s most closely watched experiments in urban school reform. Typically, its students are in school nine hours a day. They also attend school many Saturdays and for two to three weeks in the summer. Philanthropists and federal officials often hold KIPP up as a model, because it gets strong results from disadvantaged students.

Mancini said KIPP estimates that its schools receive $2,250 to $3,250 a year per student in private funding, excluding capital funds. He said that KIPP does not seek to weed out students, citing a 2010 study by Mathematica Policy Research, which found that KIPP schools do not, on the whole, have higher attrition than comparable public schools.

However, KIPP officials acknowledge that their schools tend to have a lower share of students with disabilities or who are not fluent in English, relative to neighboring schools.

Michael Casserly, executive director of the Council of the Great City Schools, which represents urban school systems, said KIPP is widely admired among public educators. But, he said, the new study underscored that there are questions about KIPP’s relevance for regular schools.

“While they’ve taught us a great deal about what could work and what the circumstances might be for that work,” Casserly said, “it’s not always clear that their business model can be sustained over the long run, in the way that we need to sustain reform and improvement in the regular schools.”