The Education Department this week sent Congress a study of private schools, including survey data showing that 5.6 percent public-school children's parents who knew about tuition tax credits said they would be "very likely" to put their children in private schools if the federal government provided a $250 credit.

Missing from the study, however, were assumptions--based on the survey data--that tax credits would prompt 1.9 million public school children to enroll in private school, significantly increasing the price tag put on the Reagan administration's tuition tax credit legislation.

According to Education Department officials and Dr. Joel Sherman, who headed the congressionally mandated School Finance Project study, the data were deleted because some officials questioned whether it was fair to calculate cost on the assumption that people will do what they tell a pollster they intend to do.

However, Gary L. Bauer, one of the education officials who reviewed the draft report, wrote a memo to Sherman's boss recommending that the section be deleted, saying: "My fundamental concern is that the secretary not be asked to send material to the Congress that contradicts the administration's position (especially with respect to tuition tax credits) and is not technically defensible on professional grounds."

In an interview yesterday, Bauer pointed out that he was not in charge of the study and was one of several officials in other divisions of the department who quarreled with some of the report's conclusions.

"It raised the costs of the legislation with data that was highly suspicious from a technical point of view," Bauer said.

"Certainly any Cabinet member would be remiss to send something to the Hill that contradicted administration policy, particularly when the technical information supporting it was inadequate," he added.

The Congressional Budget Office has estimated that the administration's bill--which would phase in over three years a maximum credit of $300 for families with incomes under $40,000--would come to $2.8 billion in its first five years, based on the number of children who would be eligible among the 5 million now attending private school.

The CBO did not estimate the number of children who might switch from public to private schools if credits were put in place. A Treasury Department cost figures, which roughly paralleled the CBO's, did include estimates of switchovers, but at a rate far below that indicated in the Education Department survey.

The push for tuition tax credits, which has been a centerpiece of the administration's educational policies, apparently was helped last month when the Supreme Court upheld the constitutionality of a Minnesota law allowing income tax deductions of up to $700 for elementary and secondary educational expenses.

That deduction applied equally to parents of children in both public and private schools; the administration's tax credit bill applies only to private school expenses.

The legislation, which offers reduced credits to those with incomes between $40,000 and $50,000 and nothing to families with incomes above $50,000, is pending before the Senate Finance Committee.

According to Education Week, a private publication that first reported the changes in the study, the draft version was completed in March and the revised version in early June. Bauer's memo--officially designated a memo of "nonconcurrence"--was dated April 21.

The final report was sent Monday to Rep. Carl D. Perkins (D-Ky.), chairman of the House Education and Labor Committee. Perkins' staff provided a copy to The Washington Post.

Among the study's conclusions:

Parents most likely to switch to private schools, according to the survey data, "tended to be blacks, Hispanics, children from lower-income and less-educated families, and residents of central cities." But these parents, according to the report, tended to know less about tax credits than the other people surveyed.

About one-fourth of public-school parents surveyed had considered switching their children to private school. The main reasons cited for not making the switch were "cost and logistical considerations . . . . "

A factor that the researchers tried to take into account in making their calculations, Sherman said, was the availability of private schools.

Sherman said yesterday that while his research group originally "did not think it unreasonable to set hypothetical examples" and extrapolate from them, "there were some legitimate methodological questions raised. I guess that, on balance, given the limitations of an extrapolation, the methodological concerns were not ungrounded."