Reagan administration changes in the program of Aid to Families with Dependent Children will save the federal government only $434 million in fiscal 1982, instead of the $1.026 billion it expected, a survey by the American Public Welfare Association concluded yesterday.

The survey showed that slow state implementation of the changes voted by Congress accounted for part of the difference, but that even if all changes were fully implemented right away, the estimated federal saving would only be $562 million.

The association of public welfare officials and agencies, which favors big federal payments and objects to much in the administration's approach, gave these reasons for the difference in the calculations:

The government used out-of-date and inaccurate earlier survey data to project the expected $1.026 billion savings.

The administration predicted 400,000 families would go off the rolls, and benefits would be reduced for 258,000 more, but the APWA said its survey showed only 310,000 going off and 415,000 with reduced benefits. "Thus, aggregate savings will be much lower than expected," it said.

The recession probably is causing more families to become eligible and others to get higher benefits because their earnings are less.

Interaction of AFDC cuts and those in other programs may have left more families eligible, and for greater benefits, than anticipated.

No state chose to count food stamps as income, and only one chose to count housing aid as income. The APWA said the administration had erroneously expected to save $100 million by counting food stamp and housing aid as income.

It had expected to save $374 million by including more income from employment and other sources in computing benefits. But the estimated saving from that change, even if the program had been fully implemented immediately, was only $157 million.

It had also expected to save $115 million by recouping overpayments, but the full-year figure was put at only $26 million.

However, on the provision limiting eligibility to families whose income totaled less than 150 percent of the state standard of need, the survey estimated a $92 million federal saving, whereas the administration had expected only negligible savings.

The APWA survey also said that savings for the state-financed share of AFDC would be $387 million if the program were fully implemented. That is half the original administration estimate.