The man selected to run the nation's largest educational testing service says he favors "some public scrutiny" of the testing system but is against the government acting as the watchdog.

Gregory R. Anrig, who will step down as Massachusetts' commissioner of education Sept. 1 to become president of Educational Testing Service in Princeton, N.J., also said that he would like to see more children have access to coaching for the Scholastic Aptitude Tests (SAT), perhaps through educational television.

Anrig will replace William W. Turnbull, whose 11-year tenure at ETS covered a period of widening controversy during which ETS came under fire for secrecy and for exaggerated claims of its tests' ability to predict academic success at college.

Its critics include the National Education Association and Ralph Nader, who sponsored a report on ETS charging that the tests were, in some cases, no more effective than a roll of the dice in predicting academic performance.

An ETS spokesman said of Anrig's appointment: "He's use to controversy. He's comfortable with it. He's been in the public eye. This was one of the factors in favor of his selection."

In an interview this week Anrig said he thought the controversy that has embroiled testing has been "healthy and has contributed to putting the tests in perspective. Although the tests will continue to be used by colleges and universities as a criteria for admission, Anrig said, the trend will be toward use of the tests to evaluate the needs of students being admitted.

This trend will be strengthened as declining enrollments reduce the ability of most colleges to pick and choose their undergraduates in the 1980s.

Anrig has testified in favor of a Massachusetts bill that would require the schools to return the state exams to students after they have been graded.

"If something is important enough to affect the life chances of an individual then this ought to be subject to some public scrutiny, said Anrig. "But better not the government. The government ought to stay out of that, just as it ought to stay out of textbooks. I think it is best left to the professions and to the media."