WHILE THE United States has made great progress toward reducing discrimination, it obviously has a distance still to go. One message of the Bakkie decision, though, is that statistics alone aren't an acceptable answer.

In each entering class the medical school of the University of California at Davis set aside 16 of 100 places for minority applicants. That's the arrangement that the U.S. Supreme Court threw out, with the result that Allen Bakke, at age 38, will at long last become a medical student.

Yet the Davis school has been by no means alone in leaning heavily on statistics. Federal agencies require businesses and universities to show that they've not discriminating in hiring, promoting and paying their employes. The proof has to be highly stastical, involving such techniques as multiple regressions.

For the nation's universities the enforcement agency is the Office of Civil Rights at the Department of Health, Education and Welfare. Last year George J. Borjas decided to see just how HEW itself would stack up against it own statistical tests.

The result? HEW flunks.

Borjas' findings appear in "Discrimination in HEW Is the Doctor Sick or Is the Patient Healthy?" a paper distributed by the Center for the Study of the Economy and the State at the University of Chicago. Borjas did his work while post-doctoral fellow in the university's department of economics; he now teaches at the University of California at Santa Barbara. His study will appear soon in the Journal of Law and Economics.

The study is based on a random sample of HEW employes collected by the Civil Service Commission. It centers on wage discrepancies between men and women and between whites and blacks - the same discrepancies that concern HEW when it finds them at universities.

HEW of course recognizes that the discrepancies often can be explained, at least in part, by factors other than discrimination. For instance, the agency recognizes that pay can vary because of the employe's department, his rank, his time in rank, the length of his experience.

The agency even acknowledges that there may be some variances not easily explained with a few simple numbers. But it's cautious about accepting any such discrepancies. In an agreement with the University of Michigan, for example, it says: "In no case will assertions, verbal or written, unsupported by specific comparative analysis be considered as justification for wage discrepancies."

In passing it is perhaps worth noting that in such cases the accused is always guilty unless he proves himself innocent. But that fact will come as no surprise to anyone experienced in dealing with federal agencies.

Here's how HEW employes stacked up in terms of average annual salaries for each ex-race group in the full-time permanent labor force:

White male $20,897

Black male $15,333

White female $13,395

Black female $11,642

The differentials are not altogether different from those in the economy as a whole, Borjas notes. "The female-male ratio is 66.1 percent in the economy. At HEW it is 73 percent."

At HEW as at the universities, there are those other factors to consider. So Borjas applied the same tests to HEW that the agency applies to the universities.

The findings? Borjas says that at least 39.8 percent of the wage gap between white males and the white females is due to discrimination - that is, it can't be explained by differences in observable personal characteristics. His results also suggest that about 35 percent of the male black-white differential is due to discrimination.

"These results," Borjas says, "raise important questions concerning HEW's handling of observed wage differentials in the higher-education sector. For example, suppose HEW argues that it does not discriminate against women and blacks, and the whole unexplained wage gap could be explained if only we could qualify unobserved productivity differences."

That may well be true. Some people simply produce more, and better, work than others of the same training and experience. How do you quantify superior judgment? How do you put a number on the ability to supervise the work of others?

If such considerations are to count for HEW, Borjas asks, shouldn't similar factors be counted at the universities? How, to give just one example, do you quantify a professor's ability to inspire his students?

If a university is found to be discriminating, punishment is easy: The government can simply cut off any federal funds. If HEW is found to be discriminating, Borjas slyly asks, what's to be done: "Is the next logical step to stop HEW's receipt of federal funds?" HEW, after all, has the largest budget of any federal agency.

Borjas is careful to stress that his purpose is not to accuse HEW of discrimination. It is merely to point out the difficulty, if not impossibility, of proving discrimination with the use of HEW's statistical techniques. As someone once said, statistics are much like bikinis. They reveal interesting figures but conceal essential details.

Policing discrimination isn't an easy job, and statistics, quotas and the like obviously simplify the tasks of administrators. But laws are not supposed to be administered for the convenience of the enforcers.

Movement toward a greater degree of equality in our society is surely desirable. But equity need not be sacrified in the process.