THE holder of a doctoral degree in science or engineering would probably make a better taxi driver or bank teller than someone without a Ph.D. But if a newly minted doctor of science is hoping for a permanent, full-time job in his or her specialty, there is a 1-in-4 chance of being disappointed, according to a recent survey.

As if that were not bad enough news for young scientists, the authors of the report have concluded that increased government spending for scientific research, even if it were granted, would eventually make the job situation even worse.

The survey, supported in part by the Alfred P. Sloan Foundation and by Federal funds, was conducted by the Institute for Higher Education Research at Stanford University and the Rand Corporation, a Santa Monica, Calif., research institution with traditional ties to the Defense Department.

The study, which covered 13 science and engineering fields, 210 doctorate-granting institutions and more than 1,000 educational institutions that employ people with doctorates, was led by two economists, Dr. William F. Massy at Stanford and Dr. Charles A. Goldman at Rand, assisted by two graduate students, Marc Chun and Beryle Hsiao. They concluded that "universities in the United States are producing about 25 percent more doctorates in science and engineering fields than the United States economy can afford."

The group experimented with mathematical models designed to predict the effects of changes in conditions, and concluded that increasing government funding for scientific research would actually exacerbate the glut of Ph.D.'s in the long run.

By increasing research funding, Dr. Massy said, "the whole system will be expanding and people will get the kinds of jobs they were trained for.

"However," he adds, "as soon as you stop increasing it and go back to a steady state -- not a decrease -- all of a sudden the underemployment comes back. In fact, it comes back worse than it was before because the whole system has scaled up."

Professors whose research projects depend on cheap, competent help from a constant supply of graduate students are among the main offenders, they said, and it is time for university administrators and professors to throttle back the flow of graduate students passing through the educational system into very uncertain careers.

Surprisingly, the overproduction of Ph.D. degrees seems to be highest in computer science at present. The surplus of doctoral computer science degrees currently awarded over the number of those who get desirable jobs in their field is 50.3 percent, Dr. Massy said. (This figure does not represent an actual unemployment rate of 50.3 percent, but merely the current estimated imbalance between supply and demand.)

The job situation in other branches of science and engineering is better, the study found, but surpluses of supply over demand are still large; for example, 31.5 percent for physics, chemistry and mathematics; 26 percent for chemical engineering; 44 percent for mechanical engineering, and 23 percent for geological sciences. The survey found that demand actually exceeds current supplies of new Ph.D. holders in psychology, but Dr. Massy said the probable reason is that doctoral-level psychologists are often siphoned off into clinical jobs not included under the heading of science and engineering.

The findings of the new study closely parallel those of several recent studies by other academic and professional groups.

A task force created by the American Chemical Society and headed by Dr. David K. Lavallee, provost at City College of New York, reported in May that its preliminary findings "indicate an annual oversupply of chemistry Ph.D.'s in the work force of between 250 and 400."

The overall unemployment rate for chemists is low, only about 2.5 percent. But substantial numbers of chemists recently awarded Ph.D.'s are unable to find permanent, full-time chemical research jobs. Many therefore accept postdoctoral academic appointments as teaching or research assistants, usually for two years at a time with relatively low pay and little chance for permanent employment.

The chemical society task force calculated that if a postdoctoral appointment persisting for more than four years is considered unacceptable, 12.5 percent of recent Ph.D.'s are either unemployed or stuck in undesirable temporary jobs. If the desirable cutoff is assumed to be anything more than three years in a postdoctoral job, the percentage rises to 19.5.

To some extent, the gloomy job prospects for aspiring scientists have already affected the degree-granting institutions of the nation.

A recent report by the education and employment statistics division of the American Institute of Physics said that the number of first-year physics graduate students has dropped by 6 percent for the second consecutive year; about 2,900 students entered physics graduate programs in 1993-94, down from 3,300 in 1991-92.

Some universities have announced their intention to hold down enrollment in physics, and one, James Madison University in Harrisonburg, Va., has announced that beginning with the coming semester, it will no longer offer a physics major program at all. The contracts of the university's 10 tenured physics faculty members will be terminated in August 1996.

The outlook for young mathematicians also looks bleak. A survey by the American Mathematical Society of the 1,125 recipients of doctoral degrees in mathematics from July 1, 1990, to June 30, 1991, found "an alarming 12 percent of this population to be unemployed and seeking employment." This rate, according to Dr. Donald E. McClure, professor of applied mathematics at Brown University, was more than twice as high as for the previous year's crop of Ph.D.'s.

Holders of doctorates are not alone in facing the slump in scientific and engineering jobs. A survey by the National Science Foundation published this year concluded that the 1993 job market for recent college graduates in the sciences and engineering was significantly worse than it was in the late 1980's.

Dr. Goldman of Rand said in an interview that it had been "surprisingly difficult" to get reliable statistics on the sizes of university faculties in scientific and engineering disciplines, or on the rate at which academic positions become open, and that many sources of data had to be compared to calculate estimates.

Most science students tend to regard their professors as role models in research careers. But instead of becoming tenured faculty members like their teachers, many end up with temporary postdoctoral jobs or worse.

In a recent satirical essay published by the journal Nature, the British physicist and humorist David Jones chided television programs that "take up science on the absurd pretense that science is fun."

"In fact," he wrote, "there is no demand for scientists, as shown by their low salaries and dismal career prospects." Dr. Jones's tongue-in-cheek advice was to have a student float stock to pay for his studies, and let market forces shape his career.

"Suppose he wants to study physics," Dr. Jones wrote. "If the market feels him to be a rotten physicist, or reckons there are too many physicists already, he will find it hard to raise capital. His shareholders will steer him toward classics, advertising studies or wherever they see the best future returns."

Dr. Massy took a more sober view. Asked what he would advise children of his own who might be considering earning Ph.D. degrees in science, Dr. Massy replied: "I'd tell them, first of all, that they should not expect, as a matter of course, to be able to replicate the kinds of careers that their mentors have had, or that I have had. The job market is just too competitive to have any expectation of that. They might be very fortunate and achieve it, but the odds are against it.

"Having said that, if they have a true, deep and abiding interest in research, they certainly could give it a try," he added. "It's a wonderful career, if you achieve success. And if you have a deep interest in teaching, as some doctoral students do, this might not be a bad time, if they select their institution carefully.

"I think there will be renewed interest in the profession of teaching as opposed to the profession of research," Dr. Massey said.