Federal court reporters, those people who sit at silent little stenotype machines copying courtroom proceedings, then transcribe the dialogue, are fighting for their survival in the wake of a study suggesting that electronic tape recorders may do a more accurate and efficient job.

Transcript accuracy is especially crucial to the judicial system because what is said in the courtroom often forms the basis for appeals, particularly in criminal cases where a judge's improper instructions to a jury or a prosecutor's comments in closing arguments can get a conviction overturned.

The study, prepared by the Federal Judicial Center, a research arm of the judiciary, pitted electronic tape equipment against stenographic reporters in 12 federal courtrooms around the country.

Eighty-two cases, producing 17,815 transcript pages, were simultaneously recorded and then transcribed using both methods. When the two transcript versions disagreed on words or phrases, the original tape was consulted to hear which was right.

The tape recorders (and the typists who prepared transcripts from the recordings) were more accurate 58 percent of the time, according to the study. In addition, a comparison of costs found that, on a nationwide basis, the district courts could save $12 million a year by using tape recordings.

The tape recorders in the test sometimes encountered a familiar problem: breakdown. In one instance, five court sessions on five separate days were missed because of equipment malfunctions, the report said. Occasionally, it was also difficult to move the equipment from courtrooms to judges' chambers for conferences.

A full-scale analysis of the study has been commissioned by the National Shorthand Reporters Association, which has begun a public relations campaign designed to show that human beings can do the job better than machines. "Human beings have the ability to interpret and to understand the sounds they are receiving," said Jill Berman Wilson of the association. "That human beings have the ability to think and be rational produces a superior record," she said.

Wilson said important questions about the methodology of the study, particularly the cost estimates, need to be answered. The organization is now promoting the use of computer-aided transcription, in which the courtroom stenography is fed into a computer to produce transcripts more rapidly. * * *

AFFIRMATIVE ACTION . . . D.C. Superior Court Judge Gladys Kessler, president of the National Association of Women Judges, delivered one of the most outspoken speeches from a judge in years at the recent American Bar Association convention. The subject was "affirmative action" in the appointment of the nation's judges.

"Our present national leadership has made it clear, by its failure to name blacks to the federal bench and its near-total failure to name women, that it is disinterested in finding qualified women and minorities and that it is disinclined to engage in any outreach efforts to identify appropriate judicial candidates," Kessler said.

" . . . There can be no publicly perceived excellence within the judiciary until it sheds its public image of being overwhelmingly composed of white male lawyers from major law firms or prosecutors' offices," Kessler told a meeting of the ABA's Judicial Administration Division.

Kessler said she was not calling for a "quota system" for filling judgeships but an "aggressive and determined seeking out and recruitment of qualified members of historically under-represented groups . . . ."

She said that fewer than 7 percent of the federal district court judges and 8.5 percent of the federal appellate judges are women. Blacks account for 7 percent of the district court and 7.6 percent of the appellate bench, she said. One Hispanic sits on a federal appeals court, and Hispanics represent 3.49 percent of all federal district court judges.

In spite of Kessler's speech, the ABA's House of Delegates deferred action on a resolution saying it is wrong for judges to belong to clubs that discriminate against women and minorities. NEW APPEALS COURT

Supreme Court Justice John Paul Stevens expressed skepticism at the convention about Chief Justice Warren E. Burger's proposal, now before Congress, for a new national appeals court to relieve the Supreme Court of some of its load.

Stevens said the high court could solve its overload problem by exercising self-discipline in managing its caseload. "The court has the power" to deny review much more often than it does, he said.