The two best known measures of President Carter's popularity, the Gallup Poll and Harris Survey ratings, may seriously distort the actual feelings of the public, a Washington Post study suggests.

In both instances, and quite dramatically in the Harris polls, the results make the President appear to have higher disapproval ratings than he may have.

Taken by themselves, they also tend to ignore or understate a key finding in The Post study: Jimmy Carter, the jury is still out. A great many Americans, perhaps almost half, say they neither approve nor disapprove the way he is handling the presidency but, instead, are neutral or uncertain or have mixed feelings.

Both Louis Harris and officials at the Gallup organization defended the validity of their ratings but agreed that they have to be read along with more detailed poll findings in order to be understood properly.

"I refuse to take the responsibility for people misreading our results." Harris said in a telephone interview, "but I do not worry about it."

Carter's approval ratings are considered to be of critical importance to him and to many aspects of national policy as well. As Robert Teeter, a pollster who worked for presidents Nixon and Ford, put it:

"The president's approval rating at any given time is a national issue. People look at it and assume the president is doing well or poorly. Ratings define the framework with which he operates with the press, the public and the Congress.

"Congress is reluctant to buck a president with a high approval rating. The whole press's attitude seems different according to the approval ratings . . . All discussion of Jimmy Carter is based on his last approval rating."

With so much at stake, however, both the Gallup and Harris ratings are based on the questions that lead to widely divergent findings and to depictions of public sentiment that appear simplistic and misleading. Both Teeter and Patrick Caddell, who conducts polls for Carter, agreed with that assessment.

The most recently reported Gallup Poll, conducted in mid-January, showed Carter with a 57 percent approval rating, a 27 percent disapproval rating and 16 percent undecided. The most recent Harris Survey, taken at the end of January, showed Carter viewed positively by 47 percent of the public but negatively by 49 percent, with 4 percent undecided.

"I agree that if a president goes down in the polls, then he is going down," Teeter said. "But that is not what is reported. What is reported is such a simple rating - say 56 percent negative - that suggests that more than half the people are against him. It sticks in people's minds. I look for the size of the disapproval rating, and the movement in direction, but I don't think the press or the public do."

Caddell, who is regarded as an influential force in the Carter White House, say that because of his position he could'nt "credibly get into a discussion of outside pollsters about their measures." He did say, however, that "a perception among elites that the President is in deep trouble" - a feeling that many borne out by his own ongoing polls.

In fact, Gallup and Harris do report attribute to his poll ratings - is not more than their overall ratings. What sticks in people's minds, however, may be something else.

What appears to cause the wide diergence between the Gallup snd Harris ratings is the difference in the wording of the questions they use to assess a president's job performance. Gallup asks, "Do you approve or disapprove of the way Jimmy Carter is handling his job as president?" That formulation tends to force people to take one view or the other, since it offers no in-between position. Gallup has been asking the question the same about presidents since the 1930s.

Harris asks, "How would you rate the job Jimmy Carter is doing as president? Would you say he is doing an excellent, pretty good, only fair or poor job? He says he has been making that question since 1963. Harris treats "only fair" as a negative response, so his formulation, like Gallup's, leaves respondents no middle position.

After noting continuing dissimilarities in Gallup and Harris findings, and because of the political importance of the matter, The Washington Post undertook a national survey of its own in an attempt to find out why the differences were so great.

In telephone interviews during the last week in January, 1,519 adults were asked to rate Carter's job performance in three different ways: in answer to the Harris question, in answer to the Gallup question and in answer to a third question that allowed them to take a middle position.

The third question was, "Suppose you were to grade President Carter, A, B, C, D, or F for the way he is handling his job as president. What grade would you give him?"

By comparing how respondents answered all three questions, certain clear trends emerged, First, while Harris treats "only fair" as a negative response, the majority of people who rate Carter that way do not.

More than four in 10 people rated Carter "only fair." It was the second most widely chosen category, closely following "pretty good."

But those who said "only fair" in response to the Harris question, only 45 percent, less than half, said they disapproved Carter's job performance in response to the Gallup question. On the other hand, 46 percent of those who said "only fair" actually approved Carter's job performance when asked to rate Carter in the Gallup manner.

In addition, 55 percent of those who chose the "only fair" rating in answer to the Harris question gave him a "C" - essentially neither favorable nor unfavorable - when offered that middle category. Only 21 percent assigned him a "D" or an "F."

The total Harris ratings shift drastically when matched against how the same people see Carter if given an in between choice. In The Post survey, respondents were 48 percent positive, 48 percent negative and 4 percent undecided in answer to the Harris question, results very close to Harris's own latest findings.

If those who gave Carter a "C" are left out, however, the Harris results are 41 percent positive and 17 percent negative. The total viewing Carter negatively is cut by two-thirds.

The new question introduced in The Post survey may have problems of its own: "C" obviously represents a mediocre rating to some, an average rating to others, or an expression by still others that they have not made up their minds.

Nevertheless, the shift of so many "only fair" choices to a "C," and a substantial number of other "only fairs" to a "B" as well, strongly suggests that Harris is on the wrong track when he lists "only fair" as a negative rating.

Harris is not exactly unfamiliar with that complaint. "Every president since Eisenhower has always come up with the same thing," he says. "'Isn't only fair really positive?'" He says that "when you asked people why they say 'only fair,' you get negatives back." Despite that, Harris appeared so concern by The Post's findings that he said he might change his question in the future.

Different kind of change occur when answers to the Gallup question are examined. Overall, the Gallup question drew 62 percent approving Carter's job performance, 28 percent disapproving and 10 percent undecided or not answering.

One apparent reason for that comparatively high approval rating is that many people whose feelings fall in between would rather say something nice about the president than something bad. For them it is harder to say "disapprove" than "approve" and the absence of a middle position pushes them to a favorable response, the opposite of what occurs in the Harris polls.

Thus, while the Harris findings tend to deflate Carter popularity, the Galllup findings appear to inflate them. However, according to The Post's survey, a much smaller but still sizeable segment of the in-between population is also drawn to the negative side the Gallup measure.

When those rating Carter with a "C" are left out, the Gallup results became 40 percent expressing approval of Carter's job performance and 16 percent disapproval. Those figures represent a decline of 22 percent and 12 percent, respectively.

So what Robert Teeter considers to be the key numbers - the ones expressing outright disapproval - are cut almost in half when a middle grade is introduced in the Gallup measure.

Viewed this way, only one in six Americans appears to disapprove Carter or have an overall negative view of his job performance, rather than the three in 10 or one in two that Gallup and Harris have been reporting. More than 40 percent are neither approving nor disapproving.

Carter as president becomes quite similar to Carter as candidate: a puzzle to a great many. Those who may like one aspect of his job performance but dislike another, those who feel it is too soon to tell, in other words, those with all manner of middle or uncertain positions - suddenly loom larger.

Andy Kohut, executive vice president of the Gallup Organization, took issue with some procedures in The Post's survey, saying that an individual's "response to the Gallup question (which was asked last in The Post survey) has to be colored by the response he gave in the prior questions."

One independent polling expert, Albert H. Cantril, president of the National Coincil on Public Polls, said that such a bias was possible but not indicated from the results. He also said that even if such a bias existed, it would not seem to affect the thrust of the Post study's findings. "I have no trouble with your argument," he said.

Kohut also said, "If you gave a respondent a middle position, he is going to take it . . . Our questioning objective is to divide people into favorable and unfavorable camps." As did Harris, Kohut pointed to the need to review more than just the overall rating to obtain an understanding of public sentiment about a president. "People tend to look at one number. We're producing more than one number," he said.

Allec Gallup Jr., vice president of the firm begun by his father, George Gallup, said in an interview that he feels the presidential ratings "are only relatively important. We feel they are reflective, and on a trend basis they are important. In abssolute terms. I don't think any of them mean a damn.