The returns from Connecticut and New York removed a major doubt: the Kennedy for President campaign most definitely has a candidate. But the doubt that survives the Tuesday victories is whether the candidate has a presidential campaign.

In what has to have been a personally punishing five months, Edward Kennedy, whose stammering debut on the Roger Mudd interview made Yogi Berra sound like Abba Eban, has developed into a confident, forceful and, yes, articulate presidential candidate. Neither defeats nor diatribes have diminished his good humor. He is the unwhining professional who communicates a conviction that he is doing what he believes is important to do, and to do well.

The campaign is another question altogether. Coming off major upsets, it has already managed to forfeit one strategic advantage: the determination of which upcoming primaries are the most important. Kennedy spokesmen, after first insisting that Pennsylvania, another of the fabled "major industrial states," is the big test, have since been quoted on their intention to campaign now in Wisconsin and Kansas, which hold primaries next Tuesday. Somebody in the Kennedy campaign even revealed the previously well-kept secret that Louisiana is holding a primary on April 5.

The problem of campaign spokesmen is not a new one for the Kennedy campaign. It has no Bob Strauss to raise those issues or ask those questions that it would be inappropriate for Jimmy Carter to raise. Unlike the Carter campaign, the Kennedy campaign has not effectively used surrogates for the candidate. The only surrogates have been the Kennedy relatives, who may draw a crowd in some precincts, but rarely rate a paragraph in the papers.

The Kennedy campaign has raised money just about as well as issues. It is reportedly $1 million in debt. The only message emanating from the entire Kennedy campaign is the candidate's: what Edward Kennedy says or does on any given day. Perhaps one explanation of this problem is the failure to utilize professional polling. The campaign, without any pollster or data for most of the first two months, was unprepared for the initial negative reaction to Kennedy. But polling apparently is not in the budget, if indeed there is a budget. It is inconceivable that Kennedy, facing 25 primaries in nine weeks and living with the fact that his is a polarizing candidacy, could unilaterally disarm himself by failing to poll.

The failure to poll may explain some of the chaos in the Kennedy advertising effort. It is the responsibility of the candidate and the campaign leadership to define their message and the job of the advertising people to refine that message, to present it imaginatively and persuasively. The campaign has already employed three different political film makers, all with distinct styles and different approaches. A competent political communications effort is a vital component of a competent political campaign: the message put before the voters, whether in a campaign commercial during "Little House on the Prairie" or in a film clip of the candidate's speech on the 11 o'clock news, must be consistent and reinforcing. This is the campaign manager's job.

Unlike its candidate, the campaign has been testy. It is a campaign that began without a coherent theme and with a palpable arrogance. Every campaign leaves some important contributor on hold and forgets to invite a key endorser to the candidate's room. But most campaigns -- and all winning ones -- learn from their mistakes and make changes. John Burton, Kennedy supporter and congressman from California, exulted Tuesday night: "Today is the first day of the rest of the campaign." We will learn very soon whether any lessons have been learned over the past five months. And in the last analysis, his campaign is no more and no less than a mirror reflection of Edward Kennedy and a preview of the kind of administration he might run.

Kennedy, the candidate, carried the campaign in New York. In broadcast advertising, he was outspent by Carter by at least three to one and probably more. But, capitalizing on events, Kennedy, the challenger -- for the first time this political year -- made Carter, the incumbent, the issue in voters' minds. Tuesday's primary became an up or down decision on the president and his performance. And Carter flunked.

New York Democrats gave us the old Three-I League of politics.Every candidate ambitious for statewide office first paid his dues by completing the obligatory pilgrimage to Ireland, Israel and Italy. County Mayo always came before Rochester on the road to Albany.

Carter had been the superstar of the new Three-I League of American politics: Inflation, which he used to defeat Gerald Ford; Israel, which he all but singlehandedly brought to a historic agreement with Egypt; and Iran, which overnight transformed Weak Jimmy into Strong Jimmy. On Tuesday, the three I's were all catching up with Carter: Inflation was up and away; Israel was up in arms; Iran was up in the air.

Which brings us to the reason all the published delegate counts are interesting, but not really important. Thirty-four presidential primaries in 14 weeks is a matter more of chemistry than math. If New York and Connecticut truly signalled a basic change in the focus of this Democratic race from the character of the challenger to the competence of the incumbent, then the chemistry of the campaign has changed and the arithmetic -- the delegate counts -- will follow. But if Edward Kennedy is to be more in 1980 than the latest New York trend that did not sweep the nation -- more than the political equivalent of Lucite Q-Tips -- then he had better make sure he has a campaign as well as a candidacy.