Dallas — Four years ago men voted for Ronald Reagan over Jimmy Carter 56 percent to 36 percent. Women gave Reagan only a 47-to-45-point margin of their votes. Women voted at a higher percentage rate than men in the 1980 presidential election. And come this November, as many as 9 million more women than men may go to the polls.
These political facts, as much as the Geraldine Ferraro factor, help explain why the Republicans have pulled out all stops to boost the role of women at their national convention and to court the female vote this fall. They want no ''gender gap'' in 1984.
Women could well decide this election, say officials of the Reagan-Bush campaign committee.
The presence of GOP women here in Dallas is conspicuous. At the 1980 convention, women comprised only 29 percent of the delegates. This year women make up 44 percent of the 2,235 delegates - a gain brought about not through quotas, say Republican officials, with self-congratulation, but simply through persuasive efforts at the state and local levels.
Women are also being highlighted at the podium. Tonight women will second the nominations of President Reagan and Vice-President Bush. Earlier this week UN Ambassador Jeane Kirkpatrick, US Treasurer Katherine Ortega, and others were featured speakers, helping set the tone and themes of the campaign.
Significantly, however, the women at the convention are divided in their views of the President's and party's present position on women's rights and such issues as abortion.
Many, like Viola I. Prineas, a delegate from Carbondale, Ill., are unabashedly behind the President. ''Mr. Reagan has named more women to high office than any other president,'' she says. ''He may have a problem with a gender gap, but it is a radical group of women who made it one.''
''People expect too much too fast,'' comments LoVene Claypole, an alternate delegate from Springfield, Mo. ''Doors need to be opened, but I don't know that we need the ERA (Equal Rights Amendment).''
Moderate Republican women, although they seek the reelection of Reagan, feel frustrated that they are not better represented at the convention and that the conservative right has put its imprint on the party platform. As in 1980, the platform does not mention the Equal Rights Amendment, an initiative which the Republican Party first proposed in 1940 and supported until four years ago.
Even Maureen Reagan, the President's daughter, is unhappy about the party's abandonment of this proposed constitutional amendment.
The platform also contains strong anti-abortion planks, even though a majority of the delegates at the convention support freedom of choice.
Republican feminists are especially embittered by what they see as the conservative right's takeover of the party and the administration.
''We have operating in this party, under this administration, what might be called a political exclusionary rule,'' says Kathy Wilson, chairwoman of the bipartisan National Women's Political Caucus.
''Those who care about economic fairness are excluded. Those who care about arms control and reduction are excluded. Those who care about preserving the environment are excluded. And those who care about women's rights are excluded.''
Ms. Wilson suggests that ultimately, Republican women will stay with the party but abandon the ticket.
''It is reprehensible that rank-and-file Republicans were excluded from the official platform process,'' says Mary Dent Crisp, former co-chairman of the Republican National Committee, who is here as a private citizen. ''Given the party's position on women's rights, the future of the Republican Party looks bleak indeed.''
But party leaders view the situation quite differently. They believe that President Reagan's many appointments of women to high office, including the Supreme Court and the Cabinet, and the economic recovery account for his high popularity among women. According to GOP polls, Reagan is running ahead of Walter Mondale among women.
Campaign officials in fact argue that the real gender gap is actually a lag in support for Democrats among male voters.
''It is more Mondale who has a serious gender gap,'' says James Lake, spokesman of the Reagan-Bush reelection committee. ''Men lead women in their support of Reagan. So it's Mondale's male gap.''
Election analyst Richard Scammon also says that the gender gap is primarily a gap among men. In recent elections prior to 1980, women tended to vote Republican more than men and have showed little movement from one party to the other. Men, on the other hand, moved from plus 8 for Carter in 1976 to plus 15 for Reagan in 1980.
Republican Party leaders hope that the female delegates, fired up by the convention, will return home to work energetically for the ticket. The party is enlisting professional and business women to give speeches around the country about the Reagan record.
Both political parties are in fact making vigorous efforts to register women voters, train women campaign managers, and fund female candidates.Table: How men and women voted in presidential elections since 1952 1952 Stevenson 47% 42% Eishenhower 53 58 1956 Stevenson 45% 39% Eisenhower %% 61 1960 Kennedy 52% 49% Nixon 48 51 1964 Johnson 60% 62% Goldwater 40% 38 1968 Humphrey 41% 45% Nixon 43 43 Wallace 16 12 1972 McGovern 37% 38% Nixon 63 62 1976 Carter 53% 48% Ford 45 51 McCarthy 1 less than 1 1980 Carter 38% 44% Reagan 53 49 Anderson 7 6 Source: Galop Poll