COLUMBUS, Ohio, Nov. 3 - Proposed state constitutional amendments banning same-sex marriage increased the turnout of socially conservative voters in many of the 11 states where the measures appeared on the ballot on Tuesday, political analysts say, providing crucial assistance to Republican candidates including President Bush in Ohio and Senator Jim Bunning in Kentucky.

The amendments, which define marriage as between only a man and a woman, passed overwhelmingly in all 11 states, clearly receiving support from Democrats and independents as well as Republicans. Only in Oregon and Michigan did the amendment receive less than 60 percent of the vote.

But the ballot measures also appear to have acted like magnets for thousands of socially conservative voters in rural and suburban communities who might not otherwise have voted, even in this heated campaign, political analysts said. And in tight races, those voters -- who historically have leaned heavily Republican -- may have tipped the balance.

In Ohio, for instance, political analysts credit the ballot measure with increasing turnout in Republican bastions in the south and west, while also pushing swing voters in the Appalachian region of the southeast toward Mr. Bush. The president's extra-strong showing in those areas compensated for an extraordinarily large Democratic turnout in Cleveland and in Columbus, propelling him to a 136,000-vote victory.