Even voters who worried that fathers might shortchange either their young children or their office were reassured if the candidates issued statements addressing that concern. But they continued to hold the strongest doubts about married mothers of young children after they issued similar statements.

“We confirmed that traditional gender roles are still powerful, influencing what we perceive to be acceptable and appropriate behavior for men and women,” said Adrienne Kimmell, executive director of the foundation. “For example, despite sweeping societal changes, many people still assume motherhood is a central role for women. That, in turn, affects how they view women candidates.”

Many women who have run for office echoed the study’s findings.

Jane Swift, who was pregnant while she was campaigning for lieutenant governor of Massachusetts in 1998, set off a national debate about political office and motherhood. Later, she drew criticism for asking aides to babysit for her daughter and for using a state helicopter so she could fly home to see her when she was sick and avoid Thanksgiving traffic. Her pregnancy with twins when she was serving as acting governor renewed the debate.

Ms. Swift believes a double standard still operates.

“The governor dad who takes his kids along to the county fair is a huge political asset, but it doesn’t work as well for the governor mom,” said Ms. Swift, now the chief executive of Middlebury Interactive Languages, an education company. “Being with children was seen as being distracted from doing your job. I found that part of my challenge was that whenever folks started to think about my children, it just took all the oxygen out of the room. Nobody knew all the work I was doing on educational reform or the work I did to improve the lives of foster children.”