Obama doubled down on this theme Tuesday at an Ohio rally: “When a guy is ambitious and out in the public arena and working hard, well, that’s okay. But when a woman does it, suddenly you’re all like, ‘Well, why is she doing that?’”

The comments come as Obama reaches out to undecided male voters, urging them to reflect on why, exactly, they may dislike Hillary Clinton. Rejecting her policy stances is one thing. Aversion based on a gut feeling, he suggests, might be sexism.

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“I want you to think about it because she is so much better qualified than the other guy,” Obama said at the Ohio rally. “She has conducted herself so much better in public life than the other guy.”

Politics aside, Obama is invoking a social phenomenon researchers have studied for years. “Ambitious” tends to be a compliment for men and a critique of women. That’s partly because a woman’s likability in the workplace (or on the campaign trail) isn’t tied to her knowledge or boldness or ability to lead, studies show. She is rewarded for projecting warmth, but penalized for appearing power-hungry.

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Men, however, generally aren’t punished for status-climbing. People tend to expect them to reach higher — and assume, perhaps subconsciously, that women are better equipped for the domestic sphere.

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“This conclusion is all too familiar to the many women on the receiving end of these penalties,” wrote Stanford University’s Marianne Cooper, who conducted research for Sheryl Sandberg's “Lean In.” “The ones who are applauded for delivering results at work but then reprimanded for being ‘too aggressive,’ ‘out for herself,’ ‘difficult,’ and ‘abrasive.’”

Male leaders, on the other hand, “are able to express dominance . . . in ways that female leaders are not,” observed business professors Melissa Williams and Larissa Tiedens in a 2015 Psychological Bulletin paper. “Past research has established, for instance, that employees must be seen as likable as well as skilled to be hired or promoted — competence alone is insufficient.”

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Consider a 2003 case study from Columbia University, in which researchers described a fictional entrepreneur to a group of business students. They told half the students that the founder’s name was “Howard,” while the other half thought they were hearing about “Heidi.” The fictional characters boasted identically successful resumes, but the students rated Howard as someone they’d enjoy as a colleague, while *they said* Heidi seemed less appealing, even selfish.

A 2010 Harvard study, meanwhile, found that female politicians who sought power came off as uncaring, but male politicians who did the same didn’t incur the same reputation.

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Clinton herself experienced a drop in popularity upon launching her second presidential campaign. In January 2013, after serving four years as secretary of state, her approval rating stood at 69 percent — “an overwhelmingly popular figure on the national political stage,” wrote the Wall Street Journal’s Patrick O’Connor.

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A week before Election Day, though, her approval ratings hover closer to 40 percent.

“The wild difference between the way we talk about Clinton when she campaigns and the way we talk about her when she’s in office can’t be explained as ordinary political mudslinging,” wrote author Sady Doyle in a piece last year for Quartz. “The predictable swings of public opinion reveal Americans’ continued prejudice against women caught in the act of asking for power.”