Yet a new analysis from the Georgetown University Center on Education and the Workforce (CEW) suggests that, despite the undeniable progress, female candidates continue to face a significant headwind that has absolutely nothing to do with their abilities or qualifications: 13% of Americans—or roughly one in 10—still believe men are better “emotionally suited” for politics than women.

That’s a question researchers have been asking via the General Social Survey since the 1970s (which explains the dated-sounding turn of phrase). And although it doesn’t specify what, exactly, the respondents believe women’s emotional shortcomings to be, Nicole Smith, chief economist at CEW and co-author of the report, says the “subtext” of the question is clear.

“When you use the word ’emotion’ and you put it in the same sentence ‘women,’ it’s playing to the stereotype that when it comes to very important decisions… women might be more likely to make an emotional determination with their heart, rather than with their head,” Smith told Fortune. “Part of the concern here plays to the stereotype that women can be hysterical, that women can fly off the handle—that women shouldn’t have their finger on the button.”

But while it’s depressing to see that the tired old trope of the “hysterical woman” persists, the analysis also shows that stereotype is on the wane. The share of Americans who said men were better suited to politics peaked at about 50% in 1975 and had been trending downward ever since. The researchers found that many of the distinctions about who is mostly likely to buy into the idea that women are less suited are breaking down. For instance, the gap between younger and older respondents has narrowed dramatically over the past decades.

There are, however, still two factors that have a significant influence on how one views this issue: political affiliation and education. The analysis shows that “strong Republicans” of both genders are almost three times as likely as “strong Democrats” to show bias against women in politics. On the education side, Americans with less than a high school diploma are almost twice as likely as those with a bachelor’s degree to say men were more emotional suited for the political arena.

For female candidates, the implications are clear. Thirteen percent could easily be, as Smith puts it, “the difference between winning and losing”—especially when women face an uphill battle on “likability” and superficial judgements on everything from their facial expressions to their clothing.

“Women are not starting at the starting line,” says Smith. “Women are starting four or five paces behind.”