Yahoo chief executive Marissa Mayer and US presidential candidate Hillary Clinton have it tough.

Activists investors say that Mayer should be fired for mismanaging Yahoo, and Clinton is fending off criticism for her use of a private email server and for taking large speaking fees from Goldman Sachs.

There is no doubt both leaders have made mistakes. And yet Mayer and Clinton have also done many things right. So as professional women watch these female leaders, they inevitably ask: would a female chief executive in the tech industry, where male leaders outnumber female leaders four to one, and the only woman to be this close to becoming president of the United States be judged differently if they were men?

Research suggests they would be. Victoria Brescoll, a social psychologist at the Yale School of Management who studies gender stereotypes, was curious about how people evaluate women who make mistakes in traditionally male occupations. She and her colleagues gave participants a fictional news story about a police chief in a major city preparing for a big protest.

Several hours in, the protest got out of hand and the chief dispatched squad cars. In one version of the story, the chief didn’t send enough officers, and 25 people were seriously injured.

Did it matter whether the police chief who made the call was male or female? Yes. When a male police chief found himself with 25 injured civilians, his rating as an effective chief dropped by about 10 per cent. When a female police chief made the same mistake, her ratings dropped by almost 30 per cent. Participants reading the story also wanted to demote her, but their counterparts did not want to demote him.

In another version of the story, the protest was successfully pacified when the chief sent squad cars. No one was injured and the protest didn’t escalate. Participants gave both leaders high marks, which means a female leader wasn’t automatically seen as a poor fit – just when she experienced a perceived failure.

Brescoll and her team looked at two other traditionally male jobs with considerable power: the chief executive of an engineering firm and the chief judge of a state supreme court. The pattern persisted.

Was there a situation in which a man was judged more harshly for making a bad call? There was – a male president of a women’s college. In this role, often played by women, men paid a price for showing poor judgment.

Brescoll's team concluded that people find it easier to accept a poor decision when it's made by a leader in a gender-appropriate role. Leaders are more severely judged when they make mistakes in the other gender's territory. But until we associate women with leadership roles, mistakes will remain much more costly for them. – Copyright Harvard Business Review 2016 Therese Huston is the author of the forthcoming book How Women Decide: What's True, What's Not, and What Strategies Spark the Best Choices.