Despite some recent progress, women still struggle to rise to leadership positions, whether in government or corporate C-suites. Even though Indian women are completing post-graduate studies at the same (or higher) rate as men, their presence in the workforce declines the higher up corporate ladder you look. Something, clearly, is preventing women from rising to senior-most positions.

Academics and activists have theorized that it’s the burden of family care that society places on women, or the threat of workplace sexual harassment and bias, or even a lack of workplace ambition. But what if one of the reasons women have such a hard time becoming leaders is that we subconsciously don’t want them to? A new study, published in the journal Sex Roles, found that prejudice against female leaders is stronger than we might think, likely because people hide their biases about women in power.

Using an indirect questioning technique designed to get to the root of people’s true feelings about women leaders, researchers found that men and women are significantly more prejudiced against women in power than results from direct questions indicate. When granted full confidentiality, 28% of women and 45% of men in the sample indicated they considered women to be less qualified for leadership positions than men. Across the two study methods, men showed more prejudice than women.

However, interestingly, the delta between expressed prejudice in response to direct versus indirect questions was far higher in women than in men, indicating that women’s responses differed more when they believed the responses were confidential.

“This pattern suggests that women are much more reluctant than men to express their prejudice against women leaders. Perhaps because women feel obligated to solidarize with members of their in-group,” explains study author Adrian Hoffmann, of the Heinrich-Heine-University Düsseldorf in Germany.

This study illustrates how gender stereotypes and bias can differ in an anonymous setting — and may influence personnel decisions in subtle, unspoken — perhaps unrecognized — ways. While social norms have progressed enough that people feel too ashamed to admit they harbor prejudice against women in leadership positions, they still haven’t progressed far enough to actually change that prejudice. Until that happens, the gray area between what people really believe, and what they think they are supposed to believe, is an interesting area for future study. Only when we really understand the roots of gender bias in leadership can we really start addressing it.