Discrimination against women is seen as one of the possible causes behind their underrepresentation in certain STEM (Science, Technology, Engineering, and Mathematics) subjects. We show that this is not the case at the competitive exams used to recruit almost all French secondary and postsecondary teachers and professors. Comparisons of oral non gender-blind tests with written gender-blind tests for about 100,000 individuals observed in 11 different fields over the period 2006-2013 reveal a bias in favor of women that is strongly increasing with the extent of a field's male-domination. This bias turns from 3 to 5 percentile ranks for men in literature and foreign languages to about 10 percentile ranks for women in math, physics or philosophy. These findings have implications for the debate over what interventions are appropriate to increase the representation of women in fields in which they are currently underrepresented.