It is one of the most famous social-science papers of all time. Carried out in the 1990s, the “blind audition” study attempted to document sexist bias in orchestra hiring. Lionized by Malcolm Gladwell, extolled by Harvard thought leaders, and even cited in a dissent by Justice Ruth Bader Ginsburg, the study showed that when orchestras auditioned musicians “blindly,” behind a screen, women’s success rates soared. Or did they?

Nobody questions the basic facts that led to the study’s publication. During the 1970s and ’80s, America’s...