I looked at the article from 2012 you linked and followed the link to pnas where this was published in 2015 titled "National hiring experiments reveal 2:1 faculty preference for women on STEM tenure track"

Part of the abstract:

National randomized experiments and validation studies were conducted on 873 tenure-track faculty (439 male, 434 female) from biology, engineering, economics, and psychology at 371 universities/colleges from 50 US states and the District of Columbia. In the main experiment, 363 faculty members evaluated narrative summaries describing hypothetical female and male applicants for tenure-track assistant professorships who shared the same lifestyle (e.g., single without children, married with children). Applicants' profiles were systematically varied to disguise identically rated scholarship; profiles were counterbalanced by gender across faculty to enable between-faculty comparisons of hiring preferences for identically qualified women versus men. Results revealed a 2:1 preference for women by faculty of both genders across both math-intensive and non–math-intensive fields, with the single exception of male economists, who showed no gender preference.

These results suggest it is a propitious time for women launching careers in academic science. Messages to the contrary may discourage women from applying for STEM (science, technology, engineering, mathematics) tenure-track assistant professorships.

Here some quotes:

Our findings, supported by real-world academic hiring data, suggest advantages for women launching academic science careers.

Real-world data ratify our conclusion about female hiring advantage. Research on actual hiring shows female Ph.D.s are disproportionately less likely to apply for tenure-track positions, but if they do apply, they are more likely to be hired, sometimes by a 2:1 ratio.