How about FactCheck.org

http://www.factcheck.org/2012/06/obamas-77-cent-exaggeration...

"that’s the median (midpoint) for all women in all jobs, not for women doing “the same work” or even necessarily working the same number of hours. Furthermore, the raw gap for all women is not quite as large when looking at weekly earnings rather than yearly earnings."

"Female bookkeeping clerks and stock clerks actually made slightly more than their male counterparts, for example. Registered nurses made nearly 96 percent, elementary and middle school teachers made 91 percent, secondary school teachers made 94 percent, and police officers made 99 percent."

"however wide or narrow the gap, discrimination by employers isn’t responsible for all of it. In fact, a women’s pay specialist in Obama’s own Department of Labor — even as she was arguing that pay discrimination is not a “myth” — said research shows discrimination accounts for less than half of the raw pay gap."

"flatly wrong to say that women are paid 77 percent of the pay of men for the “same work.” And the fact that women’s median annual earnings are 77 percent of men’s isn’t all or even mostly due to discrimination, as the ad implies."

Or a Study by the CONRADD Group
https://www.shrm.org/hr-today/public-policy/hr-public-policy...

" Statistical analysis that includes those variables has produced results that collectively account for between 65.
1 and 76.4 percent of a raw gender wage gap of 20.4 percent, and thereby leave an adjusted gender wage gap that is between 4.8 and 7.1 percent.... Additional portions of the
raw gender wage gap are attributable to other explanatory factors that have been identified in the existing economic literature, but cannot be analyzed satisfactorily using only data from the 2007 CPS. Those factors include, for example, health insurance, other fringe benefits, and detailed features of overtime work, which are sources of wage adjustments that compensate specific groups of workers for benefits or duties that disproportionately affect them. Analysis of such compensating wage adjustments generally requires data from several independent and, often,
specialized sources.

"The size and pattern of quantitative results found in those studies and their coherence with the corresponding quantitative results in this study indicate that the results in this study describe wage differentials experienced by people who actually interrupted their careers, rather than wage adjustments imposed broadly on groups of workers with specific attributes"

Basically they conclude that there is a small pay gap, that is often attributable to other factors then gender discrimination such as employers that offer more family benefits longer vacations and have more lack sick time policy often pay less as well. In additional to many women taking more time off for leave after having a child than a man does, this interruption in work experience has a negative impact on earning potential

Time has some good sources

http://time.com/3222543/wage-pay-gap-myth-feminism/
"No matter how many times this wage gap claim is decisively refuted by economists, it always comes back. The bottom line: the 23-cent gender pay gap is simply the difference between the average earnings of all men and women working full-time. It does not account for differences in occupations, positions, education, job tenure or hours worked per week. When such relevant factors are considered, the wage gap narrows to the point of vanishing."

Not a study but I think it is a good read on the subject (https://fee.org/articles/truth-and-myth-on-the-gender-pay-ga...) and more or less lays what I have been attempting to say, that there likely is sexism but it is not at the employer level at least not when it comes to wage setting

"All the economic studies say is that differences in skills, experiences, and preferences between men and women explain the clear majority of the gap. What such studies do not address is the degree to which the differences in men’s and women’s skills and knowledge (their “human capital”) is due to sexism before they come to the labor market. Nor do such studies ask whether differences in preferences or job experience by gender are also due to sexism or other aspects of socialization.

For example, if girls are told from a young age that girls aren’t very good at math and science, and are thereby discouraged from majoring in those areas and earning higher salaries as a result, those factors will contribute to the 80% figure. But notice, that’s not because employers are discriminating. If sexism pushes women into lower paying fields, that doesn’t mean that they are necessarily being paid less than men for the same work in that field. What’s causing their lower wages is sexism in places other than the markets. "

You are focusing on the aggregate earning gap when you take all the wages of all women, and then compare them to the wage of all men.

While that might have value in social science on some wider scale, in the this topic today it has none as we are talking about a law that prevents potential employers from asking about previous wages and how that can "help solve the pay gap", that type of pay gap does not exist female programmers do not earn significantly less money than male programmers at the same company, with the same experience. The problem is not a employer pay gap, but the fact there are not as many female programmers

Go work on that, not attempting to solve a none problem of a mythical pay gap