Pay should equal work. We have an accurate measure of total payment, namely income. We only have proxies for quality and quantity of work (experience, publications, etc). Regression assumes that Y = f(x) + noise. Thus, the variable that has the error in its measurement should be the Y variable. In this case, our estimate of work is much worse than our estimate of pay. So, the best test of equality is to put experience as the Y (dependent variable) and Pay as the X (independent variable). THen if the indicator for women shows that they have to "work harder" for the same pay, that would be evidence of discrimination. This doesn't appear to be the case.
Even if field is corrected for, there is still no evidence of discrimination. (Notice the t-ratio is -22). The final graph makes this clear as a picture. (Notice that women almost uniformaly have lower experience than men for a given pay.)
But, what if rank is included? The t-statistic is insignficant.