I think it is easy to nitpick studies, especially when they are trying to measure something that is this complicated. While the soundness of the paper should be grounded in the methods and the data, it is far too easy for an individual to discount it's value based on a perceived mistake in method. The more complex the methods, the more polarizing the results, the more this is the case. For this particular issue, I think the methods by definition need to be fairly complex.

I am comfortable with my assertion that I will need to see some data before I take the position that women are not paid less than men in a discriminatory fashion. In my opinion, that women are discriminated against is a historical truth. I am not trying to be insulting, but I do find it hard to believe that people disagree on this.

While you see it as a historical truth this is something that is patently false in my daily life. Sorry I don't substitute historical truth for modern truth! I don't deny the existence of sexism.

I think that is a good thing. Still, it is likely that your experience might fall in the "anecdote" category. It is a big country!

Certainly possible. Another issue I have is that I regularly see good responses to these sorts of studies linked above pointing out valid flaws and yet none-the-less I'm expected to take this issue seriously. I just don't view it as a legitimate issue, not that I'm unwilling to.

I ask out of curiosity. If the wage gap studies were peer reviewed and found to be false, would you accept this?

Yes, I would accept that.