You made a great point Meg, which I will point out to other people from now on. :)
Meanwhile I agree with Aristotelis that it is important to avoid statistical dishonesty. The aforementioned statement, “Women earn 77 cents for every dollar a man earns — for doing the same work.” appears to be a scandalous lie if it is true that the 23-cent difference is entirely explained by doing different work. Why is it necessary for activists to pathologically lie about “doing the same work,” when the statement “Women earn 77 cents for every dollar a man earns” is already very strong indictment on the status quo? It’s disheartening.