If you believe women suffer systemic wage discrimination, read the new American Association of University Women (AAUW) study Graduating to a Pay Gap. Bypass the verbal sleights of hand and take a hard look at the numbers. Women are close to achieving the goal of equal pay for equal work. They may be there already.

How many times have you heard that, for the same work, women receive 77 cents for every dollar a man earns? This alleged unfairness is the basis for the annual Equal Pay Day observed each year about mid-April to symbolize how far into the current year women have to work to catch up with men's earnings from the previous year. If the AAUW is right, Equal Pay Day will now have to be moved to early January.

The AAUW has now joined ranks with serious economists who find that when you control for relevant differences between men and women (occupations, college majors, length of time in workplace) the wage gap narrows to the point of vanishing. The 23-cent gap is simply the average difference between the earnings of men and women employed "full time." What is important is the "adjusted" wage gap-the figure that controls for all the relevant variables. That is what the new AAUW study explores.

The AAUW researchers looked at male and female college graduates one year after graduation. After controlling for several relevant factors (though some were left out, as we shall see), they found that the wage gap narrowed to only 6.6 cents. How much of that is attributable to discrimination? As AAUW spokesperson Lisa Maatz candidly said in an NPR interview, "We are still trying to figure that out."

One of the best studies on the wage gap was released in 2009 by the U.S. Department of Labor. It examined more than 50 peer-reviewed papers and concluded that the 23-cent wage gap "may be almost entirely the result of individual choices being made by both male and female workers." In the past, women's groups have ignored or explained away such findings.

"In fact," says the National Women's Law Center, "authoritative studies show that even when all relevant career and family attributes are taken into account, there is still a significant, unexplained gap in men's and women's earnings." Not quite. What the 2009 Labor Department study showed was that when the proper controls are in place, the unexplained (adjusted) wage gap is somewhere between 4.8 and 7 cents. The new AAUW study is consistent with these findings. But isn't the unexplained gap, albeit far less than the endlessly publicized 23 cents, still a serious injustice? Shouldn't we look for ways to compel employers to pay women the extra 5-7 cents? Not before we figure out the cause. The AAUW notes that part of the new 6.6-cent wage-gap may be owed to women's supposedly inferior negotiating skills -- not unscrupulous employers. Furthermore, the AAUW's 6.6 cents includes some large legitimate wage differences masked by over-broad occupational categories. For example, its researchers count "social science" as one college major and report that, among such majors, women earned only 83 percent of what men earned. That may sound unfair... until you consider that "social science" includes both economics and sociology majors.

Economics majors (66 percent male) have a median income of $70,000; for sociology majors (68 percent female) it is $40,000. Economist Diana Furchtgott-Roth of the Manhattan Institute has pointed to similar incongruities. The AAUW study classifies jobs as diverse as librarian, lawyer, professional athlete, and "media occupations" under a single rubric--"other white collar." Says Furchtgott-Roth: "So, the AAUW report compares the pay of male lawyers with that of female librarians; of male athletes with that of female communications assistants. That's not a comparison between people who do the same work." With more realistic categories and definitions, the remaining 6.6 gap would certainly narrow to just a few cents at most.

Could the gender wage gap turn out to be zero? Probably not. The AAUW correctly notes that there is still evidence of residual bias against women in the workplace. However, with the gap approaching a few cents, there is not a lot of room for discrimination. And as economists frequently remind us, if it were really true that an employer could get away with paying Jill less than Jack for the same work, clever entrepreneurs would fire all their male employees, replace them with females, and enjoy a huge market advantage.

Women's groups will counter that even if most of the wage gap can be explained by women's choices, those choices are not truly free. Women who major in sociology rather than economics, or who choose family-friendly jobs over those that pay better but offer less flexibility, may be compelled by cultural stereotypes. According to the National Organization for Women (NOW), powerful sexist stereotypes "steer" women and men "toward different education, training, and career paths" and family roles. But are American women really as much in thrall to stereotypes as their feminist protectors claim? Aren't women capable of understanding their real preferences and making decisions for themselves? NOW needs to show, not dogmatically assert, that women's choices are not free. And it needs to explain why, by contrast, the life choices it promotes are the authentic ones -- what women truly want, and what will make them happier and more fulfilled.

It will not be not easy for the AAUW and its allies to abandon the idea of systemic gender injustice. AAUW officials are trying mightily to sustain the bad-news-for-women narrative. According to "Graduating to a Pay Gap" publicity materials, "The AAUW today released a new study showing that just one year out of college, millennial women are paid 82 cents for every dollar paid to their male peers. Women are paid less than men even when they do the same work and major in the same field." Many journalists seem to have read and reported on the AAUW's press releases rather than its research.

That is the hype. Look at the numbers.

Christina Hoff Sommers is a resident scholar at the American Enterprise Institute. She is the author of Who Stole Feminism and the War Against Boys. Her new book, Freedom Feminism -- Its Surprising History and Why It Matters, will be published in 2013 by AEI press.