Post-Gazette columnist Ruth Ann Dailey recently disparaged advocates for women's equality for not understanding math -- and worse (" 'Facts' No Longer Support Equal-Pay Agenda," April 24).

Apparently, organizers of an April 8 rally in Harrisburg decried that women make 77 percent of what men make, while last year protesters in Pittsburgh claimed the figure was 69 percent, while researchers at the American Association of University Women put the figure at 80 percent.

Ms. Dailey writes: "Why the different numbers? Apparently, as Teen Talk Barbie once complained, math is tough. Either it's too hard for women's advocacy groups to master, or it's their devotion to ideology that prompts them to protest, year after year, an outrage that the math indicates may not actually exist."

I am outraged by this piece of journalism for (at least) three reasons.

First, the math involves sophisticated statistical analysis and is not the reason for the different estimates. The numbers depend on how you frame the question. Suppose the question is: How much does the average woman who works full time earn relative to the average man who works full time? In that case, the answer is straightforward: According to the Bureau of Labor Statistics, for the first quarter of 2008 that number is 80.6 percent (creating a wage "gap" of 19.4 percent).

The larger wage gaps Ms. Dailey quotes are accurate answers to different questions.

What is the national gender wage gap when median annual earnings are compared regardless of full- or part-time work status?

Answer: 77 percent.

What is the same gap for women in southwestern Pennsylvania?

Answer: 69 percent.

But there are other ways to look at the problem. One criticism of this way of calculating the wage gap is that it compares "apples" and "oranges." The average woman might have an associate's degree and eight years of experience and work in a doctor's office. The average man might be a carpenter with 12 years of experience. They are working very different jobs, so does it make sense to compare them?

Most economists don't think so. They use an "apples-to-apples" approach, employing a statistical procedure that accounts for differences in educational background, experience, industry and occupation. These calculations estimate a wage gap of about 10 percent to 15 percent and vary because of different data sources, different statistical approaches and different control variables.

As you can see, the precise size of the wage gap depends on how it is defined. Journalists as well as advocates aren't always as specific as they should be about which wage gap they are reporting.

A second reason to take Ms. Dailey to task is the claim that the observed differences in choices between men and women -- different levels of education, different career paths and the option of leaving the labor market to raise a family -- are free of discrimination.

She writes: "But the measure of our progress is that each of us gets to decide which way and how far to go. These days it is our individual abilities and choices, not institutionalized discrimination, that nudge the journey this way or that."

Let's consider the "choice" of which spouse stays at home and which one works in the labor market. While one spouse might have a stronger preference than the other to stay at home, this decision is surely influenced by which one earns more in the labor market. And if those earnings are influenced by pay practices that can be explained only by discrimination, then how is this decision an unconstrained choice? It isn't -- it is a byproduct of discrimination.

A final flaw is the claim that the wage gap is actually zero. Ms. Dailey writes: "Time after time, the research has shown that when we take into consideration career choice, length of employment, time in and out of the work force and number of hours worked, the wage gap disappears."

This claim is simply wrong. Even one of the most conservative approaches estimates a large wage gap. Work in progress at the Journal of Human Resources cites the gap as 10 percent for white women and 13 percent for black women (for men and women with a four-year college degree, with the same educational attainment, in the same field, of the same age and with similar and high labor-market attachment, to be precise).

These numbers are a long way from zero. Think about what a gap of 10 percent can mean over a woman's lifetime. If a man starts his career at age 22 earning $40,000, a woman would earn $36,000. If both the man and the woman receive 3 percent raises each year, the man would earn an extra $356,194 over the course of his career. If he took that "bonus" from being a man and saved it in an account earning only 4 percent interest, he would have an extra $778,025 when he retires.

I think that's math that even a talking Barbie can understand.