Want to know how we should communicate quantitative ideas to the public? This segment from the Rachel Maddow show nails it. At 19:52 long, the full clip is worth every second. But in case you don't have time to watch it, I will tell you what happened, and I will be very specific about why the communication was exemplary.

On Meet the Press this past weekend, commentator Rachel Maddow gets into a debate with Republican political operative Alex Castellanos about pay inequality between men and women. (The clip linked above has a flashback of the debate.) As Maddow is trying to discuss policy tools that might be used to fix the gender gap, Castellanos interrupts to say that there is, in fact, no gender gap. Maddow insists that "On average, a woman gets paid 77 cents for every dollar that a man gets paid." Castellanos says that "Actually, if you start looking at the numbers, Rachel, there are lots of reasons for that." His stated reasons include:

• "Men work an average of 44 hours a week. Women work 41 hours a week."
• "Men go into professions like engineering, science and math that earn more."
• "Women want more flexibility."
• "When you look at, for example, single women working in America today between the ages of, I think, 40 and 64, who makes more? Men or women, on average? Men make $40,000 a year. Women make $47,000."

In short, Castellanos is trying to argue that there is no gender gap. Back on her own show, Maddow dives into the details. And this is when the communication about numbers gets really excellent. Maddow first cites her source: a Bloomberg News report that crunches data from the U.S. Census Bureau. Maddow reports a few slices of the data:

• In aggregate (over all data) the average woman makes 77% of what the average man does.
• Restricted to the 20 occupations that are most common for men in this country, men get paid more than women in 19 of them.
• Restricted to the 20 occupations that are the most common for women in this country, men get paid more than women in 19 of them.
• Of the 265 different occupation categories in the study, men make more than women in 264 of them.

Maddow then interviews Dr. Heidi Hartmann, a MacArthur Genius, research professor at George Washington University, and President of the Institute for Women's Policy Research. She talks about the Census data as well as data from the Bureau of Labor Statistics and the U.S. Government Accountability Office (GAO). Hartmann says

[The GAO study] said that even when you put everything you can possibly think of in the regression equations, the statistical analyses to try to make [the gender] gap go away, you can't explain at least 20 percent of it. Now, most other studies place the part you can't explain as a quarter to a half. So, a large part of the gap probably is due to discrimination.

Maddow replies

In terms of just making it very clear, what you were talking about there about doing a statistical regression analysis on these things, controlling for other factors... What you're saying basically is when you control for things like the number of hours worked, you're still getting a gender based pay disparity that is not explained by working a different number of hours?

Hartmann's response?

Exactly. I mean, Alex seemed to believe if you put in working a different number of hours that would explain it. No, far from it. If you look at all workers and male and female in the economy, we know, let's say, during the childbearing years, about a third of women may be working part time. So count part time. Count how much women work. "OK. I'm working part time. Only making $400 a week." Compare it to all the men, more of whom are working full time. You still get a wage ratio of 72 percent. So that means that [the] 77 percent [figure we have been using] isn't going to move very much if you suddenly remove the people where the men are working 44 and the women are only making 40. No. The number of hours explains a very small part of it. I mean, these regression analysis, they include occupation. They include your education, number of years of experience, maybe sometimes marital status, number of children -- just about anything you can think of. And you cannot make the whole gap go away.

What do I admire about the job Maddow does here?

1. She disaggregates opinion ("what is the right policy solution?") from fact ("what do the data say?").
2. She cites the source of the data she calls upon.
3. She interviews an expert whose credentials are strong.
4. When the expert makes a statement that is likely too technical for the public (Harmann's statement about "putting everything in the regression equations"), Maddow makes her backtrack to explain more, and to do so with examples.
5. The information provided specifically rebuts Castellanos' contention that the gender gap is an illusion arising from factors such as age and profession.

In short, this was a public, explicit, and understandable discussion of the statistical concept of fraction of variance unexplained. I am thrilled beyond belief. We need more of this.