A statistic that Joel Klein, Al Sharpton, and Mort Zuckerman have all recently employed to bemoan the racial achievement gap appears to be wrong.

Here’s the statistic, as Klein and Sharpton recently summarized in the Wall Street Journal (and Mort Zuckerman used it here):

“today the average 12th-grade black or Hispanic student has the reading, writing and math skills of an eighth-grade white student.”

The problem isn’t the principle behind the claim; America definitely has a racial achievement gap. The problem, according to an official at the National Center for Education Statistics, is in the specific way that Klein et al describe the gap.

The best available measure we have to compare all American kids is the National Assessment of Educational Progress, or the NAEP test. But the NAEP test, which is given only to a sample of students across the country, not to every child, does not permit the kind of detailed comparison Klein’s statistic would demand, Arnold Goldstein, the NCES official, said. “It would be great if we could. It’s kind of frustrating not to be able to make these sorts of statements,” said Goldstein, who is program director for design, analysis, and reporting at NCES’s assessment division. “But that’s a limitation of the data.”

I contacted the Department of Education several times for comment but got no response this week. UPDATE: A spokesman, Andrew Jacob, wrote to say that Klein got the statistic from “No Excuses: Closing the Racial Gap in Learning,” a book by Abigail and Stephan Thernstrom.

Goldstein said that one problem is that the statistic Klein uses aims to compare students who are in different grade levels. But the NAEP test for, say, eighth-grade math, which might look at algebra, is not comparable to the test for, say, twelfth-grade math, which looks at higher-level skills. Observers cannot, then, compare a high school senior’s skill level to a middle schooler’s.

Goldstein said another problem is that NAEP relies on sampling. That means that, in order to draw conclusions about all students in a group, researchers have to make sure that enough students took the tests — in other words, that the sample size was large enough. Narrowing down what you’re looking at so that it’s not just one racial group in one grade, but comparing racial groups across subjects and grades, would require a larger sample size than federal researchers have, Goldstein said.

How should the achievement gap be described? Goldstein said the best thing to do is to stick to comparisons within grade levels. One true fact: In 2005, the most recent year high school senior were tested, 16% of black twelfth-graders scored proficient on the national reading test, compared to 43% of white twelfth-graders.

Thanks to the Education Writers Association’s president and public editor for asking Goldstein this question first.