Associated Press lead reporter Liz Sidoti, other contributors (AP Director of Surveys Trevor Tompson, AP News Survey Specialist Dennis Junius and AP writer Alan Fram), and the wire service's supposedly vaunted editors apparently don't understand what a polling margin of error is.

In a Wednesday story I found in four different places (CBS News, AP-Google, Breitbart, Yahoo! News), Sidoti et al let a paragraph stand claiming that a 3.5% margin of error in the poll results they were reporting meant that the real results could vary by as many as 14 points.

Here are the key paragraphs found in each story (bold is mine):

The presidential race tightened after the final debate, with John McCain gaining among whites and people earning less than $50,000, according to an Associated Press-GfK poll that shows McCain and Barack Obama essentially running even among likely voters in the election homestretch.

The poll, which found Obama at 44 percent and McCain at 43 percent, supports what some Republicans and Democrats privately have said in recent days: that the race narrowed after the third debate as GOP-leaning voters drifted home to their party and McCain's "Joe the plumber" analogy struck a chord.

..... Polls are snapshots of highly fluid campaigns. In this case, there is a margin of error of plus or minus 3.5 percentage points; that means Obama could be ahead by as many as 8 points or down by as many as 6. There are many reasons why polls differ, including methods of estimating likely voters and the wording of questions.

Uh, no. A 3.5% margin of error means Obama could be ahead by as many as 4.5 points or down by as many as 2.5. That's a seven-point spread.

Zheesh. If I didn't know better, I would be thinking, with their apparent failure to grasp basic math, that Sidoti et al are auditioning to join Martin Crutsinger and Jeannine Aversa as AP business reporters.

Cross-posted at BizzyBlog.com.

UPDATE: Commenters are saying AP is correct in its interpretation.

I don't think so, because if the commenters are right, newspapers would routinely write up, say, a 6-point lead by McCain or Obama as being "within the 3.5-point margin of error." That is, the one trailing could be 3.5 points higher, and the one leading could be 3.5 points lower, meaning that the person reported as leading could conceivably be trailing. But I don't think I've ever seen it reported that way, because, as I understand it, the margin of error is 3.5% for the entire poll, not 3.5% for each poll component.

—Tom Blumer is president of a training and development company in Mason, Ohio, and is a contributing editor to NewsBusters