Updated: McCain is right about 5 of 11 polls

UPDATED NOV. 1: Sen. John McCain sounded upbeat in a Halloween morning interview on CNBC. But was the enthusiasm just a mask?

We can't be sure. But we can check some data McCain cited to justify his optimism.

"I'm very optimistic, and we're coming from behind," McCain told anchor Larry Kudlow in the Oct. 31, 2008, interview. "I'm the underdog. There's where we always like to be. But we are within the margin of error, my friends. And I'm very happy where we are."

McCain was clearly talking about national polls, which are not necessarily indicative of Electoral College results. Nevertheless, only four presidents have won the election without winning the national popular vote — John Quincy Adams in 1824, Rutherford B. Hayes in 1876, Benjamin Harrison in 1888 and George W. Bush in 2000.

So we looked at every national poll we could find from the day McCain spoke and the day before to see if he really was within the margin of error.

Five polls were released the same morning McCain was speaking. Rasmussen's daily tracking poll  showed Obama up 51 to 47 with a margin of error of plus or minus 2 percentage points. That means if one gives McCain the full benefit of the margin of error, his score could be as high as 49 percent (his 47 plus the 2-point margin of error) and Obama's could be as low as 49 percent (his 51 minus the margin of error). There's a very low probability of that outcome, but still, it's within the margin of error. 

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The method we employed above of factoring in the margin of error is the one most commonly used by pollsters and political scientists. Some statisticians quibble with it and use a more complicated calculation, but we think it's fair to judge McCain's claim by the most common measure. (We can say for certain that another method the media commonly use — saying a race is within the margin of error only if the gap between the candidates is smaller than the margin of error — is wrong. You have to apply the margin to both candidates' scores.)

Let's look at more polls from Oct. 31. The Diageo/Hotline tracking poll had Obama up 48 to 41 with a margin of error of 3.3 percent, a lead that was outside the margin of error. The Reuters/C-SPAN/Zogby poll showed Obama up 50 to 43 with a margin of error of 2.9 percentage points, also outside the margin of error. Research 2000/Daily Kos had Obama up 51-45 with a 3-point margin of error, just within the margin of error. And an Associated Press-Yahoo News poll showed Obama up 51 to 43 with a margin of error of 3 percentage points, back outside the margin of error.

Let's look at the polls released the previous day, Oct. 30.

A Washington Post-ABC News poll showed Obama leading 52 to 44 with a margin of error of 2.5 percentage points — no dice for McCain on that one. The New York Times/CBS News poll showed Obama leading 51 to 40 with a margin of error of three percentage points — even worse news for McCain. The Investor's Business Daily/ TechnoMetrica Institute of Policy poll showed Obama leading 47.7 to 43.6, a lead well within the margin of error of 3.5 points. The GWU/Battleground poll showed Obama up 49 to 45, also within the 3.5 percent margin of error. The Gallup daily tracking poll had Obama up 50 to 45 with a traditional model of turnout, and 51 to 44 with an expanded turnout; both outside the 2-point margin of error. A FOX News/Opinion Dynamics poll had Obama leading 47 to 44, easily within the 3-point margin of error.

So McCain was within the "margin of error" in five of the 11 polls we checked. We find his statement Half True.

UPDATE: Our original item mistakenly calculated the margin of error without using its impact on the number for both candidates. We have changed the calculations, which changed our ruling from Barely True to Half True.