Hannity's Innumeracy: 51-45=4

Every morning I check Rasmussen Reports for the latest presidential election polling data, especially the electoral college data. Although their written contributions have a noticeable conservative bias, their polling data is widely regarded as the best available. The daily presidential tracking poll this morning had Obama collecting 51% and McCain 45% from a sample of 3000 likely voters.

So I was a little surprised when Sean Hannity read off a list of polls that showed the presidential race was "narrowing" and cited that Obama was only up by 4% in the Rasmussen tracking poll. How does 51 minus 45 equal 4?

I could give Hannity the benefit of the doubt here and just assume he misspoke. That is a likely explanation, but the mistake reminded me of something I have heard from many pundits interpreting poll data. The margin of error on the Rasmussen poll was plus/minus 2%. What that means is that Obama's number could be as high as 53% or as low as 49% and McCain could be at 43% or 47%. In reality, Obama may be up by a whopping 10% (53-43=10) or a measly 2% (49-47=2).

I suspect Hannity subtracted 45 from 51 and then subtracted 2 to account for the margin of error. Why would he subtract the margin of error? He wants the poll to seem as close as possible to keep conservatives engaged in the election. He would not be the only party guilty of poll spinning; I have also heard the liberal talking heads on MSNBC crowing about the nearly double-digit Obama leads that some polls have indicated, while completely ignoring the margin of error.

A similar, but not identical, mistake spouted forth from many pundits after last week's final presidential debate. One pollster's data gave Obama an 8 point lead over McCain the day of the debate. The following day the same pollster's results showed a 6 point lead for Obama. "The race is narrowing!" - the pundits proclaimed. No...the race fluctuated. The overnight change was within the margin of error so there was no measurable shift in the polls.

If you want to know what the polls are saying about the state of the race, read the actual poll data carefully. Remember that partisan commentators may skew the data in favor of their candidate; even nonpartisan commentators may skew the data to keep the race "narrow" and maintain their viewers' interest in the horserace. Finally, remember that the only poll that really matters is the big one... on election day.

UPDATE: Want to know why there is so much disparity between the various polls? FiveThirtyEight.com has a great analysis of the tracking polls.