The Columbus Dispatch’s final pre-election poll has Obama leading Romney 50 percent to 48 percent. Their headline calls this a “toss-up,” and Robert Wright is unhappy about that:
Presumably the reason the headline writer felt justified in calling the race a toss-up was this paragraph in the story: “The final Dispatch poll shows Obama leading 50 percent to 48 percent in the Buckeye State. However, that 2-point edge is within the survey’s margin of sampling error, plus or minus 2.2 percentage points.”
That wording suggests that Obama’s two-point edge has no meaning. And that’s a common way for journalists to interpret results that fall within the “margin of error.” For example, in September a conservative columnist in the New York Post asserted that Obama’s lead in state polls didn’t matter because the “polls separating the two candidates are within the margin of error — meaning that there is no statistical difference in support between Obama and Romney.”
Wright is right. The MOE for a single poll represents a 95 percent confidence interval for each individual’s percentage, but it doesn’t represent a 95 percent confidence for the difference between the two. In fact, a 2 percent difference in a poll with a 2.2 percent MOE suggests that there’s about an 84 percent chance that the guy in the lead really and truly is in the lead.
And guess what? Based on averaging lots of polls, and thus reducing the MOE, Nate Silver figures that Obama’s chances of winning tomorrow are 86 percent—largely because he thinks those are Obama’s chances of winning Ohio. So it turns out that everyone is saying the same thing, but the Columbus Dispatch just doesn’t know it. Obama seems to have about an 84 to 86 percent chance of winning Ohio, and therefore an 84-86 percent chance of winning the election.