Saturday, November 3, 2012

For Romney to Win, State Polls Must Be Statistically Biased

President Obama is now better than a 4-in-5 favorite to win the Electoral College, according to the FiveThirtyEight forecast. His chances of winning it increased to 83.7 percent on Friday, his highest figure since the Denver debate and improved from 80.8 percent on Thursday.

Friday’s polling should make it easy to discern why Mr. Obama has the Electoral College advantage. There were 22 polls of swing states published Friday. Of these, Mr. Obama led in 19 polls, and two showed a tie. Mitt Romney led in just one of the surveys, a Mason-Dixon poll of Florida.

Although the fact that Mr. Obama held the lead in so many polls is partly coincidental — there weren’t any polls of North Carolina on Friday, for instance, which is Mr. Romney’s strongest battleground state — they nevertheless represent powerful evidence against the idea that the race is a “tossup.” A tossup race isn’t likely to produce 19 leads for one candidate and one for the other — any more than a fair coin is likely to come up heads 19 times and tails just once in 20 tosses. (The probability of a fair coin doing so is about 1 chance in 50,000.)

Instead, Mr. Romney will have to hope that the coin isn’t fair, and instead has been weighted to Mr. Obama’s advantage. In other words, he’ll have to hope that the polls have been biased in Mr. Obama’s favor. (I recognize that ‘bias’ is a loaded term in political contexts. I’ll explain what I mean by it in a moment.)

There are essentially three reasons that a poll might provide an inaccurate forecast of an upcoming election.
The first is statistical sampling error: statistical error that comes from interviewing only a random sample of the population, rather than everyone. This is the type of error that is represented by the margin of error reported alongside a poll and it is reasonably easy to measure.

If you have just one poll of a state, the statistical sampling error will be fairly high. For instance, a poll of 800 voters has a margin of error in estimating one candidate’s vote share of about plus or minus 3.5 percentage points. In a two-candidate race, however, the margin of error in estimating the difference between the candidates (as in: “Obama leads Romney by five points”) is roughly twice that, plus or minus seven percentage points, since a vote for one candidate is necessarily a vote against the other one.

The margin of error is much reduced, however, when you aggregate different polls together, since that creates a much larger sample size. In Ohio, for example, there have been 17,615 interviews of likely voters in polls conducted there within the past 10 days. That yields a margin of error, in measuring the difference between the candidates, of about 1.5 percentage point — smaller than Mr. Obama’s current lead in the polling average there.

In other words, Mr. Obama’s current lead in Ohio almost certainly does not reflect random sampling error alone. The same is true in states like Iowa, Nevada, Wisconsin and others that would suffice for him to win 270 electoral votes. (Mr. Obama’s more tenuous leads in Colorado and Virginia, and Mr. Romney’s thin lead in Florida, potentially could be a product of sampling error.)

So why, then, do we have Mr. Obama as “only” an 83.7 percent favorite to win the Electoral College, and not close to 100 percent?  POST

No comments: