Jay Cost posted a good tutorial on the mathematics of polls, but left one case out where statistical models start to show two different possible outcomes. These are called bimodal results, where there is no consensus on a single result, but actually two highly probably results are possible. A graph of a bimodal statistical model is shown below for the duration periods between eruptions of the Old Faithful Geyser in Yellowstone National Park:

As can be seen there are two basic periods between eruptions which drive the timing of old faithful. This doesn’t really apply to polls but it is a good example of bimodal data sets.

If one looks at the polls in the election they are showing a two clusters of results. One cluster shows a runaway race for Obama, the other a very possible close win for McCain. For example, let’s look at the Polls in Ohio. We have 8 polls now on the RCP list today (which Jay Cost notes all RCP does is average, no real analysis and processing).

4 polls cluster in at one mode: Ohio Newspaper Poll (Obama +3), CNN/Time (Obama +4), FOX News/Rasmussen (McCain +2) and NBC/Mason-Dixon (McCain +1), which averages out to Obama +1 – a clear tie.

The other 4 cluster at another mode: Politico/InAdv (Obama +10), Big10 Battleground (+12), Quinnipiac (+14) and Suffolk (+9), which averages out to Obama +11 – a romp.

What this tells me is there are two classes of turnout models in play.  One is the traditional model using historic turnout models to weight their results.  They reflect the Gallup “traditional’ model which shows a very tight race. The second set of polls is using the untested or unverified turnout model which tries to claim that willingness to answer a poll has a strong and equal relationship across party affiliations (and other factors) with willingness to vote. These polls are analogous to the Gallup ‘extended’ model – which could be (and I am almost willing to predict is) pure fantasy.

Are McCain and Obama tied in Ohio in a close race, or should Obama be measuring the drapes in the oval office? For McCain-Palin supporters I can tell you the only way for the fantasy polls to be right is if you folks give up and sit home or waste your vote on a 3rd party candidate. Palin could put this away.

For example, look at VA as well, another state some people claim is gone for McCain (even though Palin will hit 3 big areas in the state Monday). Again we have two polls which are clustering around a close race: NBC/Mason-Dixon (+2) and SurveyUSA (+6) for an average of +4 Obama. Two others show a Obama blow out: CNN/Time (+10) and Rasmussen (+10), resulting in a +10% Obama lead. We can find the same pattern showing up in state after state like Florida, where one poll mode rests at a dead heat with McCain +1 and another is sitting around Obama +6.

RCP simply averages these polls, but I think the reality is one mode or another is going to be the right answer. Nationally it is either an Obama +4% close race or an Obama +10% landslide today. It is not in between these two modes. Unlike normal bimodal statistical results, where there are really two outcomes likely, in the political polling world only one mode will proven to be right, and the other will have been proven to be wrong. Which one will survive is actually up to the voters now.  But the close race mode would mean it is very easy for McCain-Palin to pull off a shocking win on election day. And as I noted early, early voting poll results from Gallup tend to show this is a close race, not a walk in the park for Obama.

Tags: 2008 Election, Bimodal, Polls