Polls released since the first presidential debate last week indicate as rapid a shift in voter preferences as we’ve seen all campaign. My model estimates a swing of about 1.5% in Romney’s direction, or a net narrowing of about 3%. Although the polls also suggest that this movement began a few days before the debate, it’s still a large effect.

What to make of it? First, and most importantly, although Romney may have cut into Obama’s lead, Obama is still comfortably ahead. The most important state to win this year is arguably Ohio – and there Obama holds on to 51.7% of the major-party vote. According to my model, Obama had been outperforming the fundamentals (which point to his reelection) prior to the debate – and now he’s running just slightly behind them. As a result, the model’s long-term forecast continues to show an Obama victory, with 332 electoral votes.

Second, there’s reason to believe that the initial estimates of Romney’s post-debate surge are going to weaken as more polls are released today and tomorrow. The surveys that made it into my Sunday morning update consisted of a number of one-day samples, which tend to draw in particularly enthusiastic respondents – in this case, Republicans excited about Romney’s debate performance. Moreover, the survey methodology used by these firms – in which interviews are conducted using recorded scripts, to save time and money – also show a Republican lean. And if anything, my model gives slightly greater weight to automated polls simply because they tend to have larger sample sizes.

The point isn’t that these polls are “wrong” – only that this is a situation where it would be wise to wait for more information before reaching any strong conclusions. My model treats every poll equally, regardless of how it was fielded, or by whom. The reason I don’t try to “correct” for potential errors in the polls isn’t because I don’t believe they exist – but because I don’t believe those adjustments can be estimated reliably enough to make much of a difference. (Consider how wide the error bars are on Simon Jackman’s house effects estimates, for example.) Instead, I assume there will eventually be enough polling in all 50 states for these errors to cancel out. Usually that is a pretty safe assumption, but I don’t think it’s happened yet.

I’m going to embed the current trend estimates for Virginia and Florida here in this post, so we can compare them to later estimates, and see if I’m right.

Finally, making sense of this small batch of post-debate polls highlights the value of using an informative Bayesian prior. If Romney is really experiencing a sudden swing in the polls, then we already have some idea of how quickly that could reasonably happen, based on previous trends. It’s certainly possible that something about public opinion has fundamentally changed within the past week. But if that’s the case, we should require extra evidence to overturn what we previously thought was going on.

Look for another site update Tuesday morning.

There’s been a lot of talk lately about how the presidential polls might be biased. So let’s look at how well – or poorly – some of the major survey firms are actually performing this year.

All polls contain error, mainly from the limitations of random sampling. But there are lots of other ways that error can creep into surveys. Pollsters who truly care about getting the right answer go through great pains to minimize these non-sampling errors, but sometimes systematic biases – or house effects – can remain. For whatever reason, some pollsters are consistently too favorable (or not favorable enough) to certain parties or candidates.

Since May 1, there have been over 400 state polls, conducted by more than 100 different survey organizations. However, a much smaller number of firms have been responsible for a majority of the polls: Rasmussen, PPP, YouGov, Quinnipiac, Purple Strategies, We Ask America, SurveyUSA, and Marist.

For each poll released by these firms, I’ll calculate the survey error as the difference between their reported level of support for Obama over Romney, and my model’s estimate of the “true” level of support on the day and state of the poll. Then each firm’s house effect is simply the average of these differences. (Note that my model doesn’t preemptively try to adjust for house effects in any way.) If a firm is unbiased, its average error should be zero. Positive house effects are more pro-Obama; negative house effects are more pro-Romney. Here’s what we find.

Survey Firm	# Polls	House Effect
PPP	61	+0.7%
Marist	15	+0.5%
SurveyUSA	22	+0.3%
Quinnipiac	35	+0.1%
YouGov	27	0%
We Ask America	17	-0.2%
Purple Strategies	18	-0.9%
Rasmussen	53	-0.9%

There are a number of pieces of information to take away from this table. First, none of the house effects are all that big. Average deviations are less than 1% in either direction. This is much smaller than the error we observe in the polls due to random sampling alone.

Second, even if, say, Rasmussen is getting the right numbers on average – so that PPP’s house effect is actually +1.6% – then that +1.6% bias still isn’t that big. It’s certainly not enough to explain Obama’s large – and increasing – lead in the polls. Of course, it’s possible that even Rasmussen is biased pro-Obama, and we just aren’t able to tell. But I don’t believe anyone is suggesting that.

Finally, the firms with the largest house effects in both directions – PPP and Rasmussen – are also the ones doing the most polls, so their effects cancel out. Just another reason to feel comfortable trusting the polling averages.

Here’s a plot highlighting each of the eight firms’ survey errors versus sample sizes. The horizontal lines denote the house effects. Dashed lines indicate theoretical 95% margins of error, assuming perfect random sampling. Again, nothing very extraordinary. We would expect PPP and Rasmussen to “miss” once or twice, simply because of how many polls they’re fielding.

Just out of curiosity (and no particular feelings of cruelty, I swear), which polls have been the most misleading – or let’s say, unluckiest – of the campaign so far? Rather than look at the raw survey error, which is expected to be larger in small samples, I’ll calculate the p-value for each poll, assuming my model represents the truth. This tells us the probability of getting a survey result with the observed level of error (or greater), at a given sample size, due to chance alone. Smaller p-values reveal more anomalous polls.

Here are all surveys with a p-value less than 0.01 – meaning we’d expect to see these results in fewer than 1 out of every 100 surveys, if the polling firm is conducting the survey in a proper and unbiased manner.

p-value	Error	Survey Firm	Date	State	Obama	Romney	Sample Size
0.001	0.07	Suffolk	9/16/2012	MA	64%	31%	600
0.002	-0.07	InsiderAdvantage	9/18/2012	GA	35%	56%	483
0.003	-0.03	Gravis Marketing	9/9/2012	VA	44%	49%	2238
0.003	-0.05	Wenzel Strategies (R)	9/11/2012	MO	38%	57%	850
0.003	0.05	Rutgers-Eagleton	6/4/2012	NJ	56%	33%	1065
0.004	-0.04	FMWB (D)	8/16/2012	MI	44%	48%	1733
0.005	-0.05	Gravis Marketing	8/23/2012	MO	36%	53%	1057
0.006	-0.03	Quinnipiac	5/21/2012	FL	41%	47%	1722
0.009	-0.04	Quinnipiac/NYT/CBS	8/6/2012	CO	45%	50%	1463

The single most… unusual survey was the 9/16 Suffolk poll in Massachusetts that overestimated Obama’s level of support by 7%. However, of the nine polls on the list, seven erred in the direction of Romney – not Obama. And what to say about Gravis Marketing, who appears twice – strongly favoring Romney – despite only conducting 10 polls. Hm.

It’s interesting that many of these surveys had relatively large sample sizes. The result is that errors of only 3%-4% appear more suspicious than if the sample had been smaller. It’s sort of a double whammy: firms pay to conduct more interviews, but all they accomplish by reducing their sampling error is to provide sharper focus on the magnitude of their non-sampling error. They’d be better off sticking to samples of 500, where systematic errors wouldn’t be as apparent.

With the pace of polling increasing, there are going to be days when some polls seem to be especially surprising – or even contradictory. For example, a recent Washington Post survey found Obama up 8 points in Virginia, even though other polls indicate a tighter race. It’s pretty safe to say that Obama is not actually winning Virginia by 8 points. But this doesn’t mean the Post poll is biased, or wrong, or should be ignored. I imagine the Post did the best job they could. The likeliest explanation for the finding is simply random sampling error.

Even in a perfectly executed survey, there’s going to be error due to random sampling. A survey only contacts a small group of respondents, and those people won’t always be representative of the broader population. The smaller the sample, the larger the sample-to-sample variability. To see just how large sampling error can be, suppose my model is correct that Obama is currently preferred by 52% of decided, major-party voters in Virginia. Then in different surveys of 750 respondents (which is about the average size of the state polls), it wouldn’t be unusual to see results ranging anywhere from 48% to 56%, because of sampling variation alone. In fact, here’s the expected distribution of all poll results under this scenario: most should be right around 52%, but many won’t.

If we added in other possible sources of survey error (question wording, interviewer effects, mode effects, sample selection, and so forth), the distribution would become even wider. So just imagine two polls on the same day showing Romney with either 52% or 60% of the two-party vote. Astounding, right? No, not really. It happened in Missouri last week.

What is actually astounding about the polls this year is how well they are behaving, compared to theoretical expectations. For a given sample size, the margin of error tells us how many polls should fall within a certain range of the true population value. I’ll assume my model is correctly estimating the current level of preference for Obama over Romney in each state during the campaign. Then I can subtract from each observed poll result the model estimate on that day. This is the survey error. It turns out that most polls have been exactly where they should be – within two or three points of the model estimates. And that’s without any correction in my model for “house effects,” or systematic biases in the results of particular polling organizations.

Plotting each poll’s error versus its sample size (excluding undecideds) produces the following graph. The dashed lines correspond to a theoretical 95% margin of error at each sample size, assuming that error arises only from random sampling.

If the model is fitting properly, and if there are no other sources of error in the polls, then 95% of polls should fall within the dashed lines. The observed proportion is 94%. Certainly some polls are especially misleading – the worst outlier, in the lower right corner, is the large 9/9 Gravis Marketing poll that had Romney ahead in Virginia (and was singly responsible for the brief downward blip in the Virginia forecast last week). But what is most important – and what helps us trust the pollsters as well as their polls – is that the overall distribution of survey errors is very close to what we would expect if pollsters were conducting their surveys in a careful and consistent way.