There has been considerable discussion among us all regarding the validity of the national polls that are being published. Obviously, when polls are being put out that use samples that are larger than the results of the 2008 election, then many of us become suspicious. With this latest round of Eeyorism (Erick and Ace, I'm looking at you), I decided that I was going to take a real look at the polls and see if I could make sense of them.
As I examined the top line numbers, I realized what has been bugging me for months about the polls. There isn't enough noise in the samples to make them credible. Let me give an example I am used to in the real world. If you sample a specific frequency for a signal, you expect to see a lot of noise from other signals in other bands interfering with your sample, due to harmonics. What is done is the sample band is run through a filter to clean up the signal, removing spurious signals first.
Look at the results of 7 polls currently being used in the RCP average:
Tipp - O+2
CBS/NYT - O+3
Fox - O+5
Ipsos - O+3
Dem Corps - O+5
ABC/WaPo - O+1
WSJ/NBC - O+5
Those are all in a nice tight grouping with an average of 3, with not a single results more than 2 away from the average. It looks like nothing is outside of a single standard deviation. That alone is a HIGHLY unlikely event. I'm not expert enough of a statistician to figure out the odds, but the probability of getting a random sample this tight is very low against a truly random signal. In the signal processing world, we would look at this result and ask what type of filter was used on the source signal, it doesn't occur in nature.
So if I want to be paranoid, I can think of an alternate sampling method that would result in these results. Suppose I start with a very large sample with a relatively even distribution, such as 100,000 marbles which are half red and half blue, then I determine that I want to end up with a result that I have selected 52% blue marbles. What I can do is keep picking marbles until I have selected enough to show a random sample was used (e.g. at least 800 selections) but not stop the selection until I reach the 52% number. I might get there at 800, or at 900, or even at 1000. But it won't take me long to get a result that is a desired small deviation away from the actual distribution of the entire population.
If I then report those results as an actual probabilistic outcome and not report that I had a specific result desired, then it is not discernible from examining the results. Hence the old saying, "lie, damn lies, and statistics".
Over the last few days there has been some discussion of a few web postings about this over sampling, and the Rasmussen Party ID poll. If you aren't familiar with the later, Scott Rasmussen conducts a monthly sample of partisan identification. It is one question, asking are you a Republican, Democrat, or Independent? The sample size is 15,000, which in polling terms is an enormous sample. Most credible polls require about 800 samples to reach a 4% margin of error.
The August result for this poll is as follows:
This R+4 results is dramatically different from the sampling results used by all of the polls above. These polls are using samples that range from D+4 (ABC/WaPo) to D+13 (CBS/NYT). The basis for such dramatic over sampling of Democrats is never given, but the Rasmussen poll (and it's inherent accuracy given sample size and simplicity) shows these samples to be inappropriate. Again, being paranoid, it looks a lot like sampling to produce an intended result, rather than justifying the sampling due to demographic expectations.
The problems with these polls are then further compounded by the RCP average. This is commonly reported by the media, even on Fox. However, the value of an average is questionable, when the demographic samples are different. A more useful average would be if every poll was using a single demographic metric, then averaging them.
I decided to see if it was possible to reweight these polls to do exactly that, using the Rasmussen party ID as a baseline.
1) I'm starting with the Rasmussen party ID results. Since August showed a dramatic rise in Republican identification, I am normalizing the results and using the average in this poll over the last three months. The partisan ID mix that I use for normalizing all of the media polls is D/R/I of 33.8/36.0/30.3. I am confident that this represents a conservative view of the actual electorate, without considering voter enthusiasm or any other demographic breakdown like ethnicity or gender.
2) I then go into the internals of each of the polls and adjust their results to account for partisan shift. I am not going to try to equalize based on factors such as number of Democrats supporting Romney or Republicans supporting Obama. I assume that a Republican is worth equal "weight" of Romney support as a Democrat is of Obama support. I also assume that an Independent or Undecided is neutral. 50% of both types will support Obama and Romney (or stay home, which is also a neutral effect).
3) If a poll identifies a level of Independent support for a candidate, then I violate the above rule and assign a weighting factor to Independents of a corresponding value. For example, if the poll shows Independents support Romney 55 to 45, then a .55 weighting factor is used for Independent voters, rather than .50.
4) Finally I add or subtract the appropriate weights corresponding to the correct demographics. If Democrats are over sampled by 4 points (38% used by the poll), then 4% worth of Obama support is subtracted. If Independents were under sampled by 4 points (26% used by the poll), then 2% worth of Obama support is added (the 50% Obama support with Independents rule).
Reweighting all of these polls results in the following:
Tipp - R+1.37
CBS/NYT - R+6.52
Fox - O+4.48
Ipsos - O+4.35
Dem Corps - O+0.79
ABC/WaPo - R+5.54
WSJ/NBC - R+2.43
The average of these reweighted polls is then a Romney lead of 0.89%, rather than an Obama lead of 3%. Almost a 4% shift. We also see a much more noisy result, with polling results ranging from Obama 4.48 to Romney 6.52. This is a much more believable result, since we are seeing variation over more standard deviations.
Note a couple items here. First of all, it is tempting to use Rasmussen's latest results, which would given Romney a 2 point lead in the average. But I took a more conservative approach and used the average. So the result is a 45,000 sample partisan ID poll conducted over 3 months. Second, for half of these polls, I am using a very conservative value of 50% for Independent support. All of the polls that report this value, report Romney with a significant advantage in Independents (with the exception of the Fox poll). This analysis also assumes that undecideds will break 50/50, which is historically untrue. Finally, this analysis does not account for partisan enthusiasm, if the reported measurement of that is true, then Republicans will turn out higher than Democrats, increasing Romney's final results.
As a final piece of data, let's go ahead and average in the Rasmussen tracking poll (Romney +3) as of Sep 18 when I did this analysis:
Current reported average: Obama +2.63%
Actual average of normalized polls: Romney +1.16%
I think this is a much better view of where the race currently stands than is being reported.