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Math Indicates Pollster Is Forging Results
An anonymous reader writes "Nate Silver suggests the political pollster Strategic Vision is 'cooking the books. And whoever is doing so is doing a pretty sloppy job.' Silver crunched five years worth of their polling data, and found their reported results followed a suspicious pattern which traditionally suggests fraud. The five-year distribution of the numbers 'is not random. It's not close to random.' The polling firm had already been reprimanded by the American Association for Public Opinion Research for failing to disclose their methodology, though the firm argues they did comply with the organization's request. Their response to Silver's accusation? 'We have a call in to our attorney on this and fully intend to take action that will vindicate us.'"
a. you can't post
b. if you do manage to post, post goes to wrong topic!
In other words, do they do stuff that actually matters?
In a word, yes. Nate Silver manages the blog FiveThirtyEight and is well-known as a statistical analyst from the 2008 US election (among other things). Strategic Vision has released quite a few polls. In Silver's words,
So yes, this is pretty big news, should it turn out that Strategic Vision's behavior is in fact illicit. They're influential enough that news agencies may pick up their polling results. This is bad enough, but when you factor in the fact that polling results can be very effective propaganda in something like a presidential race, fraudulent polling can have significant consequences.
Nope, you're looking at the webpage of a different company! See Nate's previous article:
They are a partisan, Republican-oriented polling company. They have gotten into trouble in the recent past for their questionable results.
First, the example he gives where he looks at polls from ALL sources is an example of a plausible distribution of real results because, assuming the majority of pollsters are not cooking their data, the data should be dominated by randomness. He then looks at this particular pollster and finds a much greater disparity in trailing digit frequency. The question is, is it significant, or just chance?
Given the numbers, it's not particularly hard to figure out. You can calculate the likelihood of any particular result given a theoretical distribution using a G test of goodness of fit. Technically for numbers this small you could use an exact test but I don't know of a web version and I'm too lazy to write one up. But here's a description of, and an excel spreadsheet that performs, the G test of goodness of fit: http://udel.edu/~mcdonald/statgtestgof.html
Basically, you plug in the distribution you see and compare it with the one you expected. What you get is the probability of that distribution occurring by chance. So if we plug in the observed data for all the pollsters and assume equal likelihood for all trailing digits we get a p=0.006. Whoops, looks like our assumption isn't quite correct. As the blog author notes, the observed distribution is humped a little, favouring the middle numbers. He also gives a possible explanation. For giggles, the probability of the Strategic Vision results given equally probable trailing digits is absolutely microscopic: p=1.44x10^-17. Together those tell us that our assumption of equal digit distribution is probably not quite right, but the Strategic Vision data still looks mighty funny.
Okay, so assume instead that most pollsters aren't making up their numbers. Not that their numbers are necessarily accurate, but that they're at least not making them up off the top of their heads. So using the data from all pollsters as a template, how likely is the Strategic Vision distribution? That's a G test of independence: http://udel.edu/~mcdonald/statgtestind.html. We could use Fisher's exact test, but I can't find one that will do a 2x10 table.
Plugging in the data, we get G=43.068, d.f.=9, which gives p=2.09x10^-6. The blog author was actually a little careless when he said the chances of Strategic Vision's results are millions to one against. If you insist on the equal-probability theory then the odds are 70 quadrillion to one against Strategic Vision and 166 to one against the industry as a whole. Taking the more realistic approach that the industry average is a better representation of the actual probability, the odds against Strategic Vision's results are about half a million to one against. Not millions to one, but close enough.