Political polling wunderkind, Nate Silver, has done it again. First he saw how Strategic Vision was making up polling data and now his low rating of Research 2000 has lead to a lawsuit of R2K by the Daily Kos for fraud. I would like to look at how the alleged fraud was detected. Namely, physical phenomena including the acts and beliefs of intelligent agents is marked by statistical randomness and how hard it is for humans to fake it.
There were three things that stood out with the R2K data:
1. There were too many pairs of even and odd numbers in the crosstabs. If a percentage of a male respondent was even then so was the female and the same was the case for an odd number. The odds that this would happen by random is 10^228. That’s right. 1 followed by 228 zeroes.
2. The variance between the weekly samples was too small. (9.947). A chi-squared distribution showed the odds of this happening via regular polling is 1 in 10^16.
3. There was insufficient week to week variation that was zero. There are too many times that the week-to-week variance was plus or minus one but not zero. This last one I want to focus on because it shows how our innate sense of what is “random” fails us.
First, let’s look at how Gallup’s tracking poll varies from week to week:
Now R2K’s weekly variance:
Note the “narrowness” of the R2K versus Gallup distribution. Now on to the psychology of trying to pretend to be random. On the TV series Numbers one episode showed how spatial distributions are too uniform to be random. The criminal in the story was trying to look like the crimes were in random locations but his human psychology betrayed him. There is an analogous issue here. See this 1960 study on generating a “random” sequence. What we do like the Numbers example is we have insufficient runs and clustering. It looks like 0100110110110101 and not like 1111100101111100000. We sense the repeated 1s and 0s don’t look “random” enough when in reality real random sequences act like that. Having the same approval or disapproval numbers between weeks doesn’t feel right so instead a small change one way or the other wrongly feels random. The same goes for large week-to-week jumps. Rigorous mathematical analysis shows, however, it’s not.
Intelligent Design uses the same “gut feel” rather than calculated statistics. They complain that the evolutionary process cannot be random. In the process of doing their “folk science” they make some very basic statistical mistakes.
Note Nick Matzke’s critique of Behe’s statistics of the odds of drug resistant malaria in Edge of Evolution:
Here again, Behe just assumes this. He gives no reasons in his book for why two binding sites would have to evolve *at once* anywhere in actual real-life evolution, which is the only reason you would multiply 10^20 by 10^20 to get 10^40 required organisms. In real life, evolution would most commonly evolve one binding site for one function, then the complex would sit around doing its function for awhile, and then occasionally another protein would evolve binding for some other function, or for improving the current function. It’s called exaptation — change of function in evolution — and it has been absolutely fundamental in evolutionary theory ever since Darwin.
The mistake is the assumption that the two random gene changes are statistically independent when they are not. The other “gut feel” that’s done by Intelligent Design proponents is that intelligent agency and “randomness” are mutually exclusive categories. As we see from the behavior of intelligent agents above not only is randomness not the antithesis of this, it’s required. We cannot rely on our flawed instincts. We have to do the math.
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