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First, let me say there IS something suspicious about the polling numbers versus the results. But you pick the oddest cases, then ask how likely it is that so many odd cases should be found among those you picked because they were odd. Why 4 of 8? Pure whimsey. Why then again multiply by the odds of all 4 going R when that is the reason you picked them in the first place?
Don't get me wrong, I think this kind of analysis can be very revealing, but not when you hand pick a few. What are the odds of me being a specific age, gender, occupation, height, hair color, etc. Gee, I'm just not very likely to be real given the odds against such a combination.
To do this right you must look at the whole set of available data, and then show that these few cases are marked by the data itself as being way off scale. It's a bit more work, but the result is that the oddball cases will be generated by the numbers rather than the numbers being a result of selective sampling.
The appropriate methodology involves beginning with ALL senate races and ALL polls conducted within a specific number of days before the election. Or even better analyzing the numbers from several elections. Anything less and you're using a fixed deck.
Again, if you do this I would expect to see these 4 elections way out there in terms of the normal ranges established by the rest of the results, but until this is done I'd just be guessing.
You may recall that the odds of 3 identical margins of victory in a single county was analyzed by Pobeka under the guidance of a statistician and determined to be not improbable. The 18181 number is interesting, as are many other numbers, but the triple match was not as odd as it first seemed.
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