Wednesday, November 19, 2008

Does the size of a typo matter? #mnrecount 

John Lott has commented on the StarTribune article that I discussed earlier this week.
The fact that correcting typos increased Franken�s count by 459 votes (not counting Coleman�s lost votes) and Obama�s by 106 doesn�t prove fraud. Indeed, the Star Tribune might still be right in its claims that election officials made mistakes because they were tired.

But my point was a simple one: Why did the �typo� corrections increase Franken�s total so much more than any other candidate�s? Indeed, so much more than all the other races for the presidency, Congress, and statehouse combined. The Star Tribune�s response was to deny the claim was true.
I also got this response from John to my earlier post in which I didn't think the typos were necessarily the result of fraud.
It is not simply the direction of the change, but also the size of the change that you might want to take into account in figuring out the odds. You are obviously right if you are looking at the direction of the change and the odds that they all go in the same direction, but if you looked at the odds that you would have changes of the sizes observed here going in the same direction, the odds of that are exceptionally small. That said, people do win the lottery sometimes and this might be one of those times for Franken.
I've been puzzling about that for a day. Can one think about the 'probability of a typo'? I looked at a spreadsheet that measured changes in tallies by precinct from the Wednesday morning to the end of Monday Nov. 10 (pre-machine audit, but after all counties had checked their figures and reported in.) There are 4130 precincts in my sample. I got these counts:
So the probability of a change -- typo or miscount or whatever -- could be seen as the total precinct-level changes for any of the three candidates (15+5+29+10+37+11=107) divided by three times the number of precincts (since they can each make three changes. That gives a probability of .008636, or 0.86%. There are 1.15% of Franken precinct totals that were changed. We got twelve more Franken changes than we would expect and fifteen fewer Barkley changes. How significant is that? And notice that up changes are far more likely than down changes. I wonder how likely that is. I don't have a model for that in my head. If I thought it was random and used a binomial distribution, I'd put the probability of 48 or more errors at about 1.9%, or around 50 to 1 against. The chance of having fifteen or fewer errors (as was Barkley's case) is 0.3%. Coleman's data, at least on the counting of typos, appears pretty normal even though his total went down.

But John's opinion seems to be that changes in the hundreds column should count for more. I'm unclear how to model that or why it is so. It seems to me a typo distributes randomly across the places. But we also know that the at least a few of the people who write these numbers down care about the outcome, which I think is some of the claims being made here (not necessarily mine), so that treating their scribblings as random events is also probably a bad assumption.

And at that point I'm kind of stuck. If the typos are non-random, I'm not sure how to use statistics to solve them, and I'll let other people try to figure that out.

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