This deathless line was spoken by Harvey Korman as Hedley Lamarr in Blazing Saddles, and it is good advice in many situations in today's strange and suspicious world. I use it today discussing the New Hampshire election results in which the Democratic polls released closest to the election did a very bad job of predicting the actual results. Or did they?
A few weeks back, friend of the blog Distributor Cap did a post about polls, which included a definition of margin of error WITH 95% confidence level. This means that if candidate X is preferred by 49% of the people polled and the margin of error is +/- 5%, the pollsters are saying that they are 95% confident the vote tally for X will be between (49+5)% = 54% and (49-5)% = 44%. They could be wrong about this number, but the odds of that are about 1 in 20 of being wrong and 19 in 20 of being right, which is another way to say 95%.
This works pretty well in two person contests or contests where third party candidates will only pick up some small part of the vote, probably less than 5% and certainly less than 10%. In wide open contests like both the Rep and Dem situations right now, where five candidates or more might each pick up a measurable proportion, this 95% confidence is in each number, 95% confident they get Obama right, 95% confident they get Clinton right, etc.
In a two person poll, the only ways to make a mistake are either to have one side take a massive amount of the undecided (very rare in late stages) or one side to take away from the opponent, making both numbers wrong. Here the odds are pretty much 95% right, 5% wrong, or 19 in 20, as I stated earlier.
But with five numbers to predict, and each of those predictions at the 95% confidence level, the probability of getting them all right is .95 x .95 x .95 x .95 x .95 = 77.4%. Here are all the odds in five person race.
all 5 right: 77.4%
1 wrong: 20.4%
2 wrong: 2.1%
3, 4 or all five wrong: 0.1%
One time in five these kinds of polls should have one mistake, someone doing much better or much worse than predicted. That's not really a rare occurrence. And for that I repeat the fictional evil politician Hedley Lamarr, for even evil politicians can give good advice every once in a while.
(Ladies and) Gentlemen, rest your sphincters.
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