October 30, 2006
I know I've read this complaint from others in previous election cycles, but it bears repeating: a poll in which the two candidates are within the margin of error is not a statistical tie, no matter how fond reporters may be of announcing that it is.
Yesterday I saw a poll showing Tammy Duckworth (the evil Tammy Duckworth!) at 42% and Peter Roskam (the evil Peter Roskam!) at 46%, with a 4% margin of error. This margin of error is just like a confidence interval, but this doesn't mean there's an equal probability that the true values will be anywhere within that interval! In fact, it's highly unlikely that Duckworth and Roskam are tied, or that Duckworth leads; unfortunately the term statistical tie suggests otherwise.
That poll isn't new. It was taken 10-18/24.
Why it took almost a week to publish I don't know. It is consistent with other polls from the same time at the end of Duckworth's dark cycle when she didn't have the cash to answer the NRCC and Roskam attack commercials running day and night.
The race seems more even now.
Actually, a better Wikipedia article to have linked to would have been margin of error itself, which includes a discussion of the appropriate way to interpret results like this--by calculating the difference between the two probabilities and the standard error of that difference, and then calculating the chance that a sample from the distribution that those two values represent is greater than 0.
The resulting chance is, roughly, the probability that the higher estimated value is actually higher, or what that article calls the "Probability of Leading". For the poll in question, assuming a 95% confidence level in the poll, we can be 84% sure that Roskam is actually leading (although we can't say by how much).
link added, thanks.
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