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Tuesday, August 10, 2004

Margin of Error: An Exegesis 

Altercation correspondent Bryan Gygi of Oakland, CA, explains why the incumbent is in even deeper shit than Your Innumerate Monarch had previously realized:
Todd Gitlin's statement that given the +/-4 % margin of error in the Time poll, Bush and Kerry could be in a virtual tie, shows how little the concept is understood even by media literate folks. Margin of error is another term for 'confidence limits' which are the bounds that one is 95% certain (the most common benchmark) that the estimated value lies. So the Times pollsters are 95% certain that Kerry's actual figure is between 44% and 52%, while Bush's [is] 95% likely to be between 39% and 47%.

This is similar to an exercise I used to give to my statistics class: given these figures, what is the probability that the two men are tied? You need a table of z scores to solve this, but in this case +/-4% implies a z-score of 1.65, so there is a SD of 2.42%. So for Kerry and Bush to be tied at say 45.5% (halfway between the two) that would be equivalent to a z-score of 1.03 for each, which corresponds to a probability (in the tails) for EACH man of 0.152 (15%).

Now, of course joint probabilities are multiplicative (still with me?) so the probability that Bush and Kerry are tied at 45.5% is 0.023 (2.3%). And that's actually the best case scenario for Bush. The probability that they are both tied at either 44% (worst Kerry scenario) or 47% (best Bush scenario) is 0.016 (1.6%). Now you know why most people in the media never bother to discuss this (because most don't understand it), and instead pretend that there still could be a horse race.

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