Dang, I've been waiting a long time for this one....
In the New York Times/CBS News poll released today, Obama leads McCain by 48% - 43%, a margin they point out is within the poll's sampling error. Many journalists are quick to call this a "statistical dead heat". They're wrong. Here's why.
(If you're a mathophobe, stop reading. We're going to talk statistics here.) To begin with, what they're calling "sampling error" is what's called a confidence interval. A poll uses a technique called sampling - you can't very well ask the entire electorate what they think so you can use a randomly selected group to do the same thing, with a reasonable degree of certainty. The generally accepted certainty range is usually 95%, or about two sample statistical deviations either side of the mean (the published poll result - I warned you, there is math in here). I dug really deeply into the poll and found the sampling error to be 3%. So if you're Obama, there's a 95% chance that somewhere between 45% and 52% of the electorate will vote for you. If you're McCain with his result at 43%, the margin is between 40% and 46%
So, again a warning to Mathophobes, that's really a bell curve there. The Mean in this case is the result of the survey. The 95% line is at 1.9 standard deviations, or sigmas (σ ). To see what the poll is actually telling us, we draw two of these, one centered at 43% (McCain's results) and one centered at 48% (Obama's results)
The gap between Obama and McCain is 5%. The standard deviation of the poll is 1.5%. The midpoint between Obama and McCain is 2.5 points, or 1.667 standard deviations.
90% of Obama's winning outcomes lie within plus or minus 1.69 standard deviations of his mean, or 48%. Since we're not worried at all about the plus side, the right side of the curve (he still wins), 95% of all the outcomes of the election based on this poll make Obama the winner. Even if I give McCain the right side of his curve, Obama wins 90% of the time in this polling scenario.
Doesn't sound like a dead heat to me. So next time you hear "statistical dead heat," unless the race is tied, if you know the margin of error, you can call "bullshit." Not to mention the fact that a five-point gap in the popular vote is generally an electorial blowout.
Two in one night. Nosy's on a roll.
TAGS: Polls, Bell Curve, Statistics, Lamestream Media