The Lincoln Plawg - the blog with footnotes

Politics and law from a British perspective (hence Politics LAW BloG): ''People who like this sort of thing...'' as the Great Man said

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Friday, October 01, 2004

That margin of error

There's no poll fever round here. But, perhaps, a mild curiosity.

Most of these polls run to a margin of error of around plus or minus four points. The larger the sample - and the sample in some state polls isn't that large - the smaller the margin; but the Law of Large Numbers [1] dictates that it is hard to squeeze the margin of error much lower that plus or minus three points.

My impression is that, even following his cringemakingly crappy performance at the Florida debate, Bush is maintaining a lead in the polls of four or five points: at or just outside the margin of error [2]. Which naturally feeds a instinctive feeling that the race is too close to call. (If voters have to suffer the brain-numbing tedium of a presidential election, at least let it be a sporting contest!)

However, it must be wrong to suggest that the margin of error covers all sins. Say Bush and Kerry are polled at 54-46 in a four point margin-of-error poll, with no don't knows and Nader having dropped dead. (Pause for Dem who-hoo-ing.) The headline of the poll says, it's too close to call.

But surely, it must be more comfortable to be the candidate eight points ahead than the candidate eight points behind!

Pursuing the thought: although 54-46 to Bush must - with a four point MOE - include the possibility that, in fact [3], Kerry is in front, it must be much more likely that such numbers point to a reality in which Bush is ahead.

Compare a straight 50-50 split in the polling: still within the MOE, but much more likely that the sample polled, in fact, has a majority in favour of Kerry.

Other factors may well be relevant - such as the fact (at least, I've seen it asserted as fact) that most who poll as undecided but eventually vote go for the challenger rather than the incumbent.

But it seems to be misleading to suggest that a lead within the MOE can be ignored.

"I don't even think I'm explaining it well." "You're explaining it a lot, though."

  1. Treading on dangerously mathematical ground here!

  2. Fine: that's the national polls, whereas, in fact, there are fifty different elections. But, if the consistency in the national polling is not good, that in state polling makes the yo-yo look like an instrument of stability.

  3. Obviously, we don't know the fact - that's why we take samples. But, just for the sake of argument...

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