### [Politics] How Polls Work: Intro. to Random Sampling

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From the "Better Late Than Never" department...

Since there has been understandable attention given recently to poll results, I thought some forumites might like to better understand the apparent leap from polling a thousand people to extrapolating to a hundred million or so.

Let's say that an opaque jar holds three balls. They are identical in every respect except possibly color, with zero to three of them green and the rest (if any) red.

Now we randomly draw two balls from the jar, and find that both are green. Consider the odds that the remaining ball is also green. Most people would say it's even, but the the third ball is a clear favorite to be green.

Here's why. We'll label the balls A, B, and C. Suppose A and B are green, and C is red. There are three ways to draw two balls randomly, (A, B), (A, C) and (B, C). (I'm disregarding the order that the balls are drawn, as if two balls are drawn in one swoop, but it would work out the same even if order were considered.) So if C were red, there is only a one in three chance of drawing two balls without drawing the red one. In other words, if there was a red ball in the jar, we would have likely picked it.

Polls are based on this principle, that if the characteristics of the sampled population (literally) were vastly different from the poll's result, then the latter would probably have been different. There is of course the chance that the poll results grossly misrepresent the population. That's where "margin of error" comes in.

A poll's margin of error indicates the range that the actual population is a big favorite to lie within. So if a poll shows Candidate 1 to have an 8% lead over Candidate 2, with a 5% margin of error, that's saying that there's a really low chance that Candidate 1's lead isn't somewhere between 3% and 13%. What "really low chance" means is rarely stated when a poll's result is reported, but normally it means around 10% to 15%. This means that 85% to 90% of the time, the actual population will fall within the poll's margin of error.

Note that for a poll's result to be valid, it is essential that the subjects be picked randomly. Great care is required to avoid introducing bias either in the selection of subjects or the formulation of the questions they are asked.

Feel free to direct any questions to Flint, Z, Malcolm or Jim Cooke.

-- David L (bumpkin@dnet.net), November 07, 2000