Tuesday, October 28, 2008

Margin Of Error Equals Who The Hell Knows?

Entertaining Iowahawk post.


This is, for all intents and purposes, how political pollsters compute the mysterious "margin of error," which has everything to do (and only to do) with pure mathematical sampling error. If you look at the formula above and round it just a smidge, you get a simple rule of thumb for the margin of error of a sampled probability:

Margin of Error = 1 / sqrt(n)

So if the sample size is 400, the margin of error is 1/20 = 5%; if the sample size is 625 the margin of error is 1/25 = 4%; if the sample size is 1000, it's about 3%.

Works pretty well if you're interested in hypothetical colored balls in hypothetical giant urns, or survival rates of plants in a controlled experiment, or defects in a batch of factory products. It may even work well if you're interested in blind cola taste tests. But what if the thing you are studying doesn't quite fit the balls & urns template?

* What if 40% of the balls have personally chosen to live in an urn that you legally can't stick your hand into?

* What if 50% of the balls who live in the legal urn explicitly refuse to let you select them?

* What if the balls inside the urn are constantly interacting and talking and arguing with each other, and can decide to change their color on a whim?

* What if you have to rely on the balls to report their own color, and some unknown number are probably lying to you?

* What if you've been hired to count balls by a company who has endorsed blue as their favorite color?

* What if you have outsourced the urn-ball counting to part-time temp balls, most of whom happen to be blue?

* What if the balls inside the urn are listening to you counting out there, and it affects whether they want to be counted, and/or which color they want to be?

If one or more of the above statements are true, then the formula for margin of error simplifies to

Margin of Error = Who the hell knows?

Because, in this case, so-called scientific "sampling error" is completely meaningless, because it is utterly overwhelmed by unmeasurable non-sampling error. Under these circumstances "margin of error" is a fantasy, a numeric fiction masquerading as a pseudo-scientific fact. If a poll reports it -- even if it's collected "scientifically" -- the pollster is guilty of aggravated [nonsense] in the first degree.

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