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Re: [Phys-l] Symbol for uncertainty



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From: John Denker [mailto:jsd@av8n.com]

So, we agree that it doesn't make sense to talk about u(x_i) because
x_i is just a number, and has no uncertainty. If I roll a pair of
dice and observe five dots, then x_i=5 with no uncertainty. That works with dice, but how about the measurement of the period of a pendulum? There's uncertainty in the measurement, as well as uncertainty in the distribution of the expected value of the measurement (let's say that the dominant contribution comes from the accuracy with which the length is measured in some particular experiment). Now I have kids with an uncertain prediction and an uncertain measurement. Is there a _simple_ measure that you'd suggest for characterizing the overlap of the distributions? I can get them as far as conceptually 'getting' that distributions that don't overlap aren't likely the same, and those with significant overlap are, but I haven't yet found a _simple_ measure that will allow them to compare (at least, not one that I'm super happy with: I've had them look for overlap within 1 sigma of the mean, which was easy to do, but not necessarily on good footing. ...or maybe it is? Conceptually, I'm OK with it, but I'd like a comparison measure without doing T tests or similar).

jg