From: "William A. Levinson, P.E." <wlevin02@SPAMBLOCKharris.com>
Newsgroups: sci.astro,sci.math,sci.physics,sci.stat.edu,sci.stat.math
Subject: Re: Applied statistics question.
Date: Tue, 10 Nov 1998 10:51:33 -0500

Robert Clark wrote:

>   I have a question on testing whether a physical  variable is zero or
> not. You
> have a variable which your theory says should be zero. You do some
> experiments
> and measure this variable over several repetitions of the experiment.
> You then
> compute the average and standard deviation of these measurements.
> Suppose
> however that these experiments are extraordinarily delicate and there
> are very
> large errors involved, resulting in a very large standard deviation.
> Now in
> these experiments it turns out that the average of the measurements of
> the
> variable turns out to be surprisingly large, rather than the expected
> value of
> zero. But because the standard deviation is so large, zero lies within
> the
> expected error of the experiment.

You can never prove it's exactly equal to zero. You can only test the
null hypothesis mu=0 versus the alternate hypothesis mu<>0 (mu is the
population mean). Acceptance of the null hypothesis does NOT prove mu=0;
it only shows that there is not enough evidence to prove mu<>0.  (The
null hypothesis is like the presumption of innocence in a criminal
trial.)

You also can get a confidence interval for mu. If this contains zero,
you must reject the alternate hypothesis (mu<>0). Also, you get a level
of confidence for mu; for example, you can be 95% sure that mu is
between -0.12 and +0.20. The more measurements you take, the tighter
your confidence interval.

See also http://www.ganesha.org/spc/hyptest.html

--
William A. Levinson, P.E., CQE, CMfgE
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