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Re: systematic error and statistical error



Miguel Santos asked:

Shouldn't it always be the standard error of the mean!?


I think whether one reports standard error of the mean or sample standard
deviation depends upon what one is trying to communicate.

Standard error of the mean gives an idea of how close the calculated mean is
likely to be to the true mean (where the true mean would be the mean of the
whole population, were that possible to obtain). Standard error of the mean
gets better (smaller) as we acquire more data points.

Standard deviation is essentially a measure of precision. As we take more
and more data points, our calculation of the standard deviation might be a
better approximation of the "true" standard deviation, but it should not
really change much as we collect more data. That is, the standard deviation
is essentially fixed by the resolution of the apparatus and/or method we are
using.

So what are you trying to tell the reader? Are you trying to demonstrate
that your new instrument/method has good resolution? If so, report the
standard deviation. On the other hand, if you are trying to indicate how
well you think you have pinned down the mean, you should report the standard
error of the mean.

Having been an instrument designer/builder in a former life, I often wanted
to communicate the resolution of the instrument. It wouldn't do much good
to report the standard error of the mean in this case because I could make
it arbitrarily small by taking sufficient data points. But I could not make
the standard deviation get smaller by taking more data points. I could only
make the standard deviation smaller by improving the instrument/method.


Michael D. Edmiston, Ph.D. Phone/voice-mail: 419-358-3270
Professor of Chemistry & Physics FAX: 419-358-3323
Chairman, Science Department E-Mail edmiston@bluffton.edu
Bluffton College
280 West College Avenue
Bluffton, OH 45817