> Date: Fri, 20 Apr 2001 13:02:57 -0500
> From: Jon Cryer <[EMAIL PROTECTED]>
>
> Could you please give us an example of such a situation?
>
> ">Consider first a set of measurements taken with
> >a measuring instrument whose sampling errors have a known standard
> >deviation (and approximately normal distribution)."
Sure. Suppose we use an instrument such as a micrometer, electronic
balance or ohmmeter to measure a series of similar items. (For
concreteness, suppose they are components coming off a mass production
machine such as a screw machine.) As long as the measuring instrument
isn't broken, we don't have to conduct an extensive series of repeated
measurements every time we use it to determine its error variance with a
part of the given conformation. Normality is also reasonably likely under
those circumstances.
Slightly more sophisticated version of the same: Supposed the operating
characteristics of such a machine can be characterized by slow drift (due
to tool wear, heat expansion of machine parts, settings that gradually
shift, etc.) plus independent random noise that is approximately normal.
It is plausible in that setting that the variance of measurements on a
short series of parts would be fairly constant. (I'm not just making
this up; it's consistent with my own experience in my former career as a
machinist.) Again, you don't have to calibrate the error variance of the
"measurement" (in this case, average measurement of several successive
parts to estimate the current system mean) every time you do it.
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