These examples come the closest I have seen to having a known variance.
However, often measuring instruments, such as micrometers, quote their
accuracy as a percentage of the size of the measurement. Thus, if you
don't know the mean you also don't know the variance.
Jon Cryer
At 09:28 AM 4/23/01 -0400, you wrote:
>> 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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