Sorry if you've got this mail without subject.
Also I would like to mention that I have originally posted this question on
http://mathoverflow.net/questions/32365/combining-variances but due to the lack
of answers, re-posted it here. I will keep both allstat and methoverflow.com
updated with the responses I will get.
My original question is
>I have a set of N* bodies, which is a random sample from a population whose mean
>and variance I want to estimate.
>
>A property of each body is being measured m_i times (m_i>1$ and different for
>each body index i identifies which body it is;
>the property is expected to be distributed around zero). I would like to
>describe the resulting measurement.
>
>Particularly I'm interested in average property value and in the variance.
>
>The average value is simple. First calculate the mean values for each body and
>then calculate the mean of means.
>
>The variance is more tricky. There are two variances: the variance of
>measurement and the variance of
>
> property values. In order to have an idea on the confidence we have in any
>single measurement,
>
> we need to account for both the sources. Unfortunately, I can't think of a good
>method.
>
> It is obvious that putting all the numbers in a single pool and calculating the
>stdev of this pool isn't a good idea.
Any suggestion?
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