I am looking for advice, literature, and/or comments about options for
combining data taken in a number of sample units at each of a large
number of locations into one descriptive grand mean. Taking a mean over
all data points strikes me as incorrect in that the variance is reduced
by the large apparent sample size (ie, number of sample units x number
of locations). It seems to me that I should calculate a mean across
sample units from each location, then take the mean of those means - the
actual sample size would just be the number of locations. However,
calculating a variance for just these means assumes they are not
estimates - it ignores the variability within the samples that make up
each location mean.
My question is, is there a recommended way to incorporate the variance
of each location mean into the overall mean of means? Or maybe it would
be more accurate to just ask how the variance of a mean of means should
be calculated.
Not a statistician, obviously . . .
Steve Bousquin
Stephen G. Bousquin, Ph.D.
Environmental Scientist
South Florida Water Management District
West Palm Beach, FL
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