[ai-geostats] Continuing discussion on "F and t tests"

[Donald E. Myers]

The sample variance (assuming that you use the "n-1" divisor) is an 
unbiased estimator of the population variance provided you use random 
sampling. Note the "ing" on the word sampling,  it is not quite correct 
to talk about "random samples" or "independent samples". or at least it 
may be mis-leading. Random sampling pertains to how the data is 
collected, not the end result.

Note moreover that one can always compute a sample variance for a given 
data set but this does not show that the random variable or random 
function has a finite variance.

The sample variance (even when sampling from a normal population) is 
relatively speaking more variable as an estimator of the variance than 
the sample mean is as an estimator of the population mean.  The sampling 
distribution in this restricted case is chi-square, the chi-square 
distribution has a "fat" tail (as contrasted with a normal distribution).

If correctly (or maybe you would want to say "adequately" ) estimated, 
the sill of a second order stationary random function would be the 
variance of the random function. In general, the sample variance will 
not estimate the sill (because you are not using random sampling).

Donald Myers
http://www.u.arizona.edu/~donaldm
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