Consider a balanced one-way ANOVA. Estimate the between-group component
of variance from the usual
var(between) = (MS(within)-MS(between))/n)
the mean squares being as usual and n being the number of observations
per group.
Can anyone point me to work that describes the distribution of
var(between) (assuming normality for both within- and between-group
error) or suggests confidence intervals for it?
The background: We certify reference materials for chemical
measurement. In homogeneity tests on reference materials, current
practice is to allow for between-unit variability when putting a
confidence interval on the material's value. If the between-bottle
variance is significant, that allowance is simply based on var(between).
If the between-group effect is not significant, one can, given that the
test power is rarely high, legitimately ask how large a between-bottle
variance might reasonably be left undetected. The most obvious way to
answer that would be to look at its distribution... hence the question.
[I have already looked at other approaches - for example, one can ask
what scale of between-group variance would be detected at specified
power; but that isn't quite the answer to the same question]
Any pointers gratefully received.
S Ellison
Lab of the Government Chemist
UK
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