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We have been in e-mail quarantine so I have been unable to respond to
the comments on my observations regarding the (inadvertent) shrinkage in
a small hypothetical data set with equal means presented by Reeve. A
number of people misunderstood or misinterpreted my observations. I am
available for clarifications and dialog with those who wish to pursue it
with me (katzper.at.cder.fda.gov).
I feel obliged to respond to one erroneous authoritatively stated
comment. The constancy of the F ratio = (sample var1 / sample var2) with
increased sample size was taken to refute my statement that "Doubling
each observation will yield a significant result." It doesn't refute
anything. One would expect a competent statistician to know this. Size
matters.
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Dear Meyer,
The F-ratio remains constant under linear transformations (ie doubling each
observation) as stated by RA Fisher, this refutes your claim that "Doubling
each observation will yield a significant result." However, if you
actually meant doubling the number of observations (and assuming they
replicated exactly those you had already ie your sample variances were
absolutely accurate) then you would reach significance at the 5% level. I
think this is just a simple misunderstanding of what was intended by the
word "doubling".
James
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