Hi
On Mon, 16 Oct 2000, Pat Cabe wrote:
> My old CRC Tables gives a plot of the F distribution and it
> sure as heck has two tails. The Tables references Snedecor,
> Statistical Methods. That's my authority; what's yours,
> Rick? Note that I never claimed that the "other" tail was
> useful, only that it existed and that F values could fall
> into it. Indeed, there are probabilities associated with that
> "other" tail, but they aren't interpretable.
I'm speculating here, but it seems logical to me that there is
nothing intrinsically non-meaningful about the lower tail of the
F distribution. If we went back to the basic form of F = v1/v2,
then I would guess if one did _not_ always put the larger
variance on the numerator, that a significant difference would be
represented by either a small F with p(Fobs<Fsmall=.025) or a
large F with p(Fobs>Flarge=.025). The sum would be a two-tailed
probability of .05, our desired alpha. By always putting the
larger on top (or the one expected to be larger, as in ANOVA), we
negate the need to have lower critical F values.
But even as I write this, it seems to imply a possible paradox or
at least complexity. Specifically, if we use F = max(v1,v2) /
min(v1,v2) with tabled p=.05, then it would seem that our true
alpha is .10. I haven't looked at using this variant of F for
many years, but is it the case that one indeed uses tabled p=.025
to determine the critical value for rejecting the null
hypothesis?
I hope this free association didn't muddy the waters.
Best wishes
Jim
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James M. Clark (204) 786-9757
Department of Psychology (204) 774-4134 Fax
University of Winnipeg 4L05D
Winnipeg, Manitoba R3B 2E9 [EMAIL PROTECTED]
CANADA http://www.uwinnipeg.ca/~clark
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