Rich Ulrich wrote:
>
> - BUT, Robert,
> the equal N case is different from cases with unequal N -
> - or did I lose track of what the topic really is... -
Possibly <grin>.
In the Z-for-proportion case the equal and unequal N
cases do not differ at all; the null hypothesis (under which
p-values are calculated) makes the two populations identical,
and which is in what sample doesn't matter.
In the t test case equal and unequal N are identical
IF the variances are equal, but the nominal null hypothesis
(equal means) does not imply this. It's an 'assumption' which
is sort of a copout, because (on the one hand) nobody really
believes it but (on the other hand) nobody's prepared to throw
it into the null, because that would weaken the alternative.
You could have:
Ho: the means are equal and the variances are equal
Ha: either the means or the variances differ
but the editors wouldn't like it.
A more sophisticated t test does NOT assume equal
variances but uses some sort of fiddle to adjust the degrees
of freedom. In some cases this can be simplified for equal N.
-Robert Dawson
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