Glenn Barnett wrote:
> > (1) normality is rarely important, provided the sample sizes are
> > largish. The larger the less important.
>
> The a.r.e won't change with larger samples, so I disagree here.
I don't follow. Asymptotic relative efficiency is a limit as sample
sizes go to infinity; so how does it change or not change "with sample
size"? Or does that acronym have another expansion that I can't think
of?
I hadn't had efficiency in mind so much as the validity of p-values for
the t test. However, the same point holds for efficiency. For large
samples, I would suggest that the efficiency of both tests is usually
adequate; and a small sample does not tell us enough about the
population distribution to tell much about the relative efficiency
anyway.
When you've got lots of data, you also have a choice of lots of
reliable methods of inference; when you haven't got enough, you also
can't trust the methods that look as though they might help. ("Sort of a
metaphor for life", he said cynically.)
You are of course right that when I wrote "rank-sum" I meant
"signed-rank". (Of course, as Potthoff showed, the rank-sum test *is*
valid under the assumption of symmetry, but that is another story.)
-Robert Dawson
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