On Sat, 5 Aug 2000, Gates, Christopher [OMP] wrote:
> Donald, thank you so much for your response. I had the opportunity to
> converse with my friend (HOH) on this matter again, and his explanation
> seemed to closely follow yours, or at least that's how I see it.
>
> I guess the bottom line for me is that the assumption for normality in
> the t-test relates to the population of sample averages (if one could
> get such measures) which, regardless of the type of sample distribution,
> are probably (CLT) approximately normally distributed for n > 4? 30?
The approximation is asymptotically better for larger n, of course.
> It would seem to me then, that for almost any usual (>5) sample size
> for a t-test, there is probably little need to do any testing of the
> normality of the sample since by the CLT the averages are probably
> going to be normally distributed.
There is almost certainly little _utility_ to so doing; for small sample
sizes tests for normality (or for that matter any other distribution)
have little power.
> Is this an acceptable position to take?
"Acceptable" I don't know about: depends on the universe of discourse.
But you should try to justify the assumption that the observations are
taken independently, and that the underlying within-group variances are
approximately equal. And you should also be aware that while the t-test
is well known to be fairly robust against violations of assumptions,
that robustness applies to two-sided tests; one-sided tests are, by
comparison, rather fragile.
> Also, as another chance to display my ignorance, I couldn't find "a
> fortiori" in my dictionary.
Try RHD, between "aforetime" and "afoul", not between "a" and "AA".
It will surely be in OED as well.
------------------------------------------------------------------------
Donald F. Burrill [EMAIL PROTECTED]
348 Hyde Hall, Plymouth State College, [EMAIL PROTECTED]
MSC #29, Plymouth, NH 03264 603-535-2597
184 Nashua Road, Bedford, NH 03110 603-471-7128
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