Yes <[EMAIL PROTECTED]> wrote in message
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>
> Glenn Barnett wrote:
One n in Glen.
> OK, I see what you were getting at - but I still disagree, if it is
> understood that we are talking about large samples.
Your original comment that I was replying to was:
> (1) normality is rarely important, provided the sample sizes are
> largish. The larger the less important.
And I take some issue with that. I guess it depends on what we mean by large.
> For large effects,
> and large samples, you have far more power than you need; the goal is
> not to get a p-value so small that you need scientific notation to
> express it!
Correct. If the effect is not so large - and many of the people I help deal
with pretty modest effects. Large samples don't always save you - even
with the distribution under the null hypothesis, let alone power.
>
> If the effect is small, efficiency matters; but a fairly small
> deviation from normality will not have a large effect on efficiency
> either.
Agreed.
> With an effect small enough to be marginally detectable even
> with a large sample, it is likely that a *large* deviation from
> normality will raise much more important questions about which measure
> of location is appropriate.
Yes.
> For smaller samples, your point holds - with the cynical observation
> that the times when it would most benefit us to assume normality are
> precisely the times when we have not got the information that would
> allow us to do so! I might however quibble that for smaller samples it
> is risky to assume that asymptotic relative efficiency will be a good
> indication of relative efficiency for small N.
In many cases it is. And if the samples are nice and small, even when
it's difficult to do the computations algebraically, we can simulate
from some plausible distributions to look at the properties.
Or do something nonparametric that has good power properties when
the population distribution happens to be close to normal. Permutation
tests, for example.
Glen
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