W. D. Allen Sr. <[EMAIL PROTECTED]> wrote in message
nH9u6.6370$[EMAIL PROTECTED]">news:nH9u6.6370$[EMAIL PROTECTED]...
> A common mistake made in statistical inference is to assume every data set
> is normally distributed. This seems to be the rule rather than the
> exception, even among professional statisticians.
The most common mistake to me seems to be the one where
people use the data to answer a question other than the
one in which they were interested.
> Either the Chi Square or S-K test, as appropriate, should be conducted to
> determine normality before interpreting population percentages using
> standard deviations.
1) The Chi-square test is effectively useless as a test of normality, since
it ignores the ordering in the bins (the binning itself is an additional
but relatively smaller effect).
2) A common mistake in inference is to assume, without checking, that
a formal hypothesis test of normality followed by a normal-theory
procedure will have desirable properties.
In practice the first thing to do is to find out how big a deviation from
normality you can tolerate with the procedure you have in mind, taking
into account not just level but power (if you're testing) or size of
confidence intervals (if you're doing point estimation), and so on.
If it's large, you are probably safe unless it's obvious your data are
drastically non-normal (extreme skewness can be a problem). If it's
small, then you should look at a different procedure - either a robust
or a nonparametric procedure, for example - or a different assumption.
Glen
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