"W. D. Allen Sr." wrote:
>
> 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.
>
> Either the Chi Square or S-K test, as appropriate, should be conducted to
> determine normality before interpreting population percentages using
> standard deviations.
Another common mistake made in statistical inference is confounding the
two propositions:
"The data are close enough to the model that a hypothesis test cannot
reject the model at some fixed p-value"
and
"The population is close enough to the model for the interpretation to
be useful".
Logically, these are almost entirely unrelated. In particular, for very
large samples the test will almost always reject the model, even when
the population distribution is very close; for small samples the model
will rarely be rejected even when it is in fact flagrantly wrong, due to
lack of power in the test.
What is needed in the small-sample case is outside _knowledge_ (not
"well, it _might_ be true" or "in this discipline we usually assume..."
assumptions!) about the distribution - without this we should not be
making any distributional assumptions. In the large-sample case we need
a measure of closeness that is independent of sample size and based on
the idea of "close enough for practical purposes" not "have we enough
data to quibble?"
-Robert Dawson
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