On Thu, 6 Jul 2000, John Nash wrote (to the AERA-D list):
> Many of us operate under the following assumption:
>
> For |skewness coefficient| < 1, data is considered to be normally
> distributed.
Well.
A normal distribution has skewness = 0; but I presume you know that.
Skewness only addresses the issue of symmetry, not other aspects of the
shape of a distribution. Presumably the rule-of-thumb you state must be
invoked along with some other rules, since (as other respondents have
pointed out) skewness < 1 (or any other arbitrary value) will not filter
out U-shaped or rectangular or triangular or multimodal distributions,
none of which could be reasonably described as "normal".
I take it then that you do not really mean to claim that
"If |skewness| < 1, the data are normally distributed.", since the
antecedent is not sufficient for the consequent. Probably the "rule" in
its original form was more like this:
"If |skewness| > 1, the data are NOT normally distributed."
Or, somewhat more precisely,
"If |skewness| > 1, the null hypothesis that the data are a random
sample from a normally distributed population can be rejected."
In that form, the rule presented can be investigated a bit further.
Using one or more of the techniques mentioned in other responses, under
what conditions (for openers, how large must the sample be?) would that
null hypothesis be rejected when |skewness| > 1?
I cannot think of any other reasonable way of interpreting the rule, or
of seeking a logical support (or, for that matter, a citation) for it.
OTOH, I cannot think of circumstances under which I would have any
interest whatever in applying such a rule... ;-)
> However, I'm at a loss to find a citation in the literature
> supporting such a notion.
>
> Any suggestions?
>
> Much thanks,
> --->john
>
> John Nash
> [EMAIL PROTECTED]
>
> AERA Division D: Measurement and Research Methodology Forum
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