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st: RE: sktest


From   "Nick Cox" <n.j.cox@durham.ac.uk>
To   <statalist@hsphsun2.harvard.edu>
Subject   st: RE: sktest
Date   Fri, 23 Aug 2002 10:42:55 +0100

Michael Cha

> Would anyone guide me how to interpret the output for sktest?
>
> I have tested with several variables, some of which are
> normally distributed and some are not.
>
> However, most of them gives me the same results as follows.
>
> Variable |  Pr(Skewness)   Pr(Kurtosis)  adj chi-sq(2)  Pr(chi-sq)
> ----------+--------------------------------------------------------
>         a |      0.055         0.000               .       0.0000
>         b |      0.655         0.000           64.26       0.0000
>         c |      0.000         0.000               .       0.0000
>         d |      0.000         0.000               .       0.0000
>         e |      0.000         0.000               .            .
>
> With other test of normality, variable e was not normal,
> but highly skewed.
>
> I don't have my manual handy right now.
>
> Would you please let me know how to interpret them?
> In addition, is there any other useful command to test
> skewness, kurtosis and normality, please let me know.
>

I think you have it backwards: these are significance levels,
not, as you may be thinking, the probability of normality,
whatever that would mean. Thus P = 0.000, strictly  P < 0.0005,
indicates _not_ normal on this criterion.

However, what you don't tell us are your sample sizes.

Crudely, any deviation from normality will be
declared significant at conventional levels
if the sample size is large enough. Whether
the deviation is of practical interest is often
a completely different matter.

With the auto data and n = 74, a small sample by
many standards, you can see some results from

foreach v of var price-for {
	sktest `v'
	qnorm `v'
	more
}

which produces some interesting results. For
example, -gear_ratio- yields Pr(kurtosis) = 0.014
but a look at a graph indicates that this is slight
short-tailedness and it is difficult to believe that the non-normality
of -gear_ratio- could ever be problematic.

A slide show from

foreach v of var a b c d e {
	qnorm `v'
	more
}

is more enlightening than a battery of these tests.

Nick
n.j.cox@durham.ac.uk

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