# Re: st: RE: sktest

 From "Michael Cha" To statalist@hsphsun2.harvard.edu Subject Re: st: RE: sktest Date Fri, 23 Aug 2002 13:06:35 -0400

```Thank you, Nick and Ronan,

My sample size is more than 1000.

If sktest is not that reliable, then is ther any other solution than graphics?
pnorm and qnorm are very useful but the interpretation is not always easy unless observed and expected lines exactly overlap.

summarize v, detail gives the numeric value of skewness and kurtosis. Can they be more accurate?

Then, can you guide me one more time if I am wrong?
As far as I know with summarize v, detail values,
Skewness: value 0 = not skewed
negative value = positively skewed
positive value = negatively skewed

Kurtosis: value 3 = normal
greater than 3 = slim
smaller than 3 = fat

Is this right? If not, please enlighten me.

Thanks
MCHA

--

On Fri, 23 Aug 2002 10:42:55
Nick Cox wrote:
>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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>

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