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Topic: Skewness and kurtosis p-values
Replies: 11   Last Post: May 28, 2013 6:50 AM

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David Jones

Posts: 80
Registered: 2/9/12
Re: Skewness and kurtosis p-values
Posted: May 25, 2013 4:43 PM
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"Cristiano" wrote in message news:knr09n$hha$

On 25/05/2013 18:36, David Jones wrote:
> Probably, that site knows what a "two-sided test" means whereas, judging
> by your description of simulation for the skewness, you do not.

I know what a "two-sided test" means (I wrote some 2-sided tests to test
RNG's), but I could be a bit confused in writing a simulation for a
2-sided test. Anyway, I don't think that it is very important. Here I'm
just trying to understand how they get those critical values because I
need to be sure that my simulation works fine.

> The simplest change to your procedure would be to use the absolute
value of
> the calculated skewness, since that is the test statistic for a
> two-sided test in this case. On the webpage, "alpha" is the total area
> of the two tails, not just one tail.

I know that (I saw the 2 red tails).

If I use the absolute value of the skewness calculated (many times) for
7 numbers in N(0,1) and I see that the 90th percentile is .8163, I would
argue that 90% of the times the |skewness| <= .8163. Am I wrong?
If I'm right, .8163 should be the critical values for their alpha= 0.1.
Even if I don't know anything about 2-sided tests, could someone tell
me, please, how in the earth they get 1.307?



Have you tried finding an alternative source of critical values? Judging by
values in "Biometrika Tables" (which need to be adjusted for differences in
definition, and which give values only for n=25 upwards, and which may be
subject to some approximation error), the values for skewness on that
webpage seem right. You could check "Biometrika Tables" for details of how
they got their values (Pearson ES, Hartley HO (1969) Biometrika Tables for
Statisticians, Vol 1, 3rd Edition, Cambridge University Press), but it is
unlikely that the webpage used those methods.

Thus there is at least some evidence that the webpage is correct at least
for n>=25, and there that your programming is wrong somewhere. You could try
testing against published values for the variance of the skewness, which
would potentially avoid doubts about those webpage tables.

David Jones

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