reference values for skewness and kurtosis in normal distributed data and SE

[Rasmus Tolstrup]

Dear all. I have a dataset with n>1800.
I am trying to determine if my data is not normal distributed.
I have performed the following:

1. regress var1
2. predict sdres, rstandard
3. predict fit
4. hist sdres, normal freq
5. qnorm sdres

I was in doubt about the histogram and qq-plot and I decided to use skewness and kurtosis to determine if my data could be discarded as normal hereby:

summarize sdres, detail
(Kurtosis 2.524735)
(Skewness -.5102313)

The litterature seems inconclusive about these values and I have found a suggestion on researchgate forum that the Kurtosis/SEkurtosis and the skewness/SEskew should be < 1.96 to have normal distributed data, but I have not found a way to get the SE values for skewness and kurtosis?

So, can I make the assumption that my data as normal distributed data or should I reject the assumption? If so, how do I put a value on this?


I hope you can help me

[Nick Cox]

The sampling distributions of skewness and kurtosis converge extremely slowly to asymptotic normality: various discussions of e.g. the Jarque-Bera test seem to ignore or understate this point.

But simulations show that your sample sizes should be fine.

Although it's not directed at quite your problem you might find some use or interest in

SJ-10-3 st0204 . . Speaking Stata: The limits of sample skewness and kurtosis
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . N. J. Cox
Q3/10 SJ 10(3):482--495 (no commands)
uses Stata and Mata to show that sample skewness and
kurtosis are limited by sample size and that these limits
impart bias to estimation

which does more than is indicated by the summary above. Accessible at http://www.stata-journal.com/sjpdf.h...iclenum=st0204

I would wish now also to cite

Picard, H. 1951. A Note on the Maximum Value of Kurtosis. The Annals of Mathematical Statistics 22: 480-482. http://www.jstor.org/stable/2236642

[Rasmus Tolstrup]

Thank you