Earlier this month, I posted a request re literature references on skewness and kurtosis. Thank you very much to all those who replied.
For those interested, I have posted the relevant responses below.
My own experience, perhaps in consistency with 3., below, is that the use of the Biometrika tables is rather a conservative approach by comparison with that of using Q-Q plots. Conservativeness increases enormously when the use of these tables is replaced by the chi-square test described under 4. and hinted at under 2. When asking the question, “Does my data approximate to Normality?” the conclusions are very inconsistent if based on any one of these methods alone.
I would be interested to receive details of good literature
references to rely on when interpreting values of kurtosis and skewness as
measures of Normality, particularly with respect to defining relevant
cut-off points. I have found from my own reading that the rules of thumb for
such cut-off points are not very consistent. Any useful thoughts on
best practice would be welcome.
A related point is how to transform the data appropriately to correct
for kurtosis alone.
1. Take a look at Modstat. It uses a number of tests on data to help
2. Ah, how nice to be able to return to the easygoing 1960s, and
specifically to Vol 1 of Biometrika Tables (1962)!
For cut-off points for skewness & kurtosis, I'd start with
Tables 34B (skewness) and 34C (kurtosis). I'm pretty
sure I remember that there's a bivariate test based on b_1
and b_2, as well.
3. A personal view is that though Skewness is meaningful, it measures the
relative weight given to the two tails, kurtosis is a relatively
meaningless measure, there has been little agereement down the ages on how to
interpret it, since it relates to both flatness and to tail shape.It
also depends on fourth powers so it has a high variability. A much better
approach is to look at tail shape, see Gilchrist.(2000) Statistical
Modelling with Quantile Functions. CRC/Chapman and Hall.
4. On the first point, try looking at Durbin & Koopman: Time Series
State Space Methods, OUP 2001, pp. 33-34. Note also that they give a
combination test for the simultaneous checking of skewness and
I regret that I have no thoughts on the second point.
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