[R] significance of differences in skew and kurtosis between two groups

[David Winsemius]

On Aug 6, 2011, at 1:19 PM, Timothy Bates wrote:

> Dear R-users,
> I am comparing differences in variance, skew, and kurtosis between  
> two groups.
>
> For variance the comparison is easy: just
>
> var.test(group1, group2)
>
> I am using agostino.test() for skew, and anscombe.test() for  
> kurtosis. However, I can't  find an equivalent of the F.test or  
> Mood.test for comparing kurtosis or skewness between two samples.

What are you planning on doing with these "moment-ous" tests? Most  
questions to this list about "how to test for normality" are based on  
false probabilistic premises promulgated by pendantic poseurs.

(Not that I am above pendantry, myself.)

>
> Would the test just be a 1 df test on the difference in Z or F  
> scores returned by the agostino or anscombe? How are the differences  
> distributed: chi2?
>
> Any guidance greatly appreciated.

It shouldn't be too difficult to construct a normal theory test using  
the distributional results for third and fourth sample moments at the  
Wikipedia Page for D'Agostino's test:

http://en.wikipedia.org/wiki/D%27Agostino%27s_K-squared_test

A statistic could be formed for two sample values with expected  
difference of zero and equal variances that depend on sample size :

  (k1 - k2)/sqrt(var1 +var2)


Or you could use the distributional results offered in:

Looney, S. W. (1995). How to use tests for univariate nor-
mality to assess multivariate normality. American Statis-
tician, 49, 64-70.


-- 
David.



>
> google and wikipedia return hits for measuring the third and fourth  
> standardized moments, but none I can see for comparing differences  
> on these parameters.
>
> best, tim
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David Winsemius, MD
West Hartford, CT