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

[peter dalgaard]

On Aug 7, 2011, at 20:05 , David Winsemius wrote:

> 
> 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
> 

But the trouble is that those results are valid for normal samples. This is fine if you are testing for normality, but the issue was how to compare skew and kurtosis between two arbitrary distributions, and in those cases the distribution of the sample cumulants depends on even higher moments of the distributions. So presumably, you need to go to resampling techniques (bootstrap/jackknife).

> 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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>> and provide commented, minimal, self-contained, reproducible code.
> 
> David Winsemius, MD
> West Hartford, CT
> 
> ______________________________________________
> R-help at r-project.org mailing list
> https://stat.ethz.ch/mailman/listinfo/r-help
> PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
> and provide commented, minimal, self-contained, reproducible code.

-- 
Peter Dalgaard, Professor,
Center for Statistics, Copenhagen Business School
Solbjerg Plads 3, 2000 Frederiksberg, Denmark
Phone: (+45)38153501
Email: pd.mes at cbs.dk  Priv: PDalgd at gmail.com
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