[R] Nonparametric Effect size indices

[Frank E Harrell Jr]

Chuck Cleland wrote:
> Martin Plöderl wrote:
>> Hello!
>>
>> For comparing two non-normally distributed samples, Leech (2002) suggested
>> to report nonparametric effect size indices, such as Vargha & Delaney's A or
>> Cliff's d. I tried to search the R-sites, but could not find related
>> procedures or packages that include nonparametric effect sizes. 
>> Thank you for your help!
>>
>> Citation: Leech (2002). A call for greater use of nonparametric statistics.
>> Paper presented at the Annual Meeting of the Mid-South Educational Research
>> Association, Chattanooga, TN, November 6-8.

Please beware.  That literature is just giving new names to much older 
concepts.  Look at Mann-Whitney, Wilcoxon, Kendall, Somers for better 
citations.  And Cohen's d in the pdf below should just be called a z-score.

Frank Harrell

> 
>   Based on the description of Cliff's d in
> http://www.florida-air.org/romano06.pdf, you could do something like the
> following:
> 
> g1 <- c(1,1,2,2,2,3,3,3,4,5)
> g2 <- c(1,2,3,4,4,5)
> 
> # Dominance matrix
> sign(outer(g1, g2, FUN="-"))
>       [,1] [,2] [,3] [,4] [,5] [,6]
>  [1,]    0   -1   -1   -1   -1   -1
>  [2,]    0   -1   -1   -1   -1   -1
>  [3,]    1    0   -1   -1   -1   -1
>  [4,]    1    0   -1   -1   -1   -1
>  [5,]    1    0   -1   -1   -1   -1
>  [6,]    1    1    0   -1   -1   -1
>  [7,]    1    1    0   -1   -1   -1
>  [8,]    1    1    0   -1   -1   -1
>  [9,]    1    1    1    0    0   -1
> [10,]    1    1    1    1    1    0
> 
> mean(rowMeans(sign(outer(g1, g2, FUN="-"))))
> [1] -0.25
> 
>   If you can point us to a description of Vargha & Delaney's A, someone
> can likely suggest a way of obtaining that too.
> 
>> Regards, 
>>
>> Martin Plöderl PhD
>> Suicide Prevention Research Program, Institute of Public Health
>> Paracelsus Private Medical University
>> Dept. of Suicide Prevention, University Clinic of Psychiatry and
>> Psychotherapy
>> Christian - Doppler - Klinik
>> Ignaz Harrerstrasse 79
>> A-5020 Salzburg
>> AUSTRIA
>> Phone: +43-662-4483-4345
>> Fax: +43-662-4483-4344
>> E-mail: M.Ploederl at salk.at
>>
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>> and provide commented, minimal, self-contained, reproducible code. 
> 


-- 
Frank E Harrell Jr   Professor and Chair           School of Medicine
                      Department of Biostatistics   Vanderbilt University