[R] Nonparametric Effect size indices

[Chuck Cleland]

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.

  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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-- 
Chuck Cleland, Ph.D.
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