Tsung,

This property of permutation tests has been known for some time. Generally 
speaking, as the number of permutations increases the variation in significance 
levels obtained from repeated runs decreases. Earlier work in the statistics 
literature from the 70s and 80s by Edgington and others discusses the issue.

You will also find a figure demonstrating the property for behavioral data in 
Adams and Anthony 1996 (Fig. 3).

Best,

Dean

Dr. Dean C. Adams
Professor
Department of Ecology, Evolution, and Organismal Biology
       Department of Statistics
Iowa State University
www.public.iastate.edu/~dcadams/<http://www.public.iastate.edu/~dcadams/>
phone: 515-294-3834

From: Tsung Fei Khang [mailto:[email protected]]
Sent: Sunday, May 31, 2015 12:38 PM
To: [email protected]
Subject: [MORPHMET] Stability of p-values (physignal and testing for 
morphological integration)

Dear community,

I would like to share my experience with using some (really cool) computational 
tools for phylogenetic signal and morphological integration analysis.

I am using physignal (geomorph R package) and the Phylo.Morphol.PLS function 
provided in the paper by Adams and Felice (2014; PLoS ONE, 9:e94335) in my 
work. I noticed that if the same analysis is rerun for a particular number of 
iterations, the results may vary. Additionally, I observed that increasing the 
number of iterations, up to some critical point, may push down the p-value, 
depending on data set (didn't happen with the plethspecies (9 species) data, 
but happened in my data set - 13 species, not salamanders). I attach runs (10 
times) for both data sets for iterations of 100, 1000, 10000 and 100000 here 
for Phylo.Morphol.PLS. Note that some kind of stable results is attained after 
1000 iterations (default) for the plethspecies data, but for my case, which 
needs 10000.

I think the notion that p-values returned from a permutation method are 
actually realizations of random variables with a certain mean and variance may 
not be familiar to many biologists, who are accustomed to expect a reproducible 
p-value when the same data set is rerun using common statistical tests. Perhaps 
in a future version the authors of the code can implement a checker within the 
functions that checks the number of iterations for  attaining "convergence", so 
that a more stable p-value is returned?






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