[R] Nonparametric k-way ANOVA

[peter dalgaard]

On Oct 24, 2013, at 18:59 , Vicent Giner-Bosch wrote:

> Sorry if this subject has been already dealt here.
> 
> Which are some common tests for nonparametric k-way ANOVA?
> 
> I have read about Kruskal-Wallis test as a kind of nonparametric one-way
> ANOVA, but I have not found anything about a general-setting (I mean k-way)
> nonparametric ANOVA.
> 
> Can you recommend me a good R package (or other reliable software) for that?

Can you provide reliable _theory_ for it? 

Some people have tried just to do ANOVA decompositions after replacing observations by their ranks, and referring sums of squares to chi-squared distributions. However, that derivation only holds under the global null hypothesis. In general, it is problematic to define additivity and interaction in a nonparametric setting since there are no parameters that effects can be additive in!

Stratified tests do exist and make OK sense. In those, you split data into groups and do the rank sums within groups, then look at a weighted sum of the  group rank sums, work out the mean and variance assuming no effect in any group, etc. For a two-way layout without replications, this is friedman.test(). I believe the "coin" package implements some more general cases.

-pd


> 
> Looking forward to your answers,
> 
> 
> --
> vicent
> @vginer_upv
> about.me/vginer_upv
> 
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-- 
Peter Dalgaard, Professor,
Center for Statistics, Copenhagen Business School
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