R help - Oct 2013 - Nonparametric k-way ANOVA

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?

Looking forward to your answers,


--
vicent
@vginer_upv
about.me/vginer_upv

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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
> 
> 	[[alternative HTML version deleted]]
> 
> ______________________________________________
> 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

Hello, Vincent,

you may want to take a look at "Nonparametric methods in factorial 
designs" by Edgar Brunner and Madan L. Puri in Statistical Papers 42, 1-52 
(2001).

There is the R-package nparcomp for one-way layouts, but the paper goes 
further (and mentions another software) and is maybe a starting point for 
you.

  Hth -- Gerrit

On Thu, 24 Oct 2013, 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?
>
> Looking forward to your answers,
>
>
> --
> vicent
> @vginer_upv
> about.me/vginer_upv
>
> 	[[alternative HTML version deleted]]
>
> ______________________________________________
> 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.