Depends on what the original poster really wants with a "nonparametric
k-way ANOVA".  If what they are really looking for is an approach that has
fewer distributional assumptions, then it is possible to perform
permutation tests for linear models parameterized for k-way anova that
would eliminated the normal distribution assumption for the error term but
would certainly involve estimating parameters (including possible
interactions.)   Marti Anderson and Pierre Legendre have implemented these
sorts of permutation tests for models involving means and I've implemented
them for models of quantiles.

Brian

Brian S. Cade, PhD

U. S. Geological Survey
Fort Collins Science Center
2150 Centre Ave., Bldg. C
Fort Collins, CO  80526-8818

email:  cadeb@usgs.gov <brian_cade@usgs.gov>
tel:  970 226-9326



On Thu, Oct 24, 2013 at 12:00 PM, peter dalgaard <pdalgd@gmail.com> wrote:

>
> 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@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@cbs.dk  Priv: PDalgd@gmail.com
>
> ______________________________________________
> R-help@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.
>

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