[R-sig-ME] Non-parametric 2x2 Mixed Factorial ANOVA in R?

Ben Bolker bbolker at gmail.com
Mon Nov 12 15:59:54 CET 2012

Marianne K. <mariannestephan at ...> writes:

> Hello!  My data has one between-subject factor ("group", 2 levels,
> n=10 per group) and one within-subject factor ("session", 2 levels).
> I am mainly interested in the interaction between group and
> session.Because of the small sample size (n=20 cases in total, 10
> per group), I though I should use a non-parametric test.  However,
> did I understand right that there doesn't exist any non-parametric
> mixed factorial ANOVA in R?

  Someone can correct me if I'm wrong, but as far as I'm aware
the problem is not so much "this method doesn't exist in R" as
"this method is hard to define in general" -- that is, controlling
for non-independence/grouping structure in nonparametrics is
not all that easy.

  A couple of thoughts:

 * robust methods may be an alternative -- someone posted about
this on the list recently
 * you could try bootstrapping or permutation testing (being careful
to respect the grouping structure of the data
 * two levels is not really enough to formally fit a random effect,
but depending on the details of your data structure you may be
able to do something much simpler.  For example, I'm going to guess
that your 20 observations represent paired observations (session 1,
session 2) on 5 individuals in each of two groups.  Compute the
within-subject differences between sessions for each individual:
now you have 5 differences in each group.  You can test the between-group
differences in response with an ordinary 1-way ANOVA on the
differences (for a single factor, the sums of squares etc. don't 
differ for random vs fixed effects, I think).  You can similarly
test differences in within-subject means etc.

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