[R] Robust ANOVA with variance heterogeneity

[Kjetil Halvorsen]

Hola!  see below.

On Sat, Oct 3, 2009 at 2:45 PM, David Winsemius <dwinsemius at comcast.net> wrote:
> Do you have a citation for that statement? I cannot convince myself that it
> should be true.

OK. that took some time, since I have no nonparametrics book with me,
but it is a fairly
standard assumption the friedman.test  shares with wilcox.test and
others. One online reference giving this is:

http://www.mathworks.com/access/helpdesk/help/toolbox/stats/index.html?/access/helpdesk/help/toolbox/stats/friedman.html&http://www.google.cl/search?q=assumptions+of+friedman+test&ie=utf-8&oe=utf-8&aq=t&rls=com.ubuntu:en-US:unofficial&client=firefox-a

specifically:
"Friedman's test makes the following assumptions about the data in X:

    *

      All data come from populations having the same continuous
distribution, apart from possibly different locations due to column
and row effects.
    *

      All observations are mutually independent.                 "

This is also easy to investigate by simulation in R:

I did:
> A[, 1] <- rnorm(100, 0, 1)
> A[, 2] <- rnorm(100, 0, 5)
> A[, 3] <- rnorm(100, 0, 500)
> friedman.test(A)

	Friedman rank sum test

data:  A
Friedman chi-squared = 2.96, df = 2, p-value = 0.2276

which surprised me!   This test seems to be somewhat robust against
variance heterogeneity  ???, but that case is not included in the
usual theory.

Kjetil

>
> After looking at the CRAN Task View, I would suggest the OP look at
>  rlm(MASS) or lmrob(robustbase).
>
> --
> David
>
> On Oct 2, 2009, at 11:05 AM, Kjetil Halvorsen wrote:
>
>> On Fri, Oct 2, 2009 at 8:45 AM, David Winsemius <dwinsemius at comcast.net>
>> wrote:
>>>
>>> There are multiple routes to "robust" statistics, but the quick answer to
>>> this question is probably friedman.test
>>
>> I don't think friedman.test is robust to variance heterogeneity. It is
>> only robust to
>> non-normality.
>>
>> Kjetil
>>
>>
>>
>>>
>>> I seem to remember a CRAN Task View on the area of Robust Statistics.
>>>
>>> --
>>> David Winsemius
>>>
>>>
>>> On Oct 2, 2009, at 3:05 AM, Maike Luhmann wrote:
>>>
>>>> Dear list members,
>>>>
>>>> I am looking for an alternative function for a two-way ANOVA in the case
>>>> of
>>>> variance heterogeneity. For one-way ANOVA, I found oneway.test(), but I
>>>> didn't find anything alike for two-way ANOVA. Does anyone have a
>>>> suggestion?
>>>>
>>>> Thank you!
>>>>
>>>> Maike Luhmann
>>>> Freie Universität Berlin
>>>
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>>>
>
> David Winsemius, MD
> Heritage Laboratories
> West Hartford, CT
>
>