[R] Robust ANOVA with variance heterogeneity

David Winsemius dwinsemius at comcast.net
Tue Oct 6 20:24:01 CEST 2009


On Oct 6, 2009, at 1:51 PM, Kjetil Halvorsen wrote:

>
> 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.

I do not see that your citation implied that there would be a material  
impact (especially toward false positive results which I take to be  
the meaning of "not robust") from a violation of the equi-variance  
assumption, ...  only that equivariance was the basis of the  
derivation of the statistical theory. The test might even be  
conservative for all we know until the question has been subjected to  
simulation studies. And then your simulation suggested not much of a  
problem, which does not seem surprising to me given that a rank  
transformation has been applied to the data. So I remain unconvinced.

-- 
Regards;
David.


> 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
>> ,

David Winsemius, MD
Heritage Laboratories
West Hartford, CT



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