R help - May 2010 - Question about package coin

Anyone know if coin can run a permutation test based on a (user-defined)
statistic other than the mean difference?  The function independence_test does
the permutation t-test via difference in means.  I'm wondering if it's
possible to use independence_test to run a permutation test for some other
statistic than the difference in means.  For example, I'd like to run a
permutation test using Welch's t instead of the difference in means.

The help for independence_test reveals that "teststat" is an argument
which allows for specification of standardized scalar test statistic, a maximum
type statistic, or a quadratic form.  I cannot, however, figure out if it is
possible to specify how the statistic should be calculated by, for example,
supplying a function.

There are other mentions of test statistic in the help file but they all seem to
have to do with the names of classes or objects which can be retrieved from coin
output.

Bryan

---------------
Bryan Keller, Doctoral Student/Project Assistant
Educational Psychology - Quantitative Methods
The University of Wisconsin - Madison

On Sat, 29 May 2010, Bryan Keller wrote:
> Anyone know if coin can run a permutation test based on a (user-defined) 
> statistic other than the mean difference?  The function 
> independence_test does the permutation t-test via difference in means.
...by default, that is.
> I'm wondering if it's possible to use independence_test to run a 
> permutation test for some other statistic than the difference in means.
Yes.
> For example, I'd like to run a permutation test using Welch's t
instead
> of the difference in means.
No.
> The help for independence_test reveals that "teststat" is an
argument
> which allows for specification of standardized scalar test statistic, a 
> maximum type statistic, or a quadratic form.  I cannot, however, figure 
> out if it is possible to specify how the statistic should be calculated 
> by, for example, supplying a function.
Have you considered reading the references mentioned in the documentation.
I suggest you start with
   vignette("LegoCondInf", package = "coin")
which essentially is the "The American Statistician" paper mentioned
in
the help pages.

The general framework is that the user can specify data transformations 
for which an independence test is computed. Depending on the data 
transformation, this can be a t test, chi-squared test, Wilcoxon test, 
Kruskal-Wallis test, and many many more.

Furthermore, note that the null hypothesis is always permutation 
invariance. Hence, the Welch test does not fit into this framework because 
under the null it assumes same means but with potentially different 
variances, which is not invariant with respect to permutations.

Therefore, the default t statistic in independence_test() computes a mean 
difference standardized by the one-sample standard deviation (with only a 
single mean!). This is neither the pooled two-sample standard deviation 
(with two means) that t.test(..., var.equal = TRUE) uses nor the 
two-sample standard deviation (with two means and two standard deviations) 
of the Welch test.

hth,
Z

Thanks for the reply, that answers my question.? 

I'm actually interested in using the Welch t in a randomization model
framework where the variance heterogeneity is introduced by the treatment effect
and is not present under the null hypothesis of no differential treatment
effect.? In other words, the test would be valid because exchangeability is
satisfied by random assignment of experimental units to treatments.

Much thanks to you and your colleagues for providing and maintaining this
fantastic package.

Bryan

On 05/30/10, Achim Zeileis? <Achim.Zeileis at uibk.ac.at> wrote:
> On Sat, 29 May 2010, Bryan Keller wrote:
> 
> >Anyone know if coin can run a permutation test based on a
(user-defined) statistic other than the mean difference?? The function
independence_test does the permutation t-test via difference in means.
> 
> ...by default, that is.
> 
> >I'm wondering if it's possible to use independence_test to run
a permutation test for some other statistic than the difference in means.
> 
> Yes.
> 
> >For example, I'd like to run a permutation test using Welch's t
instead of the difference in means.
> 
> No.
> 
> >The help for independence_test reveals that "teststat" is an
argument which allows for specification of standardized scalar test statistic, a
maximum type statistic, or a quadratic form.? I cannot, however, figure out if
it is possible to specify how the statistic should be calculated by, for
example, supplying a function.
> 
> Have you considered reading the references mentioned in the documentation.
> I suggest you start with
> ? vignette("LegoCondInf", package = "coin")
> which essentially is the "The American Statistician" paper
mentioned in the help pages.
> 
> The general framework is that the user can specify data transformations for
which an independence test is computed. Depending on the data transformation,
this can be a t test, chi-squared test, Wilcoxon test, Kruskal-Wallis test, and
many many more.
> 
> Furthermore, note that the null hypothesis is always permutation
invariance. Hence, the Welch test does not fit into this framework because under
the null it assumes same means but with potentially different variances, which
is not invariant with respect to permutations.
> 
> Therefore, the default t statistic in independence_test() computes a mean
difference standardized by the one-sample standard deviation (with only a single
mean!). This is neither the pooled two-sample standard deviation (with two
means) that t.test(..., var.equal = TRUE) uses nor the two-sample standard
deviation (with two means and two standard deviations) of the Welch test.
> 
> hth,
> Z
-- 
---------------
Bryan Keller, Doctoral Student/Project Assistant
Educational Psychology - Quantitative Methods
The University of Wisconsin - Madison