[R-sig-teaching] exchangeability

[Vokey, John]

On 2010-03-02, at 4:00 AM, r-sig-teaching-request at r-project.org wrote:

> I am trying to understand the assumptions for a permutation test and
> figure out how to explain those to beginning students.  (I am working
> on a project to integrate resampling methods into the first course in
> statistics.)  I have received some help from Tim Hesterberg who gave
> me the first definition of exchangeability I've seen.  One question is
> whether assumptions apply to randomized experiments or to using
> permutation tests for survey sampling applications.  In addition it
> would be helpful to have some counterexamples where the assumptions
> are NOT satisfied (and why). 

One perspective is that it makes NO assumptions.  It depends what you intend the resulting p-values to mean.  If they are to be interpreted as probabilities, then, yes, exchangeability can be seen as an enabling assumption.  On the other hand, seen only as a scale of typicality, the randomization/permutation p-values do not *assume* exchangeability so much as provide a test of it.

--
Please avoid sending me Word or PowerPoint attachments.
See <http://www.gnu.org/philosophy/no-word-attachments.html>