[R] significance in difference of proportions: What problemareyou solving?

[Torsten Hothorn]

On Thu, 27 Nov 2003, Spencer Graves wrote:

> Hi, Torsten:
>
>       Thanks for the reference to library(exactRankTests).  That seems
> like a reasonable alternative to "prop.test" with small samples.
>
>       However, aren't "exact tests" and the related bootstrap
> methodology what Deming called "enumerative techniques", more relating
> to describing a fixed finite population than "enumerative techniques"
> for describing more general processes that will likely generate similar
> samples in the future?  Don't "exact tests" and bootstraps answer
> different ("enumerative") questions from those posed by standard
> ("analytic") parametric procedures?  (I know that the chi-square
> distribution is only an approximation to the distribution of the
> contingency table chi-square;  however, that is a different issue from
> the question of enumerative vs. analytic studies.)
>

yes, thats my understanding too. The "enumerative techniques" as
you call it condition on the data actually observed and determine
the null distribution of the associated test statistic from the data. In
contrast, unconditional procedures require some assumptions to the
underlying data generating process from which the null distribution is
derived. The appropriate choice depends of the kind of experiment
under test: In a randomized trial we would like to see all possible
outcomes of the trial caused by "rerandomization" and the enumerative
techniques are natural here. When we draw many samples from predefined
populations, men and women, say, "rerandomization" of gender is of course
not that easy and we may assume something about the data generating
process :-)

Best,

Torsten