Prompted by a (fairly!) recent question from Michael Fuller, I got
to thinking about the issue of goodness-of-fit testing via chisq.test()
using p-values obtained via simulation.
I believe that such p-values are really valid only if there are no ties
in the data. Since there are only finite number of possible samples
and hence only a finite number of statistic values, ties (while perhaps
improbable) are not impossible. So the validity of the p-values obtained
via simulation is possibly slightly suspect.
I am given to understand that the p-values remain valid if the ties are
broken *randomly*.
Might it thereby be advisable to jitter the values of (the "true" and
simulated) test statistics before calculating the p-value?
Anyone have any thoughts on this?
cheers,
Rolf Turner