[Rd] Chi-squared test p-value based on simulation.

From: Rolf Turner <r.turner_at_auckland.ac.nz>
Date: Fri, 23 Dec 2011 19:16:12 +1300

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



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