# What does a confidence interval around a p-value mean when using a permutation test?

I am using the coin package in R to do a permutation test and it gives output that looks like this:

> pvalue(pt)
[1] 0.1479615
99 percent confidence interval:
0.1450811 0.1508754


Why would one want a confidence interval for a p-value? How should it be interpreted, and how should it be used?

• That's because the permutations were not exhaustive in your case, that was a Monte Carlo permutation significance test. In such a test, p-value is not a precise (point) probability but rather an interval about the obtained value of p. Mar 4, 2013 at 19:34
• cran.r-project.org/web/packages/coin/vignettes/… Mar 4, 2013 at 19:36

The pure frequentist interpretation: If your were to do this experiment $N$ times, you should expect $X$ percent of the time (99% in your case) or $N * X$ times, that the true $p$ value falls inside the range provided by this 99% confidence interval that percentage or number of times.