# Calculating p-values in R

Suppose you are doing an LR test in R, and that the test statistic has an asymptotic $$\chi^{2}$$ distribution under the null hypothesis.

You were probably taught to compare the test statistic against the appropriate critical value reported in a table in the appendix of a statistics or econometrics textbook. That becomes inconvenient once you have to do more than two or three such tests, and if you are in a situation where you are doing many tests, it's no fun (and error-prone) to return nine months later to work on a revision. A better approach is to let R calculate p-values for you. Here are some examples.

With one degree of freedom, the critical $$\chi^{2}$$ value for $$\alpha = 0.05$$ is 3.84, and with two degrees of freedom, it is 5.99. We can confirm this:

pv1 <- 1-pchisq(3.84, 1)
pv2 <- 1-pchisq(5.99, 2)

The value of pv1 and pv2 are both approximately 0.05. There's no magic here. All the pchisq function does is evaluate the cumulative distribution function at 3.84 and 5.99 for the given degrees of freedom. We subtract the result from 1 to get the probability of observing a $$\chi^{2}$$ distributed variable at least that large under the null hypothesis.

Similarly, for the standard normal distribution:

pv3 <- 1-pnorm(1.96)
pv4 <- 1-pnorm(1.645)

pv3 and pv4 are approximately 0.025 and 0.05, as expected. Recall that these are the $$\alpha=0.05$$ critical values for two-sided and one-sided tests, respectively.

Last updated: March 23, 2017

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