Does there exist some sample size threshold for choosing between the chi-squared test and the exact binomial test?

Question

I'd like to use the exact binomial test to analyze some data, but the exact binomial test takes too much computation and is unnecessary when the sample size is larger because it can be approximated by the chi-squared test when the sample size is large.

So what's a practical threshold for choosing between the chi-squared test and the exact binomial test?

Could somebody point to some references?

Answer 1

The chi square test is actually a test that compare proportions in contingency tables. The normal approximation with a continuity correction is more commonly used as a large sample size approximation to the exact binomial distribution. The exact binomial actually has other problems besides computation. One is the sawtoothed shape of the power function. See my 2002 paper in the American Statistician.

Sometimes people use 30 as a rule of thumb for using the normal approximation.
But this is a rule that may not apply when the true proportion is close to either 0 or 1.