A Binomial Test is an exact test of the statistical significances between the observations and expected distribution into two categories.
- Common use One common use of the binomial test is in the case where the null hypothesis is that two categories are equally likely to occur (such as a coin toss). Tables are widely available to give the significance observed numbers of observations in the categories for this case. However, as the example below shows, the binomial test is not restricted to this case.
- Where there are more than two categories, and an exact test is required, the multinomial test, based on the multinomial distribution, must be used instead of the binomial test.
- Large samples: For large samples such as the example below, the binomial distribution is well approximated by convenient continuous distributions, and these are used as the basis for alternative tests that are much quicker to compute, Pearson's chi-squared test and the G-test. However, for small samples these approximations break down, and there is no alternative to the binomial test.