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Binomial Probability Tests: Some Theory

A binomial probability test uses a null hypothesis that the probability of a successful trial is P, where P is the tested probability. The total number of trials performed is the number of nonmissing entries in the test variable. Since a binomial variable is all zeroes and ones, a successful trial is counted as one where the variable=1 and nonsuccessful trial is where the variable=0.

Let's think about it using an example. Mary wants to figure out if she is living in a small city or a large town. She finds out that in large towns 56% of houses have white picket fences. She drives around ten city blocks and writes either 0 (no picket fence) or 1 (picket fence) for every house. This gives her a sample of 175 houses. In this case, the test value is .65 and the number of trials is 175. Stata will then calculate what it would expect to see in her sample if the real distribution is, in fact, significantly different from 56% (this is 175 * .96) or 98 picket-fenced houses.