In statistical hypothesis testing, you typically express the belief that some effect exists in a population by specifying
an alternative hypothesis . You state a null hypothesis as the assertion that the effect does *not* exist and attempt to gather evidence to reject in favor of . Evidence is gathered in the form of sample data, and a statistical test is used to assess . If is rejected but there really is *no* effect, this is called a *Type I error*. The probability of a Type I error is usually designated “alpha” or , and statistical tests are designed to ensure that is suitably small (for example, less than 0.05).

If there is an effect in the population but is *not* rejected in the statistical test, then a *Type II error* has been committed. The probability of a Type II error is usually designated “beta” or . The probability of avoiding a Type II error (that is, correctly rejecting and achieving statistical significance) is called the *power* of the test.

Most, but not all, of the power analyses in the GLMPOWER and POWER procedures are based on such standard hypothesis tests.