Hypothesis Testing and Power

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Hypothesis Testing and Power

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.

An important goal in study planning is to ensure an acceptably high level of power. Sample size plays a prominent role in
power computations because the focus is often on determining a sufficient sample size to achieve a certain power, or assessing
the power for a range of different sample sizes.

There are several tools available in SAS/STAT software for power and sample size analysis. PROC POWER covers a variety of
analyses such as t tests, equivalence tests, confidence intervals, binomial proportions, multiple regression, one-way ANOVA, survival analysis,
logistic regression, and the Wilcoxon rank-sum test. PROC GLMPOWER supports more complex linear models. The Power and Sample
Size application provides a user interface and implements many of the analyses supported in the procedures.

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