SECTION 6.5 Summary

• The power of a significance test measures its ability to detect an alternative hypothesis. The power for a specific alternative is calculated as the probability that the test will reject when that alternative is true. This calculation requires knowledge of the sampling distribution of the test statistic under the alternative hypothesis. Increasing the size of the sample increases the power when the significance level remains fixed.
• In the case of testing versus , decision analysis chooses a decision rule on the basis of the probabilities of two types of error. A Type I error occurs if is rejected when it is in fact true. A Type II error occurs if is accepted when in fact is true.
• In a fixed level significance test, the significance level is the probability of a Type I error, and the power for a specific alternative is 1 minus the probability of a Type II error for that alternative.