Logical Extremes, Beta, and the Power of the Test

Abstract

There is a potential misuse of the power function under the logical extreme when the null hypothesis is true. The power function is defined to measure the probability of rejecting the null given any value of the parameter being tested. It can be used to obtain the power and the β values only under the alternative hypothesis. When the null is true, the power function can be used to obtain the size of the test. The power and the probability of committing a Type II error are, however, undefined and, hence, the power function should not be used to obtain these values.

• Power function
• Simulations
• Type II error

Acknowledgments

The authors wish to thank two anonymous referees for their detailed and useful comments. All remaining errors are the responsibility of the authors.