What defines the power of a statistical test?

The power of a statistical test is defined as the probability that the test will correctly reject the null hypothesis when the alternative hypothesis is true. Several factors influence this probability, including the significance level (alpha), sample size, and effect size.

The significance level is the threshold for determining statistical significance, and it influences the power of the test. A lower alpha level (e.g., 0.01 instead of 0.05) reduces the likelihood of making a Type I error but can also lower the power because it requires stronger evidence to reject the null hypothesis.

Sample size plays a critical role in determining power. Generally, as the sample size increases, the power of the test also increases. This is because larger samples provide more information, which enhances the ability to detect true effects.

Effect size measures the magnitude of the difference or relationship you're testing. A larger effect size typically results in higher power because it becomes easier to distinguish between the null and alternative hypotheses.

Since all these components—alpha level, sample size, and effect size—collectively influence the power of statistical tests, they define what the power actually is. Thus, it is correct to assert that all of these factors together determine the likelihood of correctly rejecting the null hypothesis when it is indeed false