Power (statistics)

In frequentist statistics, power is the probability of detecting an effect (i.e. rejecting the null hypothesis) given that some prespecified effect actually exists using a given test in a given context. In typical use, it is a function of the specific test that is used (including the choice of test statistic and significance level), the sample size (more data tends to provide more power), and the effect size (effects or correlations that are large relative to the variability of the data tend to provide more power). More formally, in the case of a simple hypothesis test with two hypotheses, the power of the test is the probability that the test correctly rejects the null hypothesis ( H 0 {\displaystyle H_{0}} ) when the alternative hypothesis ( H 1 {\displaystyle H_{1}} ) is true. It is commonly denoted by 1 − β {\displaystyle 1-\beta } , where β {\displaystyle \beta } is the probability of making a type II error (a false negative) conditional on there being a true effect or association.