Power of a test

In statistics, the power of a binary hypothesis test is the probability that the test correctly rejects the null hypothesis (${\displaystyle H_{0}}$) when a specific alternative hypothesis (${\displaystyle H_{1}}$) is true. It is commonly denoted by ${\displaystyle 1-\beta }$, and represents the chances of a true positive detection conditional on the actual existence of an effect to detect. Statistical power ranges from 0 to 1, and as the power of a test increases, the probability ${\displaystyle \beta }$ of making a type II error by wrongly failing to reject the null hypothesis decreases.