Type II Error vs Power

A Type II error is a miss, the mistake of overlooking an effect that truly exists. Its probability is written $\beta$ (the Greek letter beta), and the power of the test equals $1 - \beta$, the chance of catching a real effect. For example, acquitting a guilty defendant is a Type II error when the null hypothesis of innocence is false. Larger samples and bigger true effects lower $\beta$, cutting the risk of a Type II error.

Power is a test's ability to detect a real effect when one truly exists. It equals $1 - \beta$, where $\beta$ (the Greek letter beta) is the probability of a Type II error. For example, a test with power 0.80 has an 80% chance of rejecting the null hypothesis when the alternative is genuinely true. Power rises with a larger sample size, a bigger true effect, less variability, or a larger significance level $\alpha$.