The formula to calculate the beta error (β) is:
\[ \beta = 1 - \alpha - (1 - \beta) \]
Where:
Beta error, also known as Type II error, occurs when a statistical test fails to reject a false null hypothesis. In other words, it is the error of not detecting an effect that is present. The probability of committing a Type II error is denoted by β. The power of a test, which is \( 1 - \beta \), represents the probability of correctly rejecting a false null hypothesis. Understanding and minimizing beta error is crucial in hypothesis testing to ensure the reliability and validity of the test results.