TypeIIFehler

Type II error, also called a beta error, is a type of error that occurs in statistical hypothesis testing when the test fails to reject a false null hypothesis. In contrast to a Type I error (incorrectly rejecting a true null), a Type II error means missing a real effect or difference.

Formal definition: Let H0 be the null hypothesis and H1 the alternative. The Type II error probability, beta, is the probability of not rejecting H0 when H0 is false. The complement of this quantity is the test’s power, 1 minus beta, which is the probability of correctly rejecting H0 when H0 is false.

Beta depends on several factors. The true effect size (the actual difference or effect under H1), the sample size, the variance of the data, and the chosen significance level alpha all influence beta. In general, larger sample sizes, larger true effects, lower data variability, and higher alpha (at the expense of higher Type I error risk) reduce beta and increase power. The choice between one- and two-tailed tests also affects beta.

Practical implications: Type II error represents the risk of failing to detect a real effect, leading to conclusions of no effect when one exists. This concept is relevant in clinical trials, diagnostics, and any decision based on hypothesis testing.

Reducing beta typically involves increasing the study’s power: increasing sample size, reducing measurement error, selecting a more appropriate test, or accepting a higher alpha level within acceptable risk.