Question
What is Type II error?
Answers
GPT-4o mini
A Type II error, also known as a "false negative," occurs in statistical hypothesis testing when a test fails to reject a null hypothesis that is actually false. In other words, it is the error made when a test concludes that there is no effect or no difference (i.e., the null hypothesis is accepted) when, in reality, there is a true effect or difference present.
For example, consider a clinical trial testing a new medication's effectiveness compared to a placebo. A Type II error would occur if the trial concludes that the medication does not work (i.e., the null hypothesis is not rejected) when, in fact, the medication does have a positive effect.
The probability of making a Type II error is denoted by the symbol \(\beta\). The power of a test, which is the probability of correctly rejecting a false null hypothesis, is calculated as \(1 - \beta\). Therefore, increasing the power of a test reduces the likelihood of a Type II error.
For example, consider a clinical trial testing a new medication's effectiveness compared to a placebo. A Type II error would occur if the trial concludes that the medication does not work (i.e., the null hypothesis is not rejected) when, in fact, the medication does have a positive effect.
The probability of making a Type II error is denoted by the symbol \(\beta\). The power of a test, which is the probability of correctly rejecting a false null hypothesis, is calculated as \(1 - \beta\). Therefore, increasing the power of a test reduces the likelihood of a Type II error.