To calculate the Type 2 Error Probability (β):
\[ \beta = 1 - \text{Power} \]
Where:
A Type 2 error occurs in hypothesis testing when a false null hypothesis is not rejected. This means that the test fails to detect an effect or difference that actually exists. The probability of a Type 2 error is denoted by \(\beta\), and it is inversely related to the power of the test. A high power reduces the likelihood of a Type 2 error.
Let's assume the following value:
Using the formula:
\[ \beta = 1 - 0.8 = 0.2 \]
The Type 2 Error Probability is 0.2.
Let's assume the following value:
Using the formula:
\[ \beta = 1 - 0.9 = 0.1 \]
The Type 2 Error Probability is 0.1.