You read that a statistical test at significance level α =0.05 has power 0.78. What are the probabilities of Type 1 and Type 11 errors for this test?
When we draw a conclusion from a statistical significance test, there are two types of mistakes we can make:
1. If we reject H_0 when H_0 is actually true, - a type I error is committed.
2. If we fail to reject H_0 when H_0 is false, - a type II error is committed.
Type I error is the statistical significance (`alpha` ) level. So here it is 0.05.
Probability of a type I error is 0.05.
For calculating Type II error, probability for this test has to be calculated first.
Power = 1 - beta (where Beta is the probability of making a type II error)
Here, the power is 0.78.
probability = 1 - 0.78 = 0.22.
Probability of committing a type II error here, is thus 0.22.