The power of a statistical test is the probability of rejecting the null hypothesis when the null hypothesis is false (or the effect is present). It is the right decision, and before we go deeper into it, let’s recap the two types of errors in hypothesis testing.
- A type I error is when the Null hypothesis is true, but you rejected it.
- A type II error is when you fail to reject a false Null hypothesis; in other words, the effect is present.
In a tabular format,
| Null hypothesis (H0) is TRUE | Null hypothesis (H0) is FALSE | |
| FAIL to Reject | Correct Decision (probability = 1 – α) | Type II Error (probability = β) |
| Reject | Type I Error (probability = α) | Correct Decision (probability = 1 – β) |
Your guess is right, Power equals 1 – β.
