Power of a test
For any decision rule, the significance level gives the probability of an error when H0 is true — the Type I error. It is common to describe what happens if HA is true with the probability of correctly picking HA. This is called the power of the test and is one minus the probability of a Type II error.
Decision | |||
---|---|---|---|
accept H0 | reject H0 | ||
Truth | H0 is true | Significance level = P (Type I error) |
|
HA (H0 is false) | P (Type II error) | Power = 1 - P (Type II error) |
When the alternative hypothesis includes a range of possible parameter values (e.g. µ ≠ 0), the power is not a single value but depends on the actual parameter value.
Increasing the power of a test
It is clearly desirable to use a test whose power is as close to 1.0 as possible. There are three different ways to increase the power.
When the significance level is fixed, increasing the sample size is usually the only way to improve the power.