Power of a Test

The power of a significance test against a particular Ha is the probability of it rejecting H0 when that Ha is true. To find this probability we do the following: (for a one-sample t)

1.
Using the normal steps of a significance test find out which values of t will lead us to reject H0.
e.g. reject H0 when t > 3.

2.
Rearrange the one-sample test statistic to work out what values x needs to take for us to reject H0.
e.g. if t > 3 then:

3.
Find the probability of x taking such values if Ha is true. To do this we standardise using µa.
e.g. continuing from above:



Then we are simply looking at areas under a normal curve, which we can calculate easily.