NOT rejecting the null hypothesis when it is TRUE.

I am running a simulation where I know the null hypothesis is true.

The power of a hypothesis test is the probability of making the correct decision if the alternative hypothesis is true. That is, the power of a hypothesis test is the probability of rejecting the null hypothesis H0 when the alternative hypothesis HA is the hypothesis that is true.

Is there any terminology for the probability of accepting the null hypothesis when it is true?

IE, suppose I have rejection rate of .05 for a particular test where I know the null hypothesis is true. What does this say about the power of this test, if anything?

• If there is a 5% probability of falsely rejecting a true null hypothesis then there is a 95% probability of correctly failing to reject it. (Power doesn't really mean anything in the context where the null hypothesis is true, just as the false positive error rate is not relevant when the null is false.) Note that there are more ways to make false inferences than just false positive and false negative errors. Look up type M and type S errors, for example. Dec 7 '16 at 2:43
• @Michael I think your comment would make a suitable answer. Dec 7 '16 at 13:20