Question

Imagine that my study has a power of 0.60 to find a correlation of 0.30 or higher. What does this 0.60 mean in probability terms?

In what situation should we care the most about power?

Answer 1

The power of the study is 0.60 to find a correlation of 0.30 or higher.

In terms of probability this means

P[ Study detects the correlation is 0.30 or higher | Actually the correlation is 0.30 or higher] = 0.60

Power is the probability of making a correct decision (to reject the null hypothesis) when the null hypothesis is false.

We care about the power most when we have two tests performing the same task at same level of significance . It is then we choose a test on the basis of whose power is greater. The test with higher power will be considered a better test.