Why Power = P(True Positive) in Hypothesis testing? If statistical power is the probability of correctly rejecting a false null hypothesis, then shouldn't  power equal $P(\mathrm{TN})$? I am confused with naming here because in ML, true negatives simply means you do not have something (negative) and it was a correct classification  (true). That's how I look at it.

If I were to describe it using the language of classification, statistical power concerns the probability we find a true positive (the effect truly is not the null effect, and we have correctly detected it).
Indeed, the type 2 error rate is the false negative rate and power is 1-false negative rate, hence true positive rate.
