Is it possible to infer the power from the distribution of a statistic?
For instance, let's assume we are dealing with a Wald statistic, calculated from 2 survival $\beta$ coefficients. Under the hypothesis of given means and variances of the coefficients, it is possible to calculate the distribution of the statistic:
In this example, there is 2% of the Area Under the Curve of the Wald statistic distribution (black curve) that is greater than 0.
Would the proportion of the AUC that is greater than -0.05 be the power of the test at a 2-sided alpha=0.05?
(Or most likely some other value that my ingenuous, haphazard guess of -0.05)
Since we are assuming some mean and variance already, I'm not sure if we are still under either H0 or H1.