ENH: power_approximate: collection of simple formulas for large number of tests

[josef-pkt]

a possible idea for power and sample size computation

"breadth instead of depth"

Instead of getting good power computation for individual tests, we could add a large collection of simplified power and sample size computation for a large number of hypothesis tests.

I looked several times at books like Chow et al, but did not like them much.
Those power computation are simplified, e.g. proportion with same var or std under null and alternative. Those are simple asymptotic approximations.
However, they would be easy to implement, and power and sample size computation could be added for a large number of hypothesis tests that we don't have yet. PASS/NCSS referenced those in several cases.

Chow, Shein-Chung, Jun Shao, Hansheng Wang, and Yuliya Lokhnygina. Sample Size Calculations in Clinical Research. 3rd ed. New York: Chapman and Hall/CRC, 2017. https://doi.org/10.1201/9781315183084.

The plan would be to add the collection but separately from the "more serious" individual power and sample size functions, e.g. put them in a new module power_approximate.

The advantage is that we would quickly get things for different designs and cases
one sample, 2 sample parallel, cross-over (paired)
cluster randomized trials, group sequential trials
NCSS/PASS has a collection of function similarly named to the list of tests in Chow et al.

Also,
To compute the power or sample size we need almost all computation that are used in the hypothesis test.
So we might get those almost for free. We would have to split out intermediate computations either in helper functions or put them in classes.