What’s wrong with taking (1 – β)/α, as a likelihood ratio comparing H0 and H1?

Here’s a quick note on something that I often find in discussions on tests, even though it treats “power”, which is a capacity-of-test notion, as if it were a fit-with-data notion….. 1. Take a one-sided Normal test T+: with n iid samples: H0: µ ≤  0 against H1: µ >  0 σ = 10,  n = 100,  σ/√n =σx= 1,  α = … Continue reading What’s wrong with taking (1 – β)/α, as a likelihood ratio comparing H0 and H1?