Re: Question about alpha and beta

OK, I think I may see where Scharf is coming from, but I'm still a bit
puzzled.

I know that:
Prob of choosing H1 = Prob(H1|H1) + Prob(H1|H0) = 1-beta + alpha
which means that
Prob of CORRECTLY choosing H1 = [ 1 - beta ]/(1-beta+alpha)

Now, I agree with a statement along the lines of :
"The Prob of CORRECTLY choosing H1 = 1 iff alpha = 0"
and I can see where he is probably coming from if he what he calls
"probability of detection" is the "The prob of correctly choosing H1".

However, I am still hung up on the fact that it seems to me that the
probability of detection is a conditional probability and should be
just 1-beta.

Any suggestions?

Matt