Suppose I have observed an outcome O, and I know that a parameter θ has influence on the outcome and can acquire two (and only two) discrete values: θ1 or θ2.

Suppose further that P(O| θ1) = c . P(O| θ2)

and therefore L(θ1 | O) = c . L(θ2 | O)

If my set of hypotheses are:

H1: θ = θ1

H2: θ = θ2

which of these statements, if any, can I make?

• H1 is c-times more likely to be true than H2 ?

• If I choose H1 , I will be wrong 100/(c+1) % of times?

• If I choose H1 , I have a 100/(c+1) % chance of being wrong?

Thank you for your time.