Even after extensive search, am unclear on some (basic) concepts regarding likelihood vs. frequentist approach in hypothesis testing. Can you please help? Here we go:
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.
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.