kartik_newpro
08-13-2011, 10:12 PM
What is the intuition behind the Neyman Pearson Lemma?
1. Best Critical Region. What exactly is the concept of BCR? Is it the set of those observations which maximise the power of the test? Said that, is it equivalent to saying that in the Best Critical Region, the probability if rejecting the null hypothesis when it is false is the highest? I am picturing a two tailed hypothesis test. The BCR must lie at the two extreme ends of the bell curve. The probability of rejecting the null hypothesis will be the highest when the value(of parameter) I derived from the sample is very far away from the value assumed to null hypothesis. So the only way the value could be very far is because I sampled values that are at the extreme ends of the tails. Am I having the wrong perspective of this? Because when I apply these to problems, it doesnt seem to work very well.
2. The ratio of the likelihoods. Before going into the technical details of the Neyman Pearson Lemma I want to have a logical intuition of the same. What is the ratio of the Likelihood functions supposed to indicate? From what I know the Maximum Likelihood estimator of a parameter is that value(or estimator) is the maximum point in the curve of the values the parameter can take. So if Ho: p=p' and Ha: p=p'', and I take the ratio L(p')/L(p''). What will this tell me? And how will it help in finding the BCR?
I apologize if I have come across as a moron. But I come from a finance background(where everything follows logic) and taking statistics for the first time. I would be really grateful if an example is provided and explanation is a little elaborate.
Thanks for your time.
1. Best Critical Region. What exactly is the concept of BCR? Is it the set of those observations which maximise the power of the test? Said that, is it equivalent to saying that in the Best Critical Region, the probability if rejecting the null hypothesis when it is false is the highest? I am picturing a two tailed hypothesis test. The BCR must lie at the two extreme ends of the bell curve. The probability of rejecting the null hypothesis will be the highest when the value(of parameter) I derived from the sample is very far away from the value assumed to null hypothesis. So the only way the value could be very far is because I sampled values that are at the extreme ends of the tails. Am I having the wrong perspective of this? Because when I apply these to problems, it doesnt seem to work very well.
2. The ratio of the likelihoods. Before going into the technical details of the Neyman Pearson Lemma I want to have a logical intuition of the same. What is the ratio of the Likelihood functions supposed to indicate? From what I know the Maximum Likelihood estimator of a parameter is that value(or estimator) is the maximum point in the curve of the values the parameter can take. So if Ho: p=p' and Ha: p=p'', and I take the ratio L(p')/L(p''). What will this tell me? And how will it help in finding the BCR?
I apologize if I have come across as a moron. But I come from a finance background(where everything follows logic) and taking statistics for the first time. I would be really grateful if an example is provided and explanation is a little elaborate.
Thanks for your time.