class09-3-handouts

class09-3-handouts - PSTAT 120B - Probability &...

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Class # 09-3- N-P Lemma and LRTs Jarad Niemi University of California, Santa Barbara 28 May 2010 Jarad Niemi (UCSB) N-P Lemma and LRTs 28 May 2010 1 / 11
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Class overview Announcements Announcements Homework Homework 7 due 2 June @ 10am in class Evaluations Please take them seriously Only have 35 minutes today Jarad Niemi (UCSB) N-P Lemma and LRTs 28 May 2010 2 / 11
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Class overview Goals Neyman-Pearson Lemma Likelihood ratio tests Jarad Niemi (UCSB) N-P Lemma and LRTs 28 May 2010 3 / 11
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Power Definition Suppose that W is the test statistic and RR is the rejection region for a test of a hypothesis involving the value of a parameter θ . Then the power of the test is the probability that the test will lead to rejection of H 0 when the actual parameter value is θ a . That is, power( θ a ) = P ( W RR | θ = θ a ) . Relationship between power and β If θ a is a value of θ in the alternative hypothesis H a , then power( θ a ) = 1 - β ( θ a ) . Jarad Niemi (UCSB)
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class09-3-handouts - PSTAT 120B - Probability &...

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