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1power - PSTAT 120C Errors and Power in Hypothesis Testing...

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PSTAT 120C: Errors and Power in Hypothesis Testing March 31, 2009 Class Policies Power Hypothesis Testing 1. What are we trying to do with a hypothesis test? 2. What is an example of a hypothesis test? 3. What are the components of statistical testing framework? Two hypotheses 1. Null hypothesis H 0 : θ = θ 0 – default state of nature 2. Alternative hypothesis H A : θ >< 6 = θ 0 – interesting outcome More generally H 0 : θ Θ 0 , some set of possible models (eg. think of μ = 0 but any standard deviation) Critical region : set of data where we reject H 0 . Test statistic : simplifies critical region = T ( X 1 , X 2 , . . . , X n ) C . Critical value : C = { x : T ( x ) > c } . Size α = the largest value of P 0 ( C ) under the null hypothesis. Making Errors in Tests Reality H 0 H A Decision accept Ok β H 0 Type II error Rule reject α Ok H 0 Type I error Two types of error: α = probability of rejecting H 0 when it is true. Type I error β = probability of accepting H 0 when it is false.
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