1power - PSTAT 120C Errors and Power in Hypothesis Testing • Class Policies • Power Hypothesis Testing 1 What are we trying to do with a

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Unformatted text preview: 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 : θ = θ – default state of nature 2. Alternative hypothesis H A : θ >< 6 = θ – interesting outcome • More generally H : θ ∈ Θ , some set of possible models (eg. think of μ = 0 but any standard deviation) • Critical region : set of data where we reject H . • 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 ( C ) under the null hypothesis. Making Errors in Tests Reality H H A Decision accept Ok β H Type II error Rule reject α Ok H Type I error Two types of error: α = probability of rejecting H when it is true....
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This note was uploaded on 08/12/2009 for the course PSTAT 120c taught by Professor Idk during the Spring '07 term at UCSB.

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1power - PSTAT 120C Errors and Power in Hypothesis Testing • Class Policies • Power Hypothesis Testing 1 What are we trying to do with a

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