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bootstrap_hypo

# bootstrap_hypo - x calculate the mean of the remaining m...

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Bootstrap Hypothesis Testing To illustrate the technique, consider the case of two independent samples: Observed Sample 1 of size n : { x obs, 1 , x obs, 2 , ..., x obs,n } ⇒ x obs Observed Sample 2 of size m : { y obs, 1 , y obs, 2 , ..., y obs,m } ⇒ y obs Observed sample mean difference: t * obs = x * obs - y * obs Hypotheses and Alpha Level H 0 : Both samples are from the same population H 1 : Both samples are NOT from the same population and μ x > μ y α = 0 . 05 Bootstrap Procedure Step 0 : Merge the two observed samples into one sample of ( n + m ) observations Step 1 : Draw a bootstrap sample of ( n + m ) observations with replacement from the merged sample. Step 2 : Calculate the mean of the first n observations and call it
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Unformatted text preview: x * , calculate the mean of the remaining m observations and call it y * , and ﬁnally, evaluate the test statistic: t * = x *-y * (1) • Step 3 : Repeat Step 1 and Step 2 for B (e.g., 3000) times and obtain B values of the test statistic. • Step 4 : The desired p-value is then estimated as p-value ∼ = number of times { t * > t * obs } B (2) Reject H if p-value < α and retain H otherwise. Points to Note • No assumption of normality • As such, the sampling distribution (i.e., distribution of all possible t * ’s) does not gen-erally follow a t-distribution. 1...
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