15bRandomization

# 15bRandomization - Randomization Permutation tests I...

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Unformatted text preview: Randomization / Permutation tests I Bootstrapping preserves the fixed effects I Difference of two means: resample Y 1 i and resample Y 2 i bootstrap estimates, ˆ μ 1 B- ˆ μ 2 B , are centered on/near ¯ Y 1- ¯ Y 2 , which estimates μ 1- μ 2 I Regression bootstrap: resample ˆ i , add to X ˆ β ˆ β B centered on/near ˆ β , which estimates β I so a bootstrap provides a confidence interval for θ I tests of Ho: θ = k are indirect, via inclusion of k in 1- α confidence interval I Sometimes said: “bootstrapping resamples data under Ha”. c 2011 Dept. Statistics (Iowa State University) Stat 511 section 15.5 1 / 9 Randomization/permutation tests I A randomization / permutation test resamples the data under Ho. I used to test Ho without making many assumptions I Example: E Y ij = μ i , i = 1 , 2 , want to test Ho: μ 1- μ 2 = . I A permutation test would: I define a test statistic, e.g. T = ¯ Y 1- ¯ Y 2 I calculate T o from the observed data I pool all observations into a single group: { Y 1 j , Y 2 j } I permute group labels over the pooled observations maintains n 1 and n 2 I calculate T R i from the relabelled observations I repeat for all possible permutations of labels I F T R is the permutation distribution of the test statistic I If T o > , the two-sided p-value is...
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15bRandomization - Randomization Permutation tests I...

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