15bRandomization

15bRandomization - Randomization / Permutation tests I...

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

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...
View Full Document

This note was uploaded on 02/11/2012 for the course STAT 511 taught by Professor Staff during the Spring '08 term at Iowa State.

Page1 / 9

15bRandomization - Randomization / Permutation tests I...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online