15bRandomization(1)

# 15bRandomization(1) - Randomization/Permutationtests...

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Unformatted text preview: Randomization/Permutationtests Bootstrappingpreservesthefixedeffects Differenceoftwomeans: resample Y 1 i andresample Y 2 i bootstrapestimates, ˆ μ 1 B − ˆ μ 2 B ,arecenteredon/near ¯ Y 1 − ¯ Y 2 , whichestimates μ 1 − μ 2 Regressionbootstrap: resample ˆ i ,addto X ˆ β ˆ β B centeredon/near ˆ β ,whichestimates β soabootstrapprovidesaconfidenceintervalfor θ testsofHo: θ = k areindirect,viainclusionof k in 1 − α confidenceinterval Sometimessaid:“bootstrappingresamplesdataunderHa”. c 2011Dept.Statistics(IowaStateUniversity) Stat511section15.5 1/9 Randomization/permutationtests Arandomization/permutationtestresamplesthedataunderHo. usedtotestHowithoutmakingmanyassumptions Example:E Y ij = μ i , i = 1 , 2 ,wanttotestHo: μ 1 − μ 2 = . Apermutationtestwould: defineateststatistic,e.g. T = ¯ Y 1 − ¯ Y 2 calculate T o fromtheobserveddata poolallobservationsintoasinglegroup: { Y 1 j , Y 2 j } permutegrouplabelsoverthepooledobservations maintains n 1 and n 2 calculate T R i fromtherelabelledobservations repeatforallpossiblepermutationsoflabels F T R isthepermutationdistributionoftheteststatistic...
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## 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.

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15bRandomization(1) - Randomization/Permutationtests...

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