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1、PowerandSampleSizeCalculationByGaylaOlbrichtandYongWangDefinitionandApplicationStatisticalpowerisdefinedastheprobabilityofrejectingthenullhypothesiswhilethealternativehypothesisistrue.Factorsthataffectstatisticalpowerincludethesamplesize,thespecificationoftheparameter(s)inthenulland
2、alternativehypothesis,i.e.howfartheyarefromeachother,theprecisionoruncertaintytheresearcherallowsforthestudy(generallytheconfidenceorsignificancelevel)andthedistributionoftheparametertobeestimated.Forexample,ifaresearcherknowsthatthestatisticsinthestudyfollowaZorstandardnormaldistri
3、bution,therearetwoparametersthathe/sheneedstoestimate,thepopulationmean(μ)andthepopulationvariance(σ2).Mostofthetime,theresearcherknowoneoftheparametersandneedtoestimatetheother.Ifthatisnotthecase,someotherdistributionmaybeused,forexample,iftheresearcherdoesnotknowthepopulationvaria
4、nce,he/shecanestimateitusingthesamplevarianceandthatendsupwithusingaTdistribution.Inresearch,statisticalpowerisgenerallycalculatedfortwopurposes.1.Itcanbecalculatedbeforedatacollectionbasedoninformationfrompreviousresearchtodecidethesamplesizeneededforthestudy.2.Itcanalsobecalculate
5、dafterdataanalysis.Itusuallyhappenswhentheresultturnsouttobenon-significant.Inthiscase,statisticalpoweriscalculatedtoverifywhetherthenon-significantresultisduetoreallynorelationinthesampleorduetoalackofstatisticalpower.12Statisticalpowerispositivelycorrelatedwiththesamplesize,whichm
6、eansthatgiventheleveloftheotherfactors,alargersamplesizegivesgreaterpower.However,researchersarealsofacedwiththedecisiontomakeadifferencebetweenstatisticaldifferenceandscientificdifference.Althoughalargersamplesizeenablesresearcherstofindsmallerdifferencestatisticallysignificant,tha
7、tdifferencemaynotbelargeenoughbescientificallymeaningful.Therefore,asconsultants,wewouldliketorecommendthatourclientshaveanideaofwhattheywouldexpecttobeascientificallymeaningfuldifferencebeforedoingapoweranalysistodeterminetheactualsamplesizeneeded.CalculationofStatisticalPowerThepo
8、werisaprobabilityan
