Power and Sample Size CalculationWord格式文档下载.docx

Power and Sample Size CalculationWord格式文档下载.docx

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HandCalculation.

Wewilluseanexampletoillustratehowaresearchercancalculatethesamplesizeneededforastudy.Giventhataresearcherhasthenullhypothesisthatμ=μ0andalternativehypothesisthatμ=μ1≠μ0,andthatthepopulationvarianceisknownasσ2.Also,heknowsthathewantstorejectthenullhypothesisatasignificancelevelofαwhichgivesacorrespondingZscore,calleditZα/2.Therefore,thepowerfunctionwillbe

P{Z>

Zα/2orZ<

-Zα/2|μ1}=1-Φ[Zα/2-（μ1-μ0）/（σ/n）]+Φ[-Zα/2-（μ1-μ0）/（σ/n）].

Thatisafunctionofthepowerandsamplesizegivenotherinformationknownandtheresearchercangetthecorrespondingsamplesizeforeachpowerlevel.

Forexample,iftheresearcherlearnsfromliteraturethatthepopulationfollowsanormaldistributionwithmeanof100andvarianceof100underthenullhypothesisandhe/sheexpectsthemeantobegreaterthan105orlessthan95underthenullhypothesisandhe/shewantsthetesttobesignificantat95%level,theresultingpowerfunctionwouldbe:

Power=1-Φ[-（105-100）/（10/n）]+Φ[--（95-100）/（10/n）],whichis,

Power=1-Φ[n/2]+Φ[-+n/2].

Thatfunctionshowsarelationshipbetweenpowerandsamplesize.Foreachlevelofsamplesize,thereisacorrespondingsamplesize.Forexample,ifn=20,thecorrespondingpowerlevelwouldbeabout0.97,5,thecorrespondingsamplesizewouldbe16.

UsingStatisticalPackage（SAS）

StatisticalpackageslikeSASenablesaresearchertodothepowercalculationeasily.Theprocedureinwhichpowerandsamplesizearecalculatedisspecifiedinthefollowingtext.

InSAS,statisticalpowerandsamplesizecalculationcanbedoneeitherthroughprogrameditororbyclickingthemenuthemenu.Inthelatter,asetofcodeisautomaticallygeneratedeverytimeacalculationisdone.

PROCPOWERandGLMPOWER

PROCPOWERandGLMPOWERarenewadditionstoSASasofversion9.0.Asofthiswriting,isnotcurrentlyinstalledonITaPmachines,butitcanbeinstalledonyourhomecomputerusingdisksavailableinStewardB14.MakesuretobringyourPurdueID.

Thetableonthefollowingpage（takenfromtheSAShelpfile）showsthetypesofanalysesofferedbyPROCPOWER.Atleastonestatementisrequired.Thesyntaxwithineachstatementvaries,however,thereissomesyntaxcommontoall.Thesecommonfeatureswillbeexpressedbyanexampleusingapairedt-test.MoreinformationoneachprocedurecanbefoundintheSAShelpfile.

Intheexample,assumethatapilotstudyhasbeendone,andthatthestandarddeviationofthedifferencebetweenthetwogroupshasbeenfoundtobe5,withameandifferenceof2.We’dliketocalculatetherequiredsamplesizeforanexperimentwith80%power.

procpower;

pairedmeanstest=diff

meandiff=2

stddev=5

npairs=.

power=.80;

run;

Analysis

Statement

Options 

Multiplelinearregression:

TypeIIIFtest

MULTREG

Correlation:

Fisher'

sztest

ONECORR

DIST=FISHERZ

ttest

DIST=T

Binomialproportion:

Exacttest

ONESAMPLEFREQ

TEST=EXACT

ztest

TEST=Z

ztestwithcontinuityadjustment

TEST=ADJZ

One-samplettest

ONESAMPLEMEANS

TEST=T

One-samplettestwithlognormaldata

TEST=TDIST=LOGNORMAL

One-sampleequivalencetestformeanofnormaldata

TEST=EQUIV

One-sampleequivalencetestformeanoflognormaldata

TEST=EQUIVDIST=LOGNORMAL

Confidenceintervalforamean

CI=T

One-wayANOVA:

One-degree-of-freedomcontrast

ONEWAYANOVA

TEST=CONTRAST

OverallFtest

TEST=OVERALL

McNemarexactconditionaltest

PAIREDFREQ

McNemarnormalapproximationtest

DIST=NORMAL

Pairedttest

PAIREDMEANS

TEST=DIFF

Pairedttestofmeanratiowithlognormaldata

TEST=RATIO

Pairedadditiveequivalenceofmeandifferencewithnormaldata

TEST=EQUIV_DIFF

Pairedmultiplicativeequivalenceofmeanratiowithlognormaldata

TEST=EQUIV_RATIO

Confidenceintervalformeanofpaireddifferences

CI=DIFF

Pearsonchi-squaretestfortwoindependentproportions

TWOSAMPLEFREQ

TEST=PCHI

Fisher'

sexacttestfortwoindependentproportions

TEST=FISHER

Likelihoodratiochi-squaretestfortwoindependentproportions

TEST=LRCHI

Two-samplettestassumingequalvariances

TWOSAMPLEMEANS

Two-sampleSatterthwaitettestassumingunequalvariances

TEST=DIFF_SATT

Two-samplepooledttestofmeanratiowithlognormaldata

Two-sampleadditiveequivalenceofmeandifferencewithnormaldata

Two-samplemultiplicativeequivalenceofmeanratiowithlognormaldata

Two-sampleconfidenceintervalformeandifference

Log-ranktestforcomparingtwosurvivalcurves

TWOSAMPLESURVIVAL

TEST=LOGRANK

Gehanranktestforcomparingtwosurvivalcurves

TEST=GEHAN

Tarone-Wareranktestforcomparingtwosurvivalcurves

TEST=TARONEWARE

PowerandSampleSizeCalculationUsingSASMenu

PowerandsamplesizecanalsobecalculatedusingthemenuinSAS.Whenusingthemenu,theusershouldspecifythechosendesignfortheunderlyingproject,andthenfillintherequiredparametersneededtodothecalculationforeachdesign.

Thegeneralprocedureofusingthemenuisasfollows:

1）.OpenSAS

2）.Gototheenhancededitorwindow.

3）.Clickthe'

solutions'

buttononthemenu.

4）.Inthesubmenu,click'

analysis'

.

5）.Inthenextsubmenu,click'

analyst'

thenanewwindowwillpop-up.

6）.Inthenewwindow,click'

statistics'

7）.Select'

Samplesize'

thenselectthedesignyouwanttouse.（thedesignsavailableinthatmenuinclude:

one-samplet-test,pairedt-test,twosamplet-testandone-wayANOVA）.

8）.Afteryouselectthedesignanotherwindowpops-upandasksyou

toinputtheneededoptionsandparameters.Ifyouneedtoknowtheneeded

samplesizeforyourresearch,youcanselect'

NperGroup'

theninputnumberoftreatments,correctedsumofsquare,thestandarddeviationandthealpha

level.Iftheresearcherwantstocalculatethesamplesizecorrespondingtoeachpowerlevel,he/shemaywanttospecifytherangeandintervalofpowerlevelinthe‘Powe