display optionsDescription le ftjri ghtcomputeonesidedpvaluesdefaultistwosidedl evelsetcondenceleveldefaultislevel95noh eadersuppresstableheadernol egendsuppresstablelegendv erbosedisplayfu ID: 137243
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2permute—MonteCarlopermutationtests display optionsDescription le ftjri ghtcomputeone-sidedp-values;defaultistwo-sidedl evel(#)setcondencelevel;defaultislevel(95)noh eadersuppresstableheadernol egendsuppresstablelegendv erbosedisplayfulltablelegendti tle(text)usetextastitleforresultseps(#)numericaltolerance;seldomused exp listcontains(name:elist)elisteexpelistcontainsnewvar=(exp)(exp)eexpisspecname[eqno]specnamespecnameis b b[] se se[]eqnois##nameexpisastandardStataexpression;see[U]13Functionsandexpressions.Distinguishbetween[],whicharetobetyped,and,whichindicateoptionalarguments.MenuStatistics�Resampling�PermutationtestsDescriptionpermuteestimatesp-valuesforpermutationtestsonthebasisofMonteCarlosimulations.Typing.permutepermvarexp list,reps(#):commandrandomlypermutesthevaluesinpermvar#times,eachtimeexecutingcommandandcollectingtheassociatedvaluesfromtheexpressioninexp list.Thesep-valueestimatescanbeone-sided:Pr(TT)orPr(TT).Thedefaultistwo-sided:Pr(jTjjTj).HereTdenotesthevalueofthestatisticfromarandomlypermuteddataset,andTdenotesthestatisticascomputedontheoriginaldata.permvaridentiesthevariablewhoseobservedvalueswillberandomlypermuted. 4permute—MonteCarlopermutationtests nodotssuppressesdisplayofthereplicationdots.Bydefault,onedotcharacterisdisplayedforeachsuccessfulreplication.Ared`x'isdisplayedifcommandreturnsanerrororifoneofthevaluesinexp listismissing.noisilyrequeststhatanyoutputfromcommandbedisplayed.Thisoptionimpliesthenodotsoption.tracecausesatraceoftheexecutionofcommandtobedisplayed.Thisoptionimpliesthenoisilyoption.title(text)speciesatitletobedisplayedabovethetableofpermutationresults;thedefaulttitleisMonteCarlopermutationresults. � Advanced �eps(#)speciesthenumericaltolerancefortestingjTjjTj,TT,orTT.Theseareconsideredtrueif,respectively,jTjjTj�#,TT+#,orTT�#.Thedefaultis1e-7.Youwillnothavetospecifyeps()undernormalcircumstances.nowarnsuppressestheprintingofawarningmessagewhencommanddoesnotsete(sample).forcesuppressestherestrictionthatcommandmaynotspecifyweightsorbeasvycommand.permuteisnotsuitedforweightedestimation,thuspermuteshouldnotbeusedwithweightsorsvy.permutereportsanerrorwhenitencountersweightsorsvyincommandiftheforceoptionisnotspecied.Thisisaseldomusedoption,souseitonlyifyouknowwhatyouaredoing!reject(exp)identiesanexpressionthatindicateswhenresultsshouldberejected.Whenexpistrue,theresultingvaluesareresettomissingvalues.seed(#)setstherandom-numberseed.Specifyingthisoptionisequivalenttotypingthefollowingcommandpriortocallingpermute:.setseed#Remarksandexamplesstata.comPermutationtestsdeterminethesignicanceoftheobservedvalueofateststatisticinlightofrearrangingtheorder(permuting)oftheobservedvaluesofavariable. Example1:Asimpletwo-sampletestSupposethatweconductedanexperimenttodeterminetheeffectofatreatmentonthedevelopmentofcells.Furthersupposethatwearerestrictedtosixexperimentalunitsbecauseoftheextremecostoftheexperiment.Thusthreeunitsaretobegivenaplacebo,andthreeunitsaregiventhetreatment.Themeasurementisthenumberofnewlydevelopedhealthycells.Thefollowinglistinggivesthehypotheticaldata,alongwithsomesummarystatistics..inputytreatmentytreatment1.702.903.1104.1015.1216.1417.end.sorttreatment permute—MonteCarlopermutationtests5 .summarizeyVariable ObsMeanStd.Dev.MinMax y 610.52.428992714.bytreatment:summarizey �-treatment=0Variable ObsMeanStd.Dev.MinMax y 392711 �-treatment=1Variable ObsMeanStd.Dev.MinMax y 31221014Clearly,therearemorecellsinthetreatmentgroupthanintheplacebogroup,butastatisticaltestisneededtoconcludethatthetreatmentdoesaffectthedevelopmentofcells.Ifthesumofthetreatmentmeasuresisourteststatistic,wecanusepermutetodeterminetheprobabilityofobserving36ormorecells,giventheobserveddataandassumingthatthereisnoeffectduetothetreatment..setseed1234.permuteysum=r(sum),saving(permdish)rightnodropnowarn:sumyiftreatment(runningsummarizeonestimationsample)Permutationreplications(100) 1 2 3 4 5..................................................50..................................................100MonteCarlopermutationresultsNumberofobs=6command:summarizeyiftreatmentsum:r(sum)permutevar:y T T(obs)cnp=c/nSE(p)[95%Conf.Interval] sum 36101000.10000.0300.0490047.1762226 Note:confidenceintervaliswithrespecttop=c/n.Note:c=#{T�=T(obs)}Weseethat10ofthe100randomlypermuteddatasetsyieldedsumsfromthetreatmentgrouplargerthanorequaltotheobservedsumof36.Thustheevidenceisnotstrongenough,atthe5%level,torejectthenullhypothesisthatthereisnoeffectofthetreatment.Becauseofthesmallsizeofthisexperiment,wecouldhavecalculatedtheexactpermutationp-valuefromallpossiblepermutations.Therearesixunits,butwewantthesumofthetreatmentunits.Thusthereare�63=20permutationsumsfromthepossibleuniquepermutations. 8permute—MonteCarlopermutationtests Example3:Wilcoxonrank-sumtestAsanalexample,let'sconsiderestimatingthep-valueoftheZstatisticreturnedbyranksum.Supposethatwecollecteddatafromsomeexperiment:yissomemeasurewetookon17individuals,andgroupidentiesthegroupthatanindividualbelongsto..usehttp://www.stata-press.com/data/r13/permute2.list groupy 1. 16 2. 111 3. 120 4. 12 5. 19 6. 15 7. 02 8. 01 9. 06 10. 00 11. 02 12. 03 13. 03 14. 012 15. 04 16. 01 17. 05 Nextweanalyzethedatausingranksumandnoticethattheobservedvalueoftheteststatistic(storedasr(z))is�2.02withanapproximatep-valueof0.0434..ranksumy,by(group)Two-sampleWilcoxonrank-sum(Mann-Whitney)testgroup obsranksumexpected 0 1179991 67454 combined 17153153unadjustedvariance99.00adjustmentforties-0.97 adjustedvariance98.03Ho:y(group==0)=y(group==1)z=-2.020Prob�|z|=0.0434Theobservedvalueoftherank-sumstatisticis79,withanexpectedvalue(underthenullhypothesisofnogroupeffect)of99.Thereare17observations,sothepermutationdistributioncontains�176=12,376possiblevaluesoftherank-sumstatisticifweignoreties.Withties,wehavefewerpossiblevaluesbutstilltoomanytowanttocountthem.Thusweusepermutewith10,000replicationsandseethattheMonteCarlopermutationtestagreeswiththeresultofthetestbasedonthenormalapproximation.