Hypothesis testing with STATA

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1、HypothesistestingwithSTATADrEiriniKonstantinidiLecturerinFinanceUniversityofExeter,BusinessSchoolXfiCentreofFinance&Investmente.konstantinidi@exeter.ac.uk1Outline•ImportdataintoSTATA.•Testingthemeanofone(two)population(s).•Testingthevarianceofone(two)population(s

2、).2Beforewestart:Importdataset1intoSTATA•Dataset2containsdailyreturnsontheS&P500andSTOXXindices(2/2/2001–1/8/2010).•Openthedataeditorbyclickingonthe‘DataEditor(Edit)’iconontheSTATAtoolbar.22•CopycellsB1:C2132in‘data2_SPXandSTOXX.xlsx’.
CellsB1andC1containthenameo

3、fthevariables.•Pasteintothe‘DataEditor(Edit)’inSTATA.
Treatfirstrowasvariablename.3HypothesistestingwithSTATA4TestingmeansTestingvariances56Onesamplemeancomparisontest•Teststhemeanofonepopulationinthecasewherethepopulationvarianceisunknown.H:µ=µ00H:µ≠µH:µ>µH:µ<µα

4、0α0α0X-µappr.0•UnderH0:Teststatistic=~t(n-1)snH07Onesamplemeancomparisontest:Anexample•Ata5%levelofsignificancetestthat:H:µ=0%0SPX8Onesamplemeancomparisontest:Results•Thefollowingwillappearintheresultswindow:Commandthatyoucouldtypeintothecommandwindowinsteadofusi

5、ngthedropdownmenu.9Onesamplemeancomparisontest:AnexampleNumberofobservations(n)10Onesamplemeancomparisontest:AnexampleArithmeticmeanoftherandomvariable(Xbar)11Onesamplemeancomparisontest:AnexampleStandarddeviationoftherandomvariable(s2)12Onesamplemeancomparisonte

6、st:AnexampleStandarderrorofXbar,i.e.s2/n13Onesamplemeancomparisontest:Anexample95%ConfidenceintervalforµSPX14Onesamplemeancomparisontest:AnexampleCalculatedteststatistic15Onesamplemeancomparisontest:Anexample16Onesamplemeancomparisontest:AnexampleP-value17Onesamp

7、lemeancomparisontest:AnexampleP-value18Onesamplemeancomparisontest:AnexampleP-value1920Meancomparisontest,paireddata•Testthemeansoftwodependentpopulations.H:µµ-=0012H:µµ-¹0H:µµ->0H:µµ-<0α12α12α12d-µappr.0•UnderH0:Teststatistic=~t(n-1)snH0d21Meancomparisontest,pai

8、reddata(Cont’d)2223Twosamplemeancomparisontest•Testthemeansoftwoindependentpopulations.H:µµ-=0012H:µµ-¹0H:µµ->0H:µµ-<0α12α12α12•Onecanassumeequalorunequalvaria