商务统计学（第7版）英文ppt课件11 Chi-Square Tests、13 Multiple Regression.ppt

Chi-SquareTestsChapter11

ObjectivesInthischapter,youlearn:Howandwhentousethechi-squaretestforcontingencytables

ContingencyTablesContingencyTablesUsefulinsituationscomparingmultiplepopulationproportionsUsedtoclassifysampleobservationsaccordingtotwoormorecharacteristicsAlsocalledacross-classificationtable.DCOVA

Left-Handedvs.Gender DominantHand:Leftvs.Right Gender:Malevs.Female2categoriesforeachvariable,sothisiscalleda2x2tableSupposeweexamineasampleof300childrenContingencyTableExampleDCOVA

ContingencyTableExampleSampleresultsorganizedinacontingencytable:(continued)GenderHandPreferenceLeftRightFemalale2415618036264300120Females,12werelefthanded180Males,24werelefthandedsamplesize=n=300:DCOVA

?2TestfortheDifferenceBetweenTwoProportionsIfH0istrue,thentheproportionofleft-handedfemalesshouldbethesameastheproportionofleft-handedmalesThetwoproportionsaboveshouldbethesameastheproportionofleft-handedpeopleoverallH0:π1=π2(Proportionoffemaleswhoareleft handedisequaltotheproportionof maleswhoarelefthanded)H1:π1≠π2(Thetwoproportionsarenotthesame)DCOVA

TheChi-SquareTestStatisticwhere: fo=observedfrequencyinaparticularcell fe=expectedfrequencyinaparticularcellifH0istrue(Assumed:eachcellinthecontingencytablehasexpectedfrequencyofatleast5)TheChi-squareteststatisticis:DCOVA

DecisionRule?2?2αDecisionRule:If,rejectH0,otherwise,donotrejectH0Theteststatisticapproximatelyfollowsachi-squareddistributionwithonedegreeoffreedom0?RejectH0DonotrejectH0DCOVA

Computingthe

OverallProportionHere:120Females,12werelefthanded180Males,24werelefthandedi.e.,basedonall300childrentheproportionoflefthandersis0.12,thatis,12% Theoverallproportionis:DCOVA

FindingExpectedFrequen