How to Use Dunnett's Test for Multiple Comparisons - Statology

Dunnett's Test: Definition · Step 1: Find Dunnett's critical value. · Step 2: Compare the differences in group means to Dunnett's critical value. Skiptocontent Menu About Course BasicStats MachineLearning SoftwareTutorials Excel GoogleSheets MongoDB Python R SAS SPSS Stata TI-84 Tools Calculators CriticalValueTables Glossary PostedonSeptember28,2020September28,2020byZach AnANOVA(AnalysisofVariance)isusedtodeterminewhetherornotthereisastatisticallysignificantdifferencebetweenthemeansofthreeormoreindependentgroups.  Ifthe p-value fromtheANOVAislessthansomechosensignificancelevel,wecanrejectthenullhypothesisandconcludethatwehavesufficientevidencetosaythatatleastoneofthemeansofthegroupsisdifferentfromtheothers. However,thisdoesn’ttellus which groupsaredifferentfromeachother.Itsimplytellsusthatnotallofthegroupmeansareequal.Inordertofindoutexactlywhichgroupsaredifferentfromeachother,wemustconducta post-hoctest. Ifoneofthegroupsinthestudyisconsideredthecontrolgroup,thenweshoulduse Dunnett’stest asthepost-hoctestfollowingtheANOVA. Dunnett’sTest:Definition WecanusethefollowingtwostepstoperformDunnett’stest: Step1:FindDunnett’scriticalvalue. First,wemustfindDunnett’scriticalvalue.Thisiscalculatedas: Dunnett’sCriticalvalue:td√2MSw/n where: td: ThevaluefoundinDunnett’sTableforagivenalphalevel,numberofgroups,andgroupsamplesizes. MSw: TheMeanSquaresofthe“WithinGroup”intheANOVAoutputtable n: Thesizeofthegroupsamples Step2:ComparethedifferencesingroupmeanstoDunnett’scriticalvalue. Next,wecalculatetheabsolutedifferencebetweenthemeanofeachgroupwiththemeanofthecontrolgroup.IfthedifferenceexceedsDunnett’scriticalvalue,thenthatdifferenceissaidtobestatisticallysignificant. ThefollowingexampleshowshowtoperformDunnett’stestinpractice. Dunnett’sTest:Example Supposeateacherwantstoknowwhetherornottwonewstudyingtechniqueshavethepotentialtoincreaseexamscoresforherstudents.Totestthis,sherandomlysplitsherclassof30studentsintothefollowingthreegroups: ControlGroup:10students NewStudytechnique1:10students NewStudyTechnique2:10students Afteroneweekofusingtheirassignedstudytechnique,eachstudenttakesthesameexam.Theresultsareasfollows: Meanexamscoreofcontrolgroup: 81.6 Meanexamscoreofnewstudytechnique1group:85.8 Meanexamscoreofnewstudytechnique2group:87.7 MeanSquaresofthe“WithinGroup”intheANOVAoutputtable:23.3 Usingthisinformation,wecanperformDunnett’stesttodetermineifeitherofthetwonewstudytechniquesproducesignificantlydifferentmeanexamscorescomparedtothecontrolgroup. Step1:FindDunnett’scriticalvalue. Usingα=.05,groupsamplesizen=10andtotalgroups=3,Dunnett’stabletellsustouseavalueof2.57inthecriticalvaluecalculation. Next,wecanplugthisnumberintotheformulatofindDunnett’sCriticalvalue: Dunnett’sCriticalvalue:td√2MSw/n = 2.57√2(23.3)/10 = 5.548 Step2:ComparethedifferencesingroupmeanstoDunnett’scriticalvalue. Theabsolutedifferencebetweenthemeansofeachstudytechniqueandthecontrolgroupareasfollows: Abs.diffbetweennewtechnique1andcontrol:|85.8–81.6|= 4.2 Abs.diffbetweennewtechnique2andcontrol:|87.7–81.6|=6.1 Onlytheabsolutedifferencebetweentechnique2andthecontrolgroupisgreaterthanDunnett’scriticalvalueof 5.548. Thus,wecansaythatthenewstudyingtechnique#2producessignificantlydifferentexamscorescomparedtothecontrolgroup,butthenewstudyingtechnique#1doesnot. AdditionalResources AnIntroductiontotheOne-WayANOVA AGuidetoUsingPostHocTestswithANOVA HowtoPerformDunnett’sTestinR PublishedbyZach ViewallpostsbyZach Postnavigation PrevWhatisaCovariateinStatistics?NextHowtoPerformDunnett’sTestinR LeaveaReplyCancelreplyYouremailaddresswillnotbepublished.Requiredfieldsaremarked*Comment*Name* Email* Website Δ Search Searchfor: Search ABOUT Statologyisasitethatmakeslearningstatisticseasybyexplainingtopicsinsimpleandstraightforwardways.Learnmoreaboutus. StatologyStudyStatologyStudyistheultimateonlinestatisticsstudyguidethathelpsyoustudyandpracticeallofthecoreconceptstaughtinanyelementarystatisticscourseandmakesyourlifesomucheasierasastudent. IntroductiontoStatisticsCourseIntroductiontoStatisticsisourpremieronlinevideocoursethatteachesyouallofthetopicscoveredinintroductorystatistics.Getstartedwithourcoursetoday. RecentPosts GoogleSheets:Formulafor“IfTimeisGreaterThan” GoogleSheets:CreatePivotTablewithUniqueCounts GoogleSheets:CreatePivotTablewithCountofOccurrences