What Is the Tukey HSD Test? - Sciencing

The Tukey HSD test is a way of reporting ANOVA results and determining if the relationship between three independently varying quantities is ... Home⋅ScienceFairProjectIdeasforKids,Middle&HighSchoolStudents⋅Probability&StatisticsWhatIstheTukeyHSDTest?•••ChalirmpojPimpisarn/iStock/GettyImagesShareTweetEmailPrintRelatedHowtoCalculatePointBiserialCorrelationUpdatedNovember26,2018ByKevinBeckTheTukeyHSD("honestlysignificantdifference"or"honestsignificantdifference")testisastatisticaltoolusedtodetermineiftherelationshipbetweentwosetsofdataisstatisticallysignificant–thatis,whetherthere'sastrongchancethatanobservednumericalchangeinonevalueiscausallyrelatedtoanobservedchangeinanothervalue.Inotherwords,theTukeytestisawaytotestanexperimentalhypothesis.TheTukeytestisinvokedwhenyouneedtodetermineiftheinteractionamongthreeormorevariablesismutuallystatisticallysignificant,whichunfortunatelyisnotsimplyasumorproductoftheindividuallevelsofsignificance.WhyNotat-Test?Simplestatisticsproblemsinvolvelookingattheeffectsofone(independent)variable,likethenumberofhoursstudiedbyeachstudentinaclassforaparticulartest,onasecond(dependent)variable,likethestudent'sscoresonthetest.Insuchcases,youusuallysetyourcut-offforstatisticalsignificanceatP<0.05,whereintheexperimentrevealsagreaterthan95percentchancethatthevariablesinquestiontrulyrelated.Thenyourefertoat-tablethattakesintoaccountthenumberofdatapairsinyourexperimenttoseeifyourhypothesiswascorrect.Sometimes,however,theexperimentmaylookatmultipleindependentordependentvariablessimultaneously.Forexample,intheaboveexample,thehoursofsleepeachstudentgotthenightbeforethetestandhisorherclassgradegoinginmightbeincluded.Suchmultivariateproblemsrequiresomethingotherthanat-testowingtothesheernumberifindependentlyvaryingrelationships.TheANOVAANOVAstandsfor"analysisofvariance"andaddressespreciselytheproblemjustdescribed.Itaccountsfortherapidlyexpandingdegreesoffreedominasampleasvariablesareadded.Forexample,lookingathoursvs.scoresisonepairing,sleepvs.scoresisanother,gradesvs.scoresisathirdandmeanwhile,allofthoseindependentvariablesinteractwithoneanother,too.InanANOVAtest,thevariableofinterestaftercalculationshavebeenrunisF,whichisthe​found​variationoftheaveragesofallofthepairs,orgroups,dividedbythe​expected​variationoftheseaverages.Thehigherthisnumber,thestrongertherelationship,and"significance"isusuallysetat0.95.ReportingANOVAresultsusuallyrequirestheuseofabuilt-incalculatorsuchasthosefoundinMicrosoftExcelaswellasdedicatedstatisticalprogramssuchasSPSS.TheTukeyHSDTestJohnTukeycameupwiththetestthatbearshisnamewhenherealizedthemathematicalpitfallsoftryingtouseindependentP-valuestodeterminetheutilityofamultiple-variableshypothesisasawhole.Atthetime,t-testswerebeingappliedtothreeormoregroups,andheconsideredthisdishonest–hence"honestlysignificantdifference."Whathistestdoesiscomparethedifferencesbetweenmeansofvaluesratherthancomparingpairsofvalues.ThevalueoftheTukeytestisgivenbytakingtheabsolutevalueofthedifferencebetweenpairsofmeansanddividingitbythestandarderrorofthemean(SE)asdeterminedbyaone-wayANOVAtest.TheSEisinturnthesquarerootof(variancedividedbysamplesize).AnexampleofanonlinecalculatorislistedintheResourcessection.TheTukeytestisaposthoctestinthatthecomparisonsbetweenvariablesaremadeafterthedatahasalreadybeencollected.Thisdiffersfromanaprioritest,inwhichthesecomparisonsaremadeinadvance.Intheformercase,youmightlookatthemileruntimesofstudentsinthreedifferentphys-edclassesoneyear.Inthelattercase,youmightassignstudentstooneofthreeteachersandthenhavethemrunatimedmile.RelatedArticlesHowtoCalculatePointBiserialCorrelationWhatIsR2LinearRegression?WhatAreParametricandNonparametricTests?WhatDoesaNegativeT-ValueMean?WhatIsR2LinearRegression?HowtoCalculateStatisticalSignificanceHowtoUseStatstoStandOutattheScienceFairHowtoInterpretCogATScoresHowtoWriteaResultsStatementforaT-Testoran...HowDoICalculateClassWidth?DifferencesBetweenConceptualIndependentVariables...HowtoDetermineWhethertoUseaOne-Sample,Paired,...TheDisadvantagesofLinearRegressionCalculateAverageDeviationHowtoCalculatePointBiserialCorrelationHowtoCalculateaTwo-TailedTestHowtoDeterminetheSampleSizeinaQuantitative...HowtoCalculateBinomialProbabilityStatisticalAnalysisToolsSimilaritiesofUnivariate&MultivariateStatistical...ReferencesNorthernIllinoisUniversity:PostHocComparisonsSimonFraserUniversity:ANOVAReviewandTukey’sHSD(HonestlySignificantDifference)CollegeofSaintBenedictandSaintJohn's:ANOVAResourcesPsychologyWorld:TukeyHSDCalculatorAbouttheAuthorKevinBeckholdsabachelor'sdegreeinphysicswithminorsinmathandchemistryfromtheUniversityofVermont.FormerlywithScienceBlogs.comandtheeditorof"RunStrong,"hehaswrittenforRunner'sWorld,Men'sFitness,Competitor,andavarietyofotherpublications.MoreaboutKevinandlinkstohisprofessionalworkcanbefoundatwww.kemibe.com.FindYourNextGreatScienceFairProject!GO&Cross;DontGo!WeHaveMoreGreatSciencingArticles!HowtoCalculatePointBiserialCorrelationWhatIsR2LinearRegression?WhatAreParametricandNonparametricTests?WhatDoesaNegativeT-ValueMean?WhatIsR2LinearRegression?HowtoCalculateStatisticalSignificance