How to Calculate the Least Significant Difference (LSD)

The LSD calculates the smallest significant between two means as if a test had been run on those two means (as opposed to all of the groups together). This ... Skiptocontent StatisticsHowTo Menu FacebookTweet HypothesisTesting>HowtoCalculatetheLeastsignificantDifference HowtoCalculatetheLeastSignificantDifference(LSD):Overview Watchthevideoforanexample: HowtoCalculateFishersLeastSignificantDifferenceWatchthisvideoonYouTube. Can’tseethevideo?Clickhere. WhenyourunanANOVA(AnalysisofVariance)testandgetasignificantresult,thatmeansatleastoneofthegroupstesteddiffersfromtheothergroups.However,youcan’ttellfromtheANOVAtestwhichgroupdiffers.Inordertoaddressthis,Fisherdevelopedtheleastsignificantdifferencetestin1935,whichisonlyusedwhenyourejectthenullhypothesisasaresultofyourhypothesistestresults.TheLSDcalculatesthesmallestsignificantbetweentwomeansasifatesthadbeenrunonthosetwomeans(asopposedtoallofthegroupstogether).Thisenablesyoutomakedirectcomparisonsbetweentwomeansfromtwoindividualgroups.AnydifferencelargerthantheLSDisconsideredasignificantresult. LeastSignificantDifference(LSD):Formula Theformulafortheleastsignificantdifferenceis: Where: t=criticalvaluefromthet-distributiontable MSw=meansquarewithin,obtainedfromtheresultsofyourANOVAtest n=numberofscoresusedtocalculatethemeans. HowtoCalculatetheLeastSignificantDifference(LSD):ExampleProblem Exampleproblem:CalculatetheLeastSignificantDifferenceforthedifferencebetweentwomeansonGroup1andGroup2withthefollowingtestresults: Step1:Findthet-criticalvalue.Thet-criticalvalueforα=0.05,dfw=36is2.028(IusedtheTI-83calculatortofindat-distributionvalue).MakesureyouareusingtheWithingroupsDFfromyourresults! Step2:Insertthegivenvalues,theMSEfromyourresults(Iused26.65fromWithingroupsontheabovetable)thet-distributionvaluefromStep2intotheleastsignificantdifferenceformula: LSD=2.028√(26.65*(2/10))=4.68. Putthisnumberasideforamoment, Step3:Calculateybar1-ybar2fromtheresults.Forthisexample,weget-8.7. Step4:CompareStep2andStep3.If|ybar1-ybar2|≥LSD1,2thenyoucanrejectthenullhypothesisthatthemeansarethesame(H0:μ1=μ2). Ourvalueof8.7islargerthan4.68sowecanrejectthenullhypothesis. That’sit! Tip:TheLSDwillonlymakesenseifyouhaveasignificantresultfromANOVA(i.e.ifyourejectthenullhypothesis).Therefore,youshouldn’trunthetestifyoudonotgetasignificantresultfromANOVA. References Dodge,Y.(2008).TheConciseEncyclopediaofStatistics.Springer. Gonick,L.(1993).TheCartoonGuidetoStatistics.HarperPerennial. Klein,G.(2013).TheCartoonIntroductiontoStatistics.Hill&Wamg. Wheelan,C.(2014).NakedStatistics.W.W.Norton&Company CITETHISAS:StephanieGlen."HowtoCalculatetheLeastSignificantDifference(LSD)"FromStatisticsHowTo.com:ElementaryStatisticsfortherestofus!https://www.statisticshowto.com/how-to-calculate-the-least-significant-difference-lsd/ --------------------------------------------------------------------------- Needhelpwithahomeworkortestquestion?WithCheggStudy,youcangetstep-by-stepsolutionstoyourquestionsfromanexpertinthefield.Yourfirst30minuteswithaCheggtutorisfree! Comments?Needtopostacorrection?PleaseContactUs. NEEDHELPwithahomeworkproblem?CLICKHERE!Needhelpwithahomeworkortestquestion?WithCheggStudy,youcangetstep-by-stepsolutionstoyourquestionsfromanexpertinthefield.Yourfirst30minuteswithaCheggtutorisfree!NEEDHELPwithahomeworkproblem?CLICKHERE! Feellike“cheating”atStatistics?CheckoutourPracticallyCheatingStatisticsHandbook,whichgivesyouhundredsofeasy-to-followanswersinaconveniente-book. GETtheStatistics&CalculusBundleata40%discount!NEEDHELPwithahomeworkproblem?CLICKHERE! Feellike"cheating"atCalculus?CheckoutourPracticallyCheatingCalculusHandbook,whichgivesyouhundredsofeasy-to-followanswersinaconveniente-book. GETtheStatistics&CalculusBundleata40%discount! Latestarticles CensusinStatistics:SimpleDefinition BimodalDistribution:Whatisit? TI83forStatistics:EasyStepsforCommonProblems Blindingvs.DoubleBlindinStatistics:Definition,Examples HypothesisTestinExcelforthePopulationMean(LargeSample) ProbabilityDistributionTable:Whatisit? WhatisaDecile? NormalDistributionProbabilityinExcel NEEDHELPwithahomeworkproblem?CLICKHERE!