Fisher's LSD Method for Means Help - SPC for Excel

The Fisher Least Significant Difference (LSD) Method is used to compare means from multiple processes. The method compares all pairs of means. Fisher'sLSDMethodforMeansHelp TheFisherLeastSignificantDifference(LSD)Methodisusedtocomparemeansfrommultipleprocesses. Themethodcomparesallpairsofmeans. Itcontrolstheerrorrate(α)foreachindividualpairwisecomparisonbutdoesnotcontrolthefamilyerrorrate. Botherrorratesaregivenintheoutput. TheoutputfromthismethodalsoincludestheANOVAtable,thetableofmeancomparisons,andagraphcontainingallpairsofmeans. Therearetwooptionsforenteringthedata:stackedorunstacked. Stackeddatahaveeachtreatmentinasinglecolumn. Unstackeddatahavethetreatmentlabelsinonecolumnandtheresultsintheadjacentcolumn.Theexamplebelowusesunstackeddata.  Fivedifferenttreatments(AtoE)wereusedtocontroltheweightofacoatingingrams. Therewerefoursamplesforeachtreatment. WewanttouseFisher’sLSDmethodtodetermineifthereareanysignificantdifferencesinthetreatments.   1.Enterthedataasshownbelow. Thecolumnheadingsrepresentthetreatmentlabelswiththeresponsesforeachtreatmentunderthelabel. Thenumberofresultsforeachtreatmentdonothavetobeequal. Thedatacanbedownloadedatthislink. 2.Selectthedataandthecolumnheadings. 3. Select"MultipleProcesses"fromthe"StatisticalTools"panelintheSPCforExcelribbon. 4.Selectthe"Fisher'sLSDMethodforMeans"option. SelectOKandtheinputformbelowisdisplayed. DataInput:therearetwooptions:stackedandunstacked.Iftherangeselectedontheworksheetcontainsmorethantwocolumns,thedefaultisunstacked;thiscanbechanged. Formoreinformationonstackedversusunstackeddata,clickhere.  StackedOption:thesearetherangestobeentered: Rangecontainingthetreatmentlevels. Rangecontainingtheresponses. UnstackedOption: Thedatamustbecolumnswiththefirstcellineachcolumnrepresentingthetreatmentlevel. Alpha:thisistheconfidencelevel;1-alphaistheconfidenceinterval;defaultis0.05for95%confidence. SelectOKtogeneratetheresults. SelectCanceltoendtheprogram. Fisher'sLSDMethodforMeansOutput Therearetwonewworksheetsaddedfortoyourworkbookforthistest. Oneworksheetcontainsthenumericalresults. Theotherworksheetcontainstheconfidenceintervalplotsforeachpairoftreatments. Theoutputisdescribedbelowstartingwiththenumericalresults. NumericalResults Thedataaresummarizedasstackeddataalongwithsomestatisticsforeachtreatmentlevel. Thestatisticsincludethenumberofresults(count),theaverage,thestandarddeviation,andthevarianceforeachtreatmentlevel. Thevalueofalphaisalsogiven. TheANOVAtableisgivennext. Thistableprovidesthesumofsquaresofthetreatments,errorandtotalaswellasthedegreesoffreedom. ThemeansquareresultsaregivenalongwiththeFvalue. Thekeynumberisthepvalue. Ifthisislessthanorequaltoalpha,itisturnedred. Thismeansthatthereissignificantdifferenceinthetreatmentmeans. Thetableofmeansisthengiven. Thefamilyerrorrateandtheindividualerrorratearegiven. Theseareexpressedasconfidencelimits. Thecolumnsinthetableare: Comparisons:allpossiblecombinationofpairsofmeans. DiffinMeans:thedifferenceinthetwomeans. LSD:Fisher'sLeastSignificantDifferencewhichisgivenby whereN=numberoftotalresults,a=numberoftreatmentlevels,MSEisthemeansquareerrorandnisthesamplesizefortheindividualtreatmentlevels. LCon:the100(1-α)%lowerconfidenceinterval=differenceinmeans-LSD. UCon:the100(1-α)%upperconfidenceinterval=differenceinmeans+LSD. SigDiff?: ifthereisasignificantdifference,Yesisprintedandturnedtored;otherwise,Noisprinted. ThereisasignificantdifferenceiftheabsolutevalueofthedifferenceinmeansisgreaterthantheLSD. ConfidenceIntervalChart Thischartplotseachpairoftreatmentlevels. Thosethatdonotinclude0aresignificantlydifferent. SPCforExcel Buy Now TryFree SPCKnowledgeBase SignupforourFREEmonthlypublicationfeaturingSPCtechniquesandotherstatisticaltopics. CustomerStories ClickheretoseewhatourcustomerssayaboutSPCforExcel! SPCAroundtheWorld SPCforExcelisusedin80countriesinternationally. Clickhereforalistofthosecountries. Questions? ContactUs ConnectwithUs