ANOVA in R | A Complete Step-by-Step Guide with Examples

ANOVA is a statistical test for estimating how a quantitative dependent variable changes according to the levels of one or more categorical ... Havealanguageexpertimproveyourwriting ProofreadingServices Runafreeplagiarismcheckin10minutes PlagiarismChecker Generateaccuratecitationsforfree CitationGenerator Home KnowledgeBase Statistics ANOVAinR:Astep-by-stepguide StatisticsStatisticalanalysisstepbystepDatacollectionDatacollectionguideExperimentaldesignPopulationsandsamplesPopulationsandsamplesSamplingmethodsTypesofvariablesTypesofvariablesLevelsofmeasurementNominaldataOrdinaldataIntervaldataRatiodataDatacleansingDatacleansingguideMissingdataOutliersDescriptivestatisticsOverviewdescriptivestatisticsMeasuresofcentraltendencyOverviewModeMedianMeanGeometricmeanMeasuresofvariabilityOverviewRangeInterquartilerangeStandarddeviationVarianceFrequencydistributionFrequencydistributionQuartiles&quantilesProbability(distributions)ProbabilitydistributionsOverviewNormaldistributionStandardnormaldistributionPoissondistributionChi-squaredistributionChi-squaretabletdistributionttableInferentialstatisticsOverviewinferentialstatisticsDegreesoffreedomCentrallimittheoremParameters&teststatisticsParametersvs.teststatisticsTeststatisticsEstimationStandarderrorConfidenceintervalsHypothesistestingHypothesistestingguideNullvs.alternativehypothesesStatisticalsignificancepvalueTypeI&TypeIIerrorsStatisticalpowerStatisticaltestsChoosingtherighttestAssumptionsforhypothesistestingSkewnessKurtosisCorrelationCorrelationvs.causationCorrelationcoefficientPearsoncorrelationRegressionanalysisSimplelinearregressionMultiplelinearregressionLinearregressioninRttestsANOVAsOne-wayANOVATwo-wayANOVAANOVAinRChi-squareOverviewchi-squaretestsChi-squaregoodnessoffittestChi-squaretestofindependenceEffectsizeOverviewofeffectsizesCoefficientofdeterminationModelselectionAkaikeinformationcriterionReportingstatisticsinAPA Interestingtopics ChicagoStyle AMAstyle Nounsandpronouns Researchbias UKvs.USEnglish Definitions Commas Commonlyconfusedwords IEEE Workingwithsources Collegeessay APAStyle6thedition Applyingtograduateschool Statistics Languagerules Methodology MLAStyle Researchpaper Academicwriting Startingtheresearchprocess Dissertation Essay Tips APAStyle7thedition APAcitationexamples Citingsources Plagiarism Havealanguageexpertimproveyourwriting ProofreadingServices Runafreeplagiarismcheckin10minutes PlagiarismChecker Generateaccuratecitationsforfree CitationGenerator ANOVAinR|ACompleteStep-by-StepGuidewithExamples Publishedon March6,2020 by RebeccaBevans. Revisedon July9,2022. ANOVAisastatisticaltestforestimatinghowaquantitativedependentvariablechangesaccordingtothelevelsofoneormorecategoricalindependentvariables.ANOVAtestswhetherthereisadifferenceinmeansofthegroupsateachleveloftheindependentvariable. Thenullhypothesis(H0)oftheANOVAisnodifferenceinmeans,andthealternatehypothesis(Ha)isthatthemeansaredifferentfromoneanother. Inthisguide,wewillwalkyouthroughtheprocessofaone-wayANOVA(oneindependentvariable)andatwo-wayANOVA(twoindependentvariables). Oursampledatasetcontainsobservationsfromanimaginarystudyoftheeffectsoffertilizertypeandplantingdensityoncropyield. One-wayANOVAexampleIntheone-wayANOVA,wetesttheeffectsof3typesoffertilizeroncropyield. Two-wayANOVAexampleInthetwo-wayANOVA,weaddanadditionalindependentvariable:plantingdensity.Wetesttheeffectsof3typesoffertilizerand2differentplantingdensitiesoncropyield. Wewillalsoincludeexamplesofhowtoperformandinterpretatwo-wayANOVAwithaninteractionterm,andanANOVAwithablockingvariable. SampledatasetforANOVA TableofcontentsGettingstartedinRStep1:LoadthedataintoRStep2:PerformtheANOVAtestStep3:Findthebest-fitmodelStep4:CheckforhomoscedasticityStep5:Doapost-hoctestStep6:PlottheresultsinagraphStep7:ReporttheresultsFrequentlyaskedquestionsaboutANOVA GettingstartedinR Ifyouhaven’tusedRbefore,startbydownloadingRandRStudio.Onceyouhavebothoftheseprogramsdownloaded,openRStudioandclickonFile>NewFile>RScript. Nowyoucancopyandpastethecodefromtherestofthisexampleintoyourscript.Torunthecode,highlightthelinesyouwanttorunandclickontheRun buttononthetoprightofthetexteditor(orpressctrl+enteronthekeyboard). Installandloadthepackages First,installthepackagesyouwillneedfortheanalysis(thisonlyneedstobedoneonce): install.packages(c("ggplot2","ggpubr","tidyverse","broom","AICcmodavg")) ThenloadthesepackagesintoyourRenvironment(dothiseverytimeyourestarttheRprogram): library(ggplot2) library(ggpubr) library(tidyverse) library(broom) library(AICcmodavg) Step1:LoadthedataintoR Notethatthisdatawasgeneratedforthisexample,it’snotfromarealexperiment! Wewillusethesamedatasetforallofourexamplesinthiswalkthrough.Theonlydifferencebetweenthedifferentanalysesishowmanyindependentvariablesweincludeandinwhatcombinationweincludethem. ItiscommonforfactorstobereadasquantitativevariableswhenimportingadatasetintoR.Toavoidthis,youcanusetheread.csv()commandtoreadinthedata,specifyingwithinthecommandwhethereachofthevariablesshouldbequantitative(“numeric”)orcategorical(“factor”). Usethefollowingcode,replacingthepath/to/your/filetextwiththeactualpathtoyourfile: crop.dataF)columnisthep-valueoftheF-statistic.ThisshowshowlikelyitisthattheF-valuecalculatedfromthetestwouldhaveoccurredifthenullhypothesisofnodifferenceamonggroupmeansweretrue. Thep-valueofthefertilizervariableislow(p<0.001),soitappearsthatthetypeoffertilizerusedhasarealimpactonthefinalcropyield. Two-wayANOVA Inthetwo-wayANOVAexample,wearemodelingcropyieldasafunctionoftypeoffertilizerandplantingdensity.Firstweuseaov()torunthemodel,thenweusesummary()toprintthesummaryofthemodel. two.way% group_by(fertilizer,density)%>% summarise( yield=mean(yield) ) Next,addthegrouplabelsasanewvariableinthedataframe. mean.yield.data$group