meani Comparing Groups - Comparing I > 2 Groups Numeric...

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Comparing I > 2 Groups - Numeric ResponsesExtension of Methods used to Compare 2 GroupsIndependent and Dependent SamplesNormal and non-normal data structuresDataDesignNormalNon-normalIndependentSamples(CRD)F-Test1-WayANOVAKruskal-WallisTestDependentSamples(RBD)F-Test2-WayANOVAFriedman’sTest
Independent Samples - Completely Randomized Design (CRD)Controlled Experiments - Subjects assigned at random to one of the Itreatments to be comparedObservational Studies - Subjects are sampled from I existing groupsStatistical model xijis a subject from group i:ijiijxwhere is the population mean of group/treatment i, ijis a random error
1-Way ANOVA for Normal Data (CRD)For each group obtain the mean, standard deviation, and sample size:1)(2ijiijiijijinxxsnxxObtain the overall mean and sample sizeNxNxnxnxnnNijijIII 111
Analysis of Variance - Sums of Squares/Degrees of FreedomTotal Variation 1)(112 NDFTxxSSTIinjijiAmong Group Variation IinjIiiiiiIDFGxxnxxSSG111221)()(Within Group VariationDFEDFGDFTSSESSGSSTINDFEsnxxSSEIiiiIinjiiji 12112)1()(
Analysis of Variance Table and F-TestSource ofVariationSum of SquaresDegrres ofFreedomMean SquareFTreatmentsSSGI-1MSG=SSG/(I-1)F=MSG/MSEErrorSSEN-IMSE=SSE/(N-I)TotalSSTN-1H0: No differences among Group Means (I)HA: Group means are not all equal (Not all iare equal))(:value)Table(:..:..,1,obsINIobsobsFFPPEFFRRMSEMSGFST
Example - Relaxation Music in Patient-Controlled Sedation in ColonoscopyThree Conditions (Treatments): Music and Self-sedation (i = 1)Self-Sedation Only (i = 2)Music alone (i= 3)OutcomesPatient satisfaction score (all 3 conditions)Amount of self-controlled dose (conditions 1 and 2) Source: Lee, et al (2002)
Example - Relaxation Music in Patient-Controlled Sedation in ColonoscopySummary Statistics and Sums of Squares Calculations:Trt (i)niMeanStd. Dev.1557.82.12556.82.33557.42.3Total165overall mean=7.33---164162275.84046.80929.31162316546.809)3.2)(155()3.2)(155()1.2)(155(21329.31)33.74.7(55)33.78.6(55)33.78.7(55222222DFTSSTDFESSEDFGSSG
Example - Relaxation Music in Patient-Controlled Sedation in ColonoscopyAnalysis of Variance and F-Test for Treatment effectsSource ofVariationSum of SquaresDegrres ofFreedomMean SquareFTreatments31.29215.653.13Error809.461625.00Total840.75164H0: No differences among Group Means (23)HA: Group means are not all equal (Not all iare equal)05.0)13.3(:value)(055.3:..13.300.565.15:..162,2,05.FPPETableFFRRFSTobsobs
Post-hoc Comparisons of TreatmentsIf differences in group means are determined from the F-test, researchers want to compare pairs of groups. Three popular methods include:Dunnett’s Method - Compare active treatments with a control group. Consists of I-1 comparisons, and utilizes