第六讲--方差分析(下)

第5章方差分析（下）——Repeated-measure&MixeddesignANOVA1RM基本概念5.1球形检验5.2RM-ANOVA原理5.3结果分析与表达5.5数据录入与操作5.42FactorialRMDesignANOVA5.6MixedDesignANOVA5.73Repeatedmeasures（RM）是指在实验过程中，相同的实体（entities,e.g.participants）参与所有情况下的（实验控制变量的不同水平下的）实验或者在不同的时间点下提供数据。其它的表达方式：Within-participantsdesign,Relateddesign,Within-subjectsdesign5.1RM基本概念45.1RM基本概念RM-ANOVA，重复测量的方差分析适用条件：o各组样本数据不独立o控制变量的水平数在三个以上o满足球形检验55.2球形检验球形（sphericity表示为ε）指不同实验条件（即控制变量的不同水平）下的观测变量的变化是相似的。球形和方差齐次性相类似，但是方差齐次性是同一变量在不同观测水平下的方差之间无显著性差异；而球形是指不同变量（不同水平下的观测变量在RM-ANOVA中对应于不同的变量）的变化要类似。65.2.1球形检验例子varianceA-B≈varianceA-C≈varianceB-C球形检验通过的条件为：75.2.1球形检验例子当有两个组间差异的方差非常接近时，数据满足本地球形（localsphericity）检验。在本例中A-C差异和B-C差异的方差非常接近，因为球形检验是通过的。8实际检验方法：在SPSS中球形检验可以通过Mauchly’stest进行。其零假设为：实验不同情况下差异的方差是相等的。若Mauchly’stest的检验结果不显著，则球形检验通过。5.2.2在SPSS中进行球形检验9当球形检验没通过时：ε0.75,采用Huynh–Feldtestimate的结果ε0.75或未知，采用Greenhouse–Geisser修正结果5.2.3球形检验没通过怎么办？球形检验是否通过还影响我们对置信区间调整方法的选择：Shpericity满足时，采用Tukey（LSD）Shpericity不满足时，采用Bonferronimethod105.3RM-ANOVA原理115.3RM-ANOVA原理实例分析125.3RM-ANOVA原理实例分析N-1为总离差的自由度，由样本总量决定135.3RM-ANOVA原理实例分析每个人（participant）的自由度为n-1（n为水平数）SSw的自由度为8×3=24145.3RM-ANOVA原理实例分析dfM=k−1=3155.3RM-ANOVA原理实例分析165.3RM-ANOVA原理实例分析175.3RM-ANOVA原理实例分析185.4数据录入与操作每一水平下的观测值单独作为一个变量的值录入195.4数据录入与操作205.4数据录入与操作添加Within-subject因素名称与水平数215.4数据录入与操作设置变量225.4数据录入与操作设置RM模型235.4数据录入与操作设置对比方法245.4数据录入与操作设置绘图模式255.4数据录入与操作设置置信区间及其它可选项265.5结果分析与表达Measure:MEASURE_1DependentVariable1stick2testicle3eye4witchettyWithin-SubjectsFactorsAnimal275.5结果分析与表达MeanStd.DeviationNStickInsect8.132.2328KangarooTesticle4.251.8328FishEyeball4.132.7488WitchettyGrub5.752.9158DescriptiveStatistics285.5结果分析与表达ValueFHypothesisdfErrordfSig.Pillai'sTrace.94226.955b3.0005.000.002Wilks'Lambda.05826.955b3.0005.000.002Hotelling'sTrace16.17326.955b3.0005.000.002Roy'sLargestRoot16.17326.955b3.0005.000.002MultivariateTestsaEffectAnimala.Design:InterceptWithinSubjectsDesign:Animalb.Exactstatistic295.5结果分析与表达Measure:MEASURE_1Greenhouse-GeisserHuynh-FeldtLower-boundAnimal.13611.4065.047.533.666.333Teststhenullhypothesisthattheerrorcovariancematrixoftheorthonormalizedtransformeddependentvariablesisproportionaltoanidentitymatrix.a.Design:InterceptWithinSubjectsDesign:Animalb.Maybeusedtoadjustthedegreesoffreedomfortheaveragedtestsofsignificance.CorrectedtestsaredisplayedintheTestsofWithin-SubjectsEffectstable.Mauchly'sTestofSphericityaWithinSubjectsEffectMauchly'sWApprox.Chi-SquaredfSig.Epsilonb305.5结果分析与表达Measure:MEASURE_1TypeIIISumofSquaresdfMeanSquareFSig.SphericityAssumed83.125327.7083.794.026Greenhouse-Geisser83.1251.59952.0013.794.063Huynh-Feldt83.1251.99741.6193.794.048Lower-bound83.1251.00083.1253.794.092SphericityAssumed153.375217.304Greenhouse-Geisser153.37511.19013.707Huynh-Feldt153.37513.98110.970Lower-bound153.3757.00021.911TestsofWithin-SubjectsEffectsSourceAnimalError(Animal)315.5结果分析与表达Measure:MEASURE_1TypeIIISumofSquaresdfMeanSquareFSig.Level1vs.Level2120.1251120.12522.803.002Level2vs.Level3.1251.125.011.920Level3vs.Level421.125121.125.796.402Level1vs.Level236.87575.268Level2vs.Level380.875711.554Level3vs.Level4185.875726.554TestsofWithin-SubjectsContrastsSourceAnimalError(Animal)325.5结果分析与表达Measure:MEASURE_1TransformedVariable:AverageTypeIIISumofSquaresdfMeanSquareFSig.Intercept247.5311247.531398.899.000Error4.3447.621TestsofBetween-SubjectsEffectsSource335.5结果分析与表达Measure:MEASURE_1LowerBoundUpperBound18.125.7896.2599.99124.250.6482.7185.78234.125.9721.8276.42345.7501.0313.3138.187EstimatesAnimalMeanStd.Error95%ConfidenceInterval345.5结果分析与表达Measure:MEASURE_1LowerBoundUpperBound23.875*.811.012.9256.82534.000*.732.0061.3396.66142.3751.7921.000-4.1418.8911-3.875*.811.012-6.825-.9253.1251.2021.000-4.2444.4944-1.5001.3361.000-6.3593.3591-4.000*.732.006-6.661-1.3392-.1251.2021.000-4.4944.2444-1.6251.8221.000-8.2494.9991-2.3751.7921.000-8.8914.14121.5001.3361.000-3.3596.35931.6251.8221.000-4.9998.249PairwiseComparisons(I)AnimalMeanDifference(I-J)Std.ErrorSig.b95%ConfidenceIntervalforDifferencebb.Adjustmentformultiplecomparisons:Bonferroni.1234Basedonestimatedmarginalmeans*.Themeandifferenceissignificantatthe.05level.355.5结果分析与表达365.5结果分析与表达Mauchly’stestindicatedthattheassumptionofsphericityhadbeenviolated,χ2(5)=11.41,p=.047,thereforeGreenhouse–Geissercorrectedtestsarereported(ε=.53).Theresultsshowthatthetimetoretchwasnotsignificantlyaffectedbythetypeofanimaleaten,F(1.60,11.19)=3.79,p=.063.375.5结果分析与表达Mauchly’stestindicatedthattheassumptionofsphericityhadbeenviolated,χ2(5)=11.41,p=.047,thereforemultivariatetestsarereported(ε=.53).Theresultsshowthatthetimetoretchwassignificantlyaffectedbythetypeofanimaleaten,V=0.94,F(3,5)=26.96,p=.002385.6Factorialrepeated-measuredesign指在RMdesign中有两个以上的控制因素。对应的方差分析称为FactorialRM-ANOVA。基本的原理和分析方法与OnewayRM-ANOVA类似。395.6.1FactorialRM-ANOVA实例控制因素：Drink和ImageDrink有三个水平：Beer、Wine、Water。Image有三个水平：Positive、Neutral、Negative。405.6.2录入数据每个控制要素中作为基准或参考水平的数据放在第一位或者最后一位。415.6.2分析步骤425.6.2分析步骤设置Within-SubjectFactor：定义因素的顺序要和控制要素顺序及数据录入的顺序相一致。435.6.2分析步骤445.6.2分析步骤按顺序添加Within-SubjectsVariables455.6.2分析步骤根