第六讲方差分析(下)

.,1,第5章方差分析（下）Repeated-measure&MixeddesignANOVA,.,2,.,3,.,4,Repeatedmeasures（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-subjectsdesign,5.1RM基本概念,.,5,5.1RM基本概念,RM-ANOVA，重复测量的方差分析适用条件：各组样本数据不独立控制变量的水平数在三个以上满足球形检验,.,6,5.2球形检验,球形（sphericity表示为）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。,.,7,5.2.1球形检验例子,varianceA-BvarianceA-CvarianceB-C,球形检验通过的条件为：,.,8,5.2.1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。,.,9,实际检验方法：在SPSS中球形检验可以通过Mauchlystest进行。其零假设为：实验不同情况下差异的方差是相等的。若Mauchlystest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,.,10,当球形检验没通过时：0.75,采用HuynhFeldtestimate的结果0.75或未知，采用GreenhouseGeisser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Bonferronimethod,.,11,5.3RM-ANOVA原理,.,12,5.3RM-ANOVA原理实例分析,.,13,5.3RM-ANOVA原理实例分析,N-1为总离差的自由度，由样本总量决定,.,14,5.3RM-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83=24,.,15,5.3RM-ANOVA原理实例分析,dfM=k1=3,.,16,5.3RM-ANOVA原理实例分析,.,17,5.3RM-ANOVA原理实例分析,.,18,5.3RM-ANOVA原理实例分析,.,19,5.4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,.,20,5.4数据录入与操作,.,21,5.4数据录入与操作,添加Within-subject因素名称与水平数,.,22,5.4数据录入与操作,设置变量,.,23,5.4数据录入与操作,设置RM模型,.,24,5.4数据录入与操作,设置对比方法,.,25,5.4数据录入与操作,设置绘图模式,.,26,5.4数据录入与操作,设置置信区间及其它可选项,.,27,5.5结果分析与表达,.,28,5.5结果分析与表达,.,29,5.5结果分析与表达,.,30,5.5结果分析与表达,.,31,5.5结果分析与表达,.,32,5.5结果分析与表达,.,33,5.5结果分析与表达,.,34,5.5结果分析与表达,.,35,5.5结果分析与表达,.,36,5.5结果分析与表达,.,37,5.5结果分析与表达,Mauchlystestindicatedthattheassumptionofsphericityhadbeenviolated,2(5)=11.41,p=.047,thereforeGreenhouseGeissercorrectedtestsarereported(=.53).Theresultsshowthatthetimetoretchwasnotsignificantlyaffectedbythetypeofanimaleaten,F(1.60,11.19)=3.79,p=.063.,.,38,5.5结果分析与表达,Mauchlystestindicatedthattheassumptionofsphericityhadbeenviolated,2(5)=11.41,p=.047,thereforemultivariatetestsarereported(=.53).Theresultsshowthatthetimetoretchwassignificantlyaffectedbythetypeofanimaleaten,V=0.94,F(3,5)=26.96,p=.002,.,39,5.6Factorialrepeated-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。,.,40,5.6.1FactorialRM-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。,.,41,5.6.2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。,.,42,5.6.2分析步骤,.,43,5.6.2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。,.,44,5.6.2分析步骤,.,45,5.6.2分析步骤,按顺序添加Within-SubjectsVariables,.,46,5.6.2分析步骤,根据问题的实际性质设置对比方式,.,47,5.6.2分析步骤,设置ProfilePlots,.,48,5.6.2分析步骤,设置Options,.,49,5.6.3结果分析,.,50,5.6.3结果分析,球形检验结果：两个主因素效果Significant交互因素效果non-significant,.,51,5.6.3结果分析,.,52,5.6.3结果分析,自由度的计算：dfD-M=KD-1=3-1=2dfD-W=ndfD-M=202=40dfR-D=dfD-W-dfD-M=40-2=38dfDI-M=dfD-MdfI-M=22=4dfDI-W=ndfDI-M=204=80dfR-DI=dfDI-W-dfDI-M=80-4=76,.,53,5.6.3结果分析,自由度的计算：dfD-M=KD-1（dfD-Mfreedomdegrees,df,ofmodeleffectsfordrinks）=3-1=2dfD-W=ndfD-M（dfD-wdfofwithin-subjecteffectsfordrinks）=202=40dfR-D=dfD-W-dfD-M（dfR-Ddfofresidualeffectsfordrinks）=40-2=38dfDI-M=dfD-MdfI-M（dfDI-Mdfofmodelinteractioneffectsfordrinks*Imagery）=22=4dfDI-W=ndfDI-M（dfDI-Wdfofwithin-subjectinteractioneffectsfordrinks*Imagery）=204=80dfR-DI=dfDI-W-dfDI-M（dfDI-Wdfofresidualinteractioneffectsfordrinks*Imagery）=80-4=76,.,54,5.6.3结果分析,dfGG-D=dfDGG=20.577=1.154dfR-GG-D=dfR-DGG=380.577=21.926调整F检验中的其余各项自由度计算方法相同。,.,55,5.6.3结果分析,.,56,5.6.3结果分析,.,57,5.6.3结果分析,不一致！,.,58,5.6.3结果分析,.,59,5.6.3结果分析,当Posthoc和Contracts的结果不一致时，以后者为准。,.,60,5.6.3结果分析,.,61,5.6.3结果分析,.,62,5.6.3结果分析,Mauchlystestindicatedthattheassumptionofsphericityhadbeenviolatedforthemaineffectsofdrink,2(2)=23.75,p.001,andimagery,2(2)=7.42,p=.024.ThereforedegreesoffreedomwerecorrectedusingGreenhouseGeisserestimatesofsphericity(=.58forthemaineffectofdrinkand.75forthemaineffectofimagery).,Reporttheresults:,.,63,5.6.3结果分析,Reporttheresults:,Therewasasignificantmaineffectofthetypeofdrinkonratingsofthedrink,F(1.15,21.93)=5.11,p=.011.Contrastsrevealedthatratingsofbeer,F(1,19)=6.22,p=.022,andwine,F(1,19)=18.61,weresignificantlyhigherthanwater.Therewasalsoasignificantmaineffectofthetypeofimageryonratingsofthedrinks,F(1.50,28.40)=122.57.,.,64,5.6.3结果分析,Contrastsrevealedthatratingsafterpositiveimageryweresignificantlyhigherthanafterneutralimagery,F(1,19)=142.19.Conversely,ratingsafternegativeimageryweresignificantlylowerthanafterneutralimagery,F(1,19)=47.07.,Reporttheresults:,.,65,5.6.3结果分析,Therewasasignificantinteractioneffectbetweenthetypeofdrinkandthetypeofimageryused,F(4,76)=17.16.Thisindicatesthatimageryhaddifferenteffectsonpeoplesratingsdependingonwhichtypeofdrinkwasused.Tobreakdownthisinteraction,contrastswereperformedcomparingalldrinktypestotheirbaseline(water)andallimagerytypestotheirbaseline(neutralimagery).Theserevealedsignificantinteractionswhencomparingnegativeimagerytoneutralimagerybothforbeercomparedtowater,F(1,19)=6.75,p=.018,andwinecomparedtowater,F(1,19)=26.91.,Reporttheresults:,.,66,Lookingattheinteractiongraph,theseeffectsreflectthatnegativeimagery(comparedtoneutral)loweredscoressignificantlymoreinwaterthanitdidforbeer,andloweredscoressignificantlymoreforwinethanitdidforwater.Theremainingcontrastsrevealednosignificantinteractiontermwhencomparingpositiveimagerytoneutralimagerybothforbeercomparedtowater,F(1,19)=1.58,p=.225,andwinecomparedtowater,F(1,19)=0.24,p=.633.However,thesecontrastsdidyieldsmalltomediumeffectsizes.,5.6.3结果分析,Reporttheresults:,.,67,5.7MixeddesignANOVA,Mixeddesign是指在实验过程中有多个控制因素，其中有些因素（within-subjectsfactor）的不同水平为所有的实验实体（Entity，如subjects）都参与测试，而另外一部分的因素(between-subjectsfactor)的不同水平则由不同的实验实体参与测试。,.,68,5.7.1数据录入,组内因素（within-subjectsfactor)的每个水平都按照单独的变量进行数据录入，一个组间因素（between-subjectsfactor)的作为一个单独的变量进行数据录入。录入组内因素的不同水平时，需要考虑不同水平的次序关系，把参考水平（referencelevelorbaseline）排在该因素不同水平的第一位或最后一位。若某因素的各个水平之间地位对等，则在排列时没有特殊要求，在对比时一般采用repeated方式进行对比。,.,69,5.7.2实例,问题：测试长相（looks）和个性魅力(personality)对快速约会效果的影响。控制因素：长相（3个水平）个性魅力（3个水平）性别（2个水平）测试值：愿意和同一个人再次约会的意愿。,.,70,5.7.3关键分析步骤,按照实验测试的顺序（该顺序和数据录入顺序相一致），添加组内因素名称及各因素水平数。,.,71,5.7.3关键分析步骤,映射组内因素变量指定组间因素,.,72,5.7.3关键分析步骤,设置各因素的对比方式,.,73,5.7.3关键分析步骤,设置绘图方式,.,74,5.7.3关键分析步骤,设置可选项因有组间因素，所以需要进行方差齐次性检验,.,75,5.7.4结果分析,因素摘要表,.,76,5.7.4结果分析,描述性统计,.,77,5.7.4结果分析,检查组间因素方差分析的条件是否满足方差齐次性检验,.,78,5.7.4结果分析,检查组内因素方差分析的条件是否满足球形检验,.,79,5.7.4结果分析,组间因素效果,.,80,5.7.4结果分析,组间因素效果对比,.,81,5.7.4结果分析,Maineffect-Gender,.,82,5.7.4结果分析,Maineffect-Looks,.,83,5.7.4结果分析,Interaction-Looks,.,84,5.7.4结果分析-Report,Alleffectsarereportedassignificantatp.001unlessotherwisestated.Therewasasignificantmaineffectoftheattractivenessofthedateoninterestexpressedbyparticipant,F(2,36)=423.73.Contrastsrevealedthatattractivedatesweresignificantlymoredesirablethanaverage-lookingones,F(1,18)=226.99,anduglydatesweresignificantlylessdesirablethanaverage-lookingones,F(1,18)=160.07.,.,85,5.7.4结果分析-Report,Therewasalsoasignificantmaineffectoftheamountofcharismathedatepossessedontheinterestexpressedindatingthem,F(2,36)=328.25.Contrastsrevealedthatdateswithhighcharismaweresignificantlymoredesirablethandateswithsomecharisma,F(1,18)=109.94,anddullardsweresignificantlylessdesirablethandateswithsomecharisma,F(1,18)=227.94.,.,86,5.7.4结果分析-Report,Therewasnosignificanteffectofgender,indicatingthatratingsfrommaleandfemaleparticipantsweresimilar,F(1,18)=0.005,p=.946.Therewasasignificantinteractioneffectbetweentheattractivenessofthedateandthegenderoftheparticipant,F(2,36)=80.43.Thiseffectindicatesthatthedesirabilityofdatesofdifferentlevelsofattractivenessdifferedinmenandwomen.,.,87,5.7.4结果分析-Report,Tobreakdownthisinteraction,contrastscomparedeachlevelofattractivenesstoaveragelooks,acrossmaleandfemaleparticipants.Thesecontrastsrevealedsignificantinteractionswhencomparingmaleandfemalescorestoattractivedatescomparedtoaveragelookingdates,F(1,18)=43.26,andtouglydatescomparedtoaverage-lookingdates,F(1,18)=30.23.,.,88,5.7.4结果分析-Report,Theinteractiongraphshowsthatalthoughbothmalesandfemalesinterestdecreasedasattractivenessdecreased,thisdecreasewasmorepronouncedformen,suggestingthatwhencharismaisignored,mensinterestindatingapersonwasmoreinfluencedbytheirlooksthanwomens.,.,89,5.7.4结果分析-Report,Therewasasignificantinteractioneffectbetweenthelevelofcharismaofthedateandthegenderoftheparticipant,F(2,36)=62.45,indicatingthatthedesirabilityofdatesofdifferentlevelsofcharismadifferedinmenandwomen.Contrastswereperformedcomparingeachlevelofcharismatothemiddlecategoryofsomecharismaacrossmaleandfemaleparticipants.Thesecontrastsrevealedsignificantinteractionswhencomparingmaleandfemalescorestohighlycharismaticdatescomparedtodateswithsomecharisma,F(1,18)=27.20,andtodullardscomparedtodateswithsomecharismaF(1,18)=33.69.,.,90,5.7.4结果分析-Report,Theinteractiongraphrevealsthatbothmalesandfemalesinterestdecreasedascharismadecreased,butthisdecreasewasmorepronouncedforfemales,suggestingwomensinterestindatingapersonwasmoreinfluencedbytheircharismathanmens.,.,91,5.7.4结果分析-Report,Therewasasignificantcharismaattractivenessinteraction,F(4,72)=36.63,indicatingthatthedesirabilityofdatesofdifferentlevelsofcharismadifferedaccordingtotheirattractiveness.Contrastswereperformedcomparingeachlevelofcharismatothemiddlecategoryofsomecharismaacrosseachlevelofattractivenesscomparedtothecategoryofaverageattractiveness.Thefirstcontrastrevealedasignificantinteractionwhencomparingattractivedatestoaverage-lookingdateswhenthedatehadhighcharismacomparedtosomecharisma,F(1,1