Transcription of Statistics 203: Introduction to Regression and Analysis of ...
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- p. 1/19 Statistics203 s classlTwo-way ANOVAlRandomvs. fixedeffectslWhentouserandomeffects?lExa mple:sodiumcontentinbeerlOne-way randomeffectsmodellImplicationsformodell One-way randomANOVA tablelInferencefor lEstimating 2 lExample:productivitystudylTwo-way randomeffectsmodellANOVA tables:Two-way(random)lMixedeffectsmodel lTwo-way mixedeffectsmodellANOVA tables:Two-way(mixed)lConfidenceinterval sforvarianceslSattherwaite s procedure- p. 2/19 Today s mixed& s s classlTwo-way ANOVAlRandomvs. fixedeffectslWhentouserandomeffects?lExa mple:sodiumcontentinbeerlOne-way randomeffectsmodellImplicationsformodell One-way randomANOVA tablelInferencefor lEstimating 2 lExample:productivitystudylTwo-way randomeffectsmodellANOVA tables:Two-way(random)lMixedeffectsmodel lTwo-way mixedeffectsmodellANOVA tables:Two-way(mixed)lConfidenceinterval sforvarianceslSattherwaite s procedure- p. 3/19 Two-way ANOVA model:observations:(Yijk);1 i r;1 j m;1 k nij:rgroupsin firstgroupingvariable,mgroupsinssecondan dnijsamplesin(i; j)- cell :Yijk= + i+ j+ ( )ij+"ijk;"ijk N(0; 2):nConstraints:uPri=1 i= 0uPmj=1 j= 0uPmj=1( )ij= 0;1 i ruPri=1( )ij= 0;1 j m:lToday s classlTwo-way ANOVAlRandomvs.
Simplest example: repeated measures, where more than one (identical) measurement is taken on the same individual. In this case, the “group” effect i is best thought of as
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