two-way anova and interactions - university of michiganacfoos/courses/381/11 - two-way an… ·...
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When ANOVA gets BIG:When ANOVA gets BIG:Factorial ANOVA and Interactions
Psychology 381A l Cl k FArlo Clark-Foos
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Bigger ANOVAsBigger ANOVAs
• More Independent VariablesMore Independent Variables– One-Way, Two-Way, Three-Way,
FactorialFactorial– Between, Within, Mixed
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Statistical InteractionsStatistical Interactions
• “It Depends”It Depends– Food and Drink Pairing
• Main Effects and InteractionsMain Effects and Interactions
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Statistical InteractionsStatistical Interactions
• Lipitor and Grapefruit JuiceLipitor and Grapefruit Juice– Increases in liver enzymes
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Statistical InteractionStatistical Interaction
• More Source Tables!More Source Tables!
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Statistical InteractionStatistical Interaction
vs
• Rows, Columns, Cells vs• Marginal means• Main Effect of Beverage (Rows)?• Main Effect of Mediation (Columns)?• Interaction between Beverage and Medication (Cells)?
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Main Effect of MedicationMain Effect of Medication
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Main Effect of BeverageMain Effect of Beverage
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Statistical InteractionStatistical Interaction
Not parallel
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Two-Way Mixed Model ANOVATwo Way Mixed Model ANOVA• Will Cognitive or Traditional therapy
work better for reducing depression?• DV: Depression• IV1: Pre vs. Post TestIV1: Pre vs. Post Test
• Within-Subjects• IV2: Cognitive vs. Traditional Therapy
• Between-SubjectsBetween Subjects
Pre-Test Post-Test
Cognitive Therapy Cognitive Pre-Test Cognitive Post-Test
Traditional Therapy Traditional Pre-Test Traditional Post-Test
Source: http://web.mst.edu/~psyworld/experimental/2x2mixeddesign.html
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Two-Way Mixed Model ANOVATwo Way Mixed Model ANOVAOne of these is not
like the other
Source: http://web.mst.edu/~psyworld/experimental/2x2mixeddesign.html
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MEMORY FOR FALSE MEDICAL CLAIMSLet’s Work out an Example:
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Memory and AgingMemory and Aging
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Factorial ANOVA FormulaeFactorial ANOVA Formulae
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Factorial ANOVA df FormulaeFactorial ANOVA df Formulae
1Ndf 1−= rowsrows Ndf
1−= ll Ndf 1columnscolumns Ndf
))(( columnsrowsninteractio dfdfdf = ))(( columnsrowsninteractio fff
3131 OOYYithi dfdfdfdfdf +++=
1−= ll Ndf
3,1,3,1, OOYYwithin dfdfdfdfdf +++
1totaltotal Ndf
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Memory and AgingMemory and Aging
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Memory and AgingMemory and Aging
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Memory and AgingMemory and Aging
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Memory and AgingMemory and Aging
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Memory and AgingMemory and Aging
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Memory and AgingMemory and Aging
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Filling in the Source TableFilling in the Source Table
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Filling in the Source TableFilling in the Source Table
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How BIG is the effect?How BIG is the effect?
)(2
ninteractiocolumnstotal
rowsrows SSSSSS
SSR−−
=
)(2 columnscolumns SSSSSS
SSR =)( ninteractiorowstotal
columns SSSSSS −−
)(2
columnsrowstotal
ninteractioctionintera SSSSSS
SSR−−
=
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How BIG is the effect?How BIG is the effect?
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VarietyVariety
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SummarySummary
• Naming your ANOVANaming your ANOVA
i ff d i• Main Effects and Interactions
• Rows, Columns, Interactions
• Effect Size, R2