Two-Way ANOVA and Interactions - University of Michiganacfoos/Courses/381/11 - Two-Way AN… · When ANOVA gets BIG:When ANOVA gets BIG: Factorial ANOVA and Interactions Psychology

When ANOVA gets BIG:When ANOVA gets BIG:Factorial ANOVA and Interactions

Psychology 381A l Cl k FArlo Clark-Foos

Bigger ANOVAsBigger ANOVAs

• More Independent VariablesMore Independent Variables– One-Way, Two-Way, Three-Way,

FactorialFactorial– Between, Within, Mixed

Statistical InteractionsStatistical Interactions

• “It Depends”It Depends– Food and Drink Pairing

• Main Effects and InteractionsMain Effects and Interactions

Statistical InteractionsStatistical Interactions

• Lipitor and Grapefruit JuiceLipitor and Grapefruit Juice– Increases in liver enzymes

Statistical InteractionStatistical Interaction

• More Source Tables!More Source Tables!

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)?

Main Effect of MedicationMain Effect of Medication

Main Effect of BeverageMain Effect of Beverage

Statistical InteractionStatistical Interaction

Not parallel

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

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

MEMORY FOR FALSE MEDICAL CLAIMSLet’s Work out an Example:

Memory and AgingMemory and Aging

Factorial ANOVA FormulaeFactorial ANOVA Formulae

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

Memory and AgingMemory and Aging

Memory and AgingMemory and Aging

Memory and AgingMemory and Aging

Memory and AgingMemory and Aging

Memory and AgingMemory and Aging

Memory and AgingMemory and Aging

Filling in the Source TableFilling in the Source Table

Filling in the Source TableFilling in the Source Table

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−−

=

How BIG is the effect?How BIG is the effect?

VarietyVariety

SummarySummary

• Naming your ANOVANaming your ANOVA

i ff d i• Main Effects and Interactions

• Rows, Columns, Interactions

• Effect Size, R2