07. Factorial ANOVA part 2

# 07. Factorial ANOVA part 2 - Factorial ANOVA Part 2...

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Factorial ANOVA Part 2

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Interaction Interaction Can occur if there is more than one factor Total s.s. = SSA + SSB +SSAB+ SSE SSA measures s.s for factor A (having a levels) SSB measures s.s for factor B (having b levels) SSAB measures interaction between factors A and B SSE measures residual variation
ANOVA table for Interaction Need more than one observation per call to measure interaction Source s.s. d.f. m.s. F Sig. Factor A SSA dfA=a-1 MSA= SSA/dfA MSA/MSE p-value Factor B SSB dfB=b-1 MSB= SSB/dfB MSB/MSE p-value Interaction A x B SSAB dfAB=(a-1)(b- 1) MSAB= SSAB/dfAB MSAB/MS E p-value Error SSE dfE=found by subtraction MSE= SSE/dfE Total Total s.s df=n-1 H 0 : No interaction between A and B Reject if ) ), 1 )( 1 (( dfE b a F MSE MSAB - - α Need more than one observation of each treatment in each row and column

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What to do if you have significant interaction? No Interaction Interaction Plots roughly parallel – Accept H 0 : No interaction between A and B ANOVA table Interaction
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