Psychology 513: Advanced Research Methods

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Psychology 513 Advanced Research Methods

• Factorial ANOVA

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Overview

• Factorial refers to multiple independent
  variables
• Can examine main effects and interactions

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SS for a 2-way ANOVA

• SScells deviation of each condition mean from
  the grand mean this is the total treatment
  effect (between-cells)
• Decompose into main effect of A, main effect of
  B, and AB interaction
• SSerror within-cells variability within
  conditions

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Structural Model

• Xij m ai bj abij eijk
• Expected Mean Squares
• A s2e nbs2a
• B s2e nas2b
• AB s2e ns2ab
• Error s2e

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Interaction

• Lines are not parallel
• Ordinal interactions one group consistently
  above another group
• Disordinal interactions - crossover

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Examining the interaction

• Follow-up a significant interaction effect with
  analysis of simple effects
• Simple effects effect of one IV at one level of
  the other IV

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Example- 3 x 2 design
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Example (cont.)

• Interaction F(2,24) 5.55, p 0.01
• Main effect for A F(2,24) 3.54, p 0.04
• Main effect for B F(1,24) 59.85, p 0.00

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Example (cont.)

• Test of simple effects
• A at B1 F(2,24) 0.61, p 0.55
• A at B2 F(2,24) 8.48, p 0.00
• Or
• B at A1 F(1,24) 18.89, p 0.00
• B at A2 F(1,24) 4.72, p 0.04
• B at A3 F(1,24) 47.34, p 0.00

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Example- Plot of Cell Means
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Power Analysis

• Compute power for main effects and interaction
• In a 2 x 2 design, power will be the same for all
  effects (assuming ES is the same)
• fab fab(sqrt of n)

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Example

• Assume effect size for interaction is moderate
  (f 0.25) and our design is a 2 x 2
• Need to identify f from Appendix ncF use df of
  1 and infinity to get f of 2.0
• Need an n of 64 (N 256)

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Calculating Effect Sizes

• Eta-squared
• h2A SSA / SStotal
• h2B SSB / SStotal
• Omega-squared