PSY248 Lecture Notes - Lecture 8: Family-Wise Error Rate, Null Hypothesis, Decision Rule
2 Jun 2018
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PSY248 Weeks 8-10: Two-Way ANOVA
- most in ANOVA notes
Factorial design:
Drug X
Drug Y
Therapy A
Cell 1,1
Therapy A
Drug X
Cell 1, 2
Therapy A
Drug Y
Therapy B
Cell 2,1
Therapy B
Drug X
Cell 2,2
Therapy B
Drug Y
Contrast testing
• planned vs. post-hoc designs
• two decision rules as before
• Control family-wise error rate (FER)
• Post-hoc designs: Scheffe decision rule
o Reject null hypothesis: contrast = 0 if F(contrast) > df
• Planned designs: Bonferroni decision rule
o Reject null: contrast = 0 if F(contrast) > F
Testing interactions
• Interaction contrasts will have as many coefficients as cells
• Sum of coefficients across rows and columns must equal 0
• To get coefficients, cross-multiple coefficients of row contrasts by those of
column contrasts and apply to cell means
Interpretation of interactions
• Presence of significant interactions have implications for the main effects
• It’s a matter of opinion whether to interpret main effects when an interaction is
significant
o Some say never
o Some take a ‘sometimes’ approach, depending on the interaction itself
(ordinal vs. disordinal)
Interaction contrasts
• Choosing an interaction contrast follows same rules as main effects (up to the
researcher what to test, if post-hoc)
• A good place to start is the biggest ‘difference of differences’
(diverging/converging lines)
find more resources at oneclass.com
find more resources at oneclass.com
Document Summary
Interaction contrasts will have as many coefficients as cells: sum of coefficients across rows and columns must equal 0, to get coefficients, cross-multiple coefficients of row contrasts by those of column contrasts and apply to cell means. Interpretation of interactions: presence of significant interactions have implications for the main effects. It"s a matter of opinion whether to interpret main effects when an interaction is significant: some say never, some take a sometimes" approach, depending on the interaction itself (ordinal vs. disordinal)
