PSY 1950 Interactions October 15, 2008
Dec 20, 2015
Preamble• Midterm review next Tuesday at 3pm on 7th floor
• Midterm handout later this week• Problem set #4 due Monday by 5pm• Consulting
Interactions… Who Cares?• Interactions abound
– Sternberg, S. (1969) Memory-scanning: Mental processes revealed by reaction-time experiments. American Scientist, 57, 421-457.
– Alcohol myopia, risky shift
• Interactions illuminate – Lazarsfeld: “You never understand a phenomenon unless you can make it go away”
– McGuire: “…all theories are right…empirical confrontation is a discovery process… clarifying circumstances under which a hypothesis is true and those under which it is false”
– Kosslyn: “There are no main effects”
Definition of an Interaction
• Conceptual– When the effect of one factor depends upon the level of one or more other factors
– When the effect of two or more variables are not simply additive
• Statistical– Residual effect, i.e., an effect remaining in an analysis after lower-order ones have been removedSSA B C = SSBetween – SSA – SSB – SSC – SSA B – SSB C – SSA x C
• Graphical– Nonparallel line plots
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Higher Order Factorial ANOVA
Young OldControl 5 5
Treatment 5 5
Young Old
Control 5 5
Treatment 5 5
Grand MeanWomen
Men
Young Old+1 -1+1 -1
Young Old+1 -1+1 -1
Age Effect
Men
WomenYoung Old6 46 4
Young Old6 46 4
Men
WomenYoung Old0 00 0
Young Old0 00 0
Sex Effect
Women
Men
Young Old-1 -1+1 +1
Young Old-1 -1+1 +1
Drug Effect
Women
Men
Young Old5 37 5
Young Old5 37 5
Men
WomenYoung Old-1 +1-1 +1
Young Old+1 -1+1 -1
Age x Sex
Women
Men
Young Old4 46 6
Young Old6 28 4
Men
WomenYoung Old+1 -1-1 +1
Young Old+1 -1-1 +1
Age x Drug
Women
Men
Young Old5 35 7
Young Old7 17 5
Men
WomenYoung Old0 00 0
Young Old0 00 0
Men
Sex x Drug
WomenYoung Old0 00 0
Young Old0 00 0
Men
Age x Sex x DrugWomen
2 Age (young, old)2 Sex (male, female)2 Drug (control, treatment)
Interpreting Interactions• Population (college, athlete) X Difficulty (easy, medium, hard)– Non-significant main effect of Population– Significant main effect of Difficulty– Significant Population by Difficulty interaction
• Three ways to interpret– Eyeball plots– Analyze simple main effects– Conduct interaction contrasts
Describing Interactions• The effect of one variable on another
– The treatment effect depended on participants’ age
– The effect of age depended on which treatment participants’ were assigned
• In terms of prediction– To accurately predict how a participant will respond to a drug, we must know both their age and gender
• In terms of differences– The gender difference in drug efficacy existed only for younger participants
Eyeball It
• Only athletes are affected by difficulty
• Population effect is reversed for high difficulty Beware of false appearances!
Simple Main EffectsOne-way Difficulty ANOVA for
athletes
One-way Difficulty ANOVA for college students
Beware of categoritis!
Interaction Contrasts• Expand design into one-way ANOVA• Make contrast for one factor• Make contrast for the other factor• Multiple weights to generate interaction contrast
Tests whether the population effect is reversed for high difficulty
Tests whether the linear difficulty effect varies with populations
Relational Re-labeling
300
350
400
450
500
550
600
650
Low Arousal High Arousal
Current Trial
Response Time (ms)
Previous Trial = Low ArousalPrevious Trial = High Arousal
300
350
400
450
500
550
600
650
Low Arousal High Arousal
Current Trial
Response Time (ms)
Congruent Incongruent
Warning• Be cautious when interpreting lower-order effects in the presence of higher-order effects– e.g., a main effect in the presence of an interaction
– e.g., a two-way interaction in the presence of a three-way interaction
• Only valid when lower-order effect is large relative to higher-order effect and when higher-order interaction is ordinal (vs. disordinal)
Contrast Weighting w/ Zero• With odd number of groups, contrast weights for some trends require weight of zero– e.g., linear trend w/ 3 groups: -1, 0, 1
ANOVA Effect Size: Eta
Advantages: conceptual simplicityDisadvantages: biased, depends on other factors/effects, depends on design/blocking
Advantages: does not depend on other factors/effects
Disadvantages: biased, conceptually complexity, depends on design/blocking
ANOVA Effect Size: Beyond Eta
• Omega-squared (2) and partial omega-squared (partial 2)– Not biased estimators of population effect size
– Better than eta for inferential purposes
• Generalized eta and omega– cf. Bethany’s presentation– Correct/control for research design
•Independent measures ANOVA and dependent measures ANOVA designs that investigate the same effect produce comparable effect sizes