PSY 1950 Interactions October 15, 2008

1. PSY 1950 Interactions October 15, 2008

2. Preamble • Midterm review next Tuesday at 3pm on 7th floor • Midterm handout later this week • Problem set #4 due Monday by 5pm • Consulting

3. 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”

4. 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 removed SSA  B  C = SSBetween – SSA – SSB – SSC – SSA  B – SSB  C – SSA x C • Graphical • Nonparallel line plots

5. TA  B  C TA  B

6. Higher Order Factorial ANOVA 2 Age (young, old) • 2 Sex (male, female) • 2 Drug (control, treatment)

9. 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

10. 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

11. Eyeball It • Only athletes are affected by difficulty • Population effect is reversed for high difficulty Beware of false appearances!

12. Simple Main Effects One-way Difficulty ANOVA for athletes One-way Difficulty ANOVA for college students Beware of categoritis!

13. 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

14. Relational Re-labeling

15. 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)

16. 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

18. ANOVA Effect Size: Eta Advantages: conceptual simplicity Disadvantages: 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

19. 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

20. t-test is Special Case of ANOVA (k=2)