PSY 1950 Interactions October 15, 2008

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, –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 removed SS A  B  C = SS Between – SS A – SS B – SS C – SS A  B – SS B  C – SS A x C Graphical –Nonparallel line plots

T A  B T A  B  C

Higher Order Factorial ANOVA 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 Effects One-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

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

a1a1 a2a2 a3a3 01 M1M1 M2M2 M3M3 234 a1M1a1M1 a2M2a2M2 a3M3a3M3 -204

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

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

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