You found an interaction! Now what?

1. You found an interaction! Now what? A practical guide to graphing & probing significant interactions Design and Statistical Analysis Lab Colloquium Laura J. Sherman umdconsulting@gmail.com

2. Bauer & Curran (2005)

3. Interaction/Moderation • X and Z interact to predict Y • The effect of X on Y is moderated by Z • I have a theory... X Y (Antisocial Behavior) (Math Ability) Z (Hyperactivity)

4. Interaction/Moderation • X and Z interact to predict Y • The effect of X on Y is moderated by Z • I have a theory... X * Z Y (Antisocial x Hyperactivity) (Math Ability) Y = b0 + b1X+ b2Z+ b3 (X*Z)

5. Remember Slopes? b = 5 Positive relationship between X and Y b = 0 No relationship between X and Y Math Ability b = -5 Negative relationship between X and Y Antisocial Behavior

6. Types of Interactions • Dichotomous x Dichotomous • Antisocial (yes/no) x Hyperactivity (yes/no) • Variables were actually measured dichotomously • Continuous x Dichotomous • Antisocial (range: -5 to 5) x Hyperactivity (yes/no) • Continuous x Continuous • Antisocial (range: -5 to 5) x Hyperactivity (range: -5 to 5)

7. Dichotomous x Dichotomous Hyperactivity

8. SPSS walk-through

16. Dichotomous x Continuous

17. Continuous x Continuous • “Pick-a-point” approach (Rogosa, 1980) • Plotting and testing the conditional effect of X at designated levels of Z Hyperactivity (Z)

18. Problems with pick-a-point approach • Values selected arbitrarily • May even be outside range of observed sample data • Sample dependent • You designated a continuous variable, but you are only testing its effect at a few values

19. Johnson-Neyman Technique • Computation of regions of significance • Indicates over what range of the moderator the effect of X is significantly positive, nonsignificant, or significantly negative • Plotting of confidence bands for the conditional effect • APA task force: confidence intervals are much more informative than null hypothesis tests • In the case of conditional effects, both the effect estimate and its standard error vary as a function of M. Cannot plot just one confidence interval, must plot bands over full range of M.

20. Empirical Example • Child math ability, antisocial, & hyperactivity • Hypothesis: There would be a negative relation between antisocial behavior and math ability that would be moderated by the presence of child hyperactive behavior. • Stated alternatively, antisocial behavior and hyperactive behavior interact to predict math ability (assessment of the Children of the National Longitudinal Survey of Youth, 1990)

21. Prepping Variables Mean center X and Z Calculate X * Z variable (do not center that)

22. Empirical Example • Regression results Now what?

23. Empirical Example: Pick-a-point Y = 38.07 + .0373(A) - .799(H) - .397(A x H) +/- 1 SD Hyperactivity: Low (-1.54), Medium (0), High (1.54) *Prior to running regression, mean center or standardize predictors involved in interactions

24. Empirical Example: Pick-a-point *

25. Problems with pick-a-point approach • Values selected arbitrarily • May even be outside range of observed sample data • Sample dependent • You designated a continuous variable, but you are only testing its effect at a few values

26. Empirical Example: J-N Technique • Regression Results

27. *

31. 1.49

32. Empirical Example Regression Results

33. http://www.quantpsy.org

34. 38.07 .0373 -.799 -.397 -1.54 0.00 1.54 .1039 .0719 .0461 .0204 -5 5 952 -.0003 -.0124

35. Region of Significance =========================== Z at lower bound of region = -2.3285 Z at upper bound of region = 1.4948 (simple slopes are significant *outside* this region.)

38. Summary • Major points: • When probing interactions, use information from your ANOVA/Regression equation • Pick-a-point is a limited, out-dated approach to testing and displaying Continuous x Continuous interactions • www.quantpsy.org

39. Which variable is the moderator? Theory-driven, no statistical test Mean centering Covariates 3-way interactions Simple slopes difference testing Non-linear Additional comments/next steps

40. umdconsulting@gmail.com Thank you!