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

Bauer & Curran (2005)

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

Interaction/Moderation ► X and Z interact to predict Y ► The effect of X on Y is moderated by Z ► I have a theory... X * ZY (Antisocial x Hyperactivity)(Math Ability) Y = b 0 + b 1 X + b 2 Z + b 3 (X*Z)

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

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)

Dichotomous x Dichotomous Hyperactivity

SPSS walk-through

Dichotomous x Continuous

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

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

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.

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)

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

Empirical Example ► Regression results Now what?

Empirical Example: Pick-a-point Y = (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

Empirical Example: Pick-a-point *

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

Empirical Example: J-N Technique ► Regression Results

*

1.49

Empirical Example ► Regression Results

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

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 ►

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

Thank you!