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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. Bauer & Curran (2005). Interaction/Moderation. X and Z interact to predict Y

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you found an interaction now what

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

interaction moderation
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)

interaction moderation4
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)

remember slopes
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

types of interactions
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)
continuous 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
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
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
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
Prepping Variables

Mean center X and Z

Calculate X * Z variable (do not center that)

empirical example22
Empirical Example
  • Regression results

Now what?

empirical example pick a point
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

problems with pick a point approach25
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 example32
Empirical Example

Regression Results

slide34

38.07

.0373

-.799

-.397

-1.54

0.00

1.54

.1039

.0719

.0461

.0204

-5

5

952

-.0003

-.0124

slide35
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.)

summary
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
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

Additional comments/next steps