Interactions

1
Interactions

• Up to this point, when weve discussed the causal
  effect of one variable upon another weve assumed
  that the effect is additive and independent of
  other variables.
• There may be situations, however, where the
  influence of one variable upon another is
  contingent upon a third variable.
• For example, whether watching violent television
  leads to aggressive behavior might be dependent
  upon whether someone has been provoked or not.

2
Interactions

• In such situations, we say that the two variables
  interact to influence the outcome variable.
• main effects vs. interactions
• The combination of main effects and interactions
  with just two variables can lead to a wide array
  of predictions.

3
In these situations, we say that the two
variables interact to influence the dependent
variable
4
Aggressive TV viewing (X1) Aggressive TV viewing (X1)
Provocations (X2) -1 1
-1 5 5 5
1 5 5 5
5 5
This represents a situation in which the
experimental manipulations have no effects on the
dependent variable.
5
Aggressive TV viewing (X1) Aggressive TV viewing (X1)
Provocations (X2) -1 1
-1 2 8 5
1 2 8 5
2 8
6
Aggressive TV viewing (X1) Aggressive TV viewing (X1)
Provocations (X2) -1 1
-1 2 2 2
1 8 8 8
5 5
7
Aggressive TV viewing (X1) Aggressive TV viewing (X1)
Provocations (X2) -1 1
-1 -1 5 2
1 5 11 8
2 8
8
Aggressive TV viewing (X1) Aggressive TV viewing (X1)
Provocations (X2) -1 1
-1 8 2 5
1 2 8 5
5 5
9
Aggressive TV viewing (X1) Aggressive TV viewing (X1)
Provocations (X2) -1 1
-1 5 5 5
1 1 9 5
3 7
10
Aggressive TV viewing (X1) Aggressive TV viewing (X1)
Provocations (X2) -1 1
-1 5 1 3
1 5 9 7
5 5
11
Aggressive TV viewing (X1) Aggressive TV viewing (X1)
Provocations (X2) -1 1
-1 3 3 3
1 3 11 7
3 7
12
Interaction terms can be easily incorporated into
the standard regression model that weve already
developed The interaction is represented as a
product term Doing so allows us to formally
represent the notion that X1, for example, is a
function of X2.
13
If we go back through the previous slides, we can
see that the means for each group are provided by
this equation. coded 1 and 1 (-1, -1) 5 - 2
0 2 5 (-1, 1) 5 - 2 0 - 2 1 (1, -1)
5 2 0 - 2 5 (1, 1) 5 2 0 2 9
14
Interactions

• Interactions with continuous variables