Statistical Methods for Psychology

Simple Interaction Effects

With higher-order factorials, not only can we look at the effects of one variable at individual

levels of some other variable (what we have called simple effects but what should more accu-

rately be called simple main effects), but we can also look at the interaction of two variables

at individual levels of some third variable. This we will refer to as a simple interaction effect.

Although our second-order interaction (ABC) was not significant, you might have a

theoretical reason to expect an interaction between Experience (A) and Road (B) under

night conditions, because driving at night is more difficult, but would expect no AB inter-

action during the day. As an example, I will break down the ABC interaction to get at those

two simple interaction effects. (I should stress, however, that it is not good practice to test

everything in sight just because it is possible to do so.)

In Figure 13.5 the ABinteraction has been plotted separately for each level of C. It ap-

pears that there is no ABinteraction under C 1 , but there may be an interaction under C 2. We

can test this hypothesis by calculating the ABinteraction at each level of C, in a manner

logically equivalent to the test we used for simple main effects. Essentially, all we need to

do is treat the C 1 (day) and C 2 (night) data separately, calculating for C 1 data and then

for C 2 data. These simple interaction effects are then tested using from the overall

analysis. This has been done in Table 13.16.

From the analysis of the simple interaction effects, it is apparent that the ABinteraction

is not significant for the day data, but it is for the night data. When night conditions ( ) and

dirt roads ( ) occur together, differences between experienced ( ) and inexperienced ( )

drivers are magnified.

B 3 A 2 A 1

C 2

MSerror

SSAB

Section 13.12 Higher-Order Factorial Designs 451

Table 13.15 Simple effects for data in Table 13.14

(a) Data

C 1 C 2 Mean

A 1 16.000 29.000 22.500

A 2 9.833 14.333 12.083

(b) Computations

(c) Summary table

Source df SS MS F

Cat A 1 1 1014.00 1014.00 37.99*

Cat A 2 1 121.50 121.50 4.55*

Error 36 961.00 26.69

*p,.05

(d) Decomposition of sums of squares

1135.50=1135.50

1014.00 1 121.50=918.75 1 216.75

SSC at A 11 SSC at A 2 =SSC 1 SSAC

= 43 3[(9.833 2 12.083)^21 (14.333 2 12.083)^2 ]=121.50

SSC at A 2 =nba(X2.k 2 X2..)^2

= 43 3[(16.000 2 22.500)^21 (29.000 2 22.500)^2 ]=1014.00

SSC at A 1 =nba(X1.k 2 X1..)^2

simple main
effects

simple
interaction effect