Statistical Methods for Psychology

show up on only those tasks involving higher levels of processing. This is basically what

Eysenck set out to demonstrate.

In general, we seldom look at simple effects unless a significant interaction is present.

However it is not difficult to imagine data for which an analysis of simple effects would be

warranted even in the face of a nonsignificant interaction, or to imagine studies in which

the simple effects are the prime reason for conducting the experiment.

Additivity of Simple Effects

All sums of squares in the analysis of variance (other than ) represent a partitioning

of some larger sum of squares, and the simple effects are no exception. The simple effect

of Condition at each level of Age represents a partitioning of and , whereas the

effects of Age at each level of Condition represent a partitioning of and. Thus

and

A similar additive relationship holds for the degrees of freedom. The fact that the sums of

squares for simple effects sum to the combined sums of squares for the corresponding main

effect and interaction affords us a quick and simple check on our calculations.

13.5 Analysis of Variance Applied to the Effects of Smoking

This next example is based on a study by Spilich, June, and Renner (1992), who investi-

gated the effects of smoking on performance. They used three tasks that differed in the

level of cognitive processing that was required to perform them, with different participants

serving in each task. The first task was a Pattern recognition task in which the participants

had to locate a target on a screen. The second was a Cognitive task in which the partici-

pants were required to read a passage and then recall it at a later time. The third task was a

Driving simulation video game. In each case the dependent variable was the number of er-

rors that the participant committed. (This wasn’t really true for all tasks in the original

study, but it allows me to treat Task as an independent variable. I am not seriously distort-

ing the results that Spilich et al. obtained.)

Participants were further divided into three Smoking groups. Group AS was composed

of people who actively smoked during or just before carrying out the task. Group DS par-

ticipants were regular smokers who had not smoked for 3 hours before the task (D stands

for delay). Group NS were nonsmokers.

The data follow, but before you look at those data you should make some predictions

the kinds of effects that you might find for Task, Smoking, and about their interaction.

Pattern Recognition

NS: 981210710 911810 810 81110

DS: 127144811161756966716

AS: 8 8 9 1 9 7 16 19 1 1 22 12 18 8 10

SSA 1 SSA 3 C=240.25 1 190.30=430.55

aSSA at C=1.25^1 2.45^1 72.20^1 88.20^1 266.45=430.55

SSC 1 SSA 3 C=1514.94 1 190.30=1705.24

aSSC at A=351.52^1 1353.72=1705.24

SSA SSA 3 C

SSC SSA 3 C

SStotal

426 Chapter 13 Factorial Analysis of Variance