**Effects**

Statistical
relationships between independent and dependent variables are often referred to
as __effects__. So the difference
between the average concentration score in the quiet condition and the average
concentration score in the noisy condition can be called “the effect of noise
level on concentration.” Likewise, the
difference between the average intelligence rating in the smile condition and
the average intelligence rating in the no-smile condition can be called “the
effect of smiling on intelligence ratings.”
So whenever we manipulate an independent variable, we are interested in
its effect on the dependent variable.

**Main Effects**

In a factorial
design, a __main effect__ is the *overall*
effect of *one* independent variable. In an experiment in which both the type of
psychotherapy (cognitive vs. behavioral) and the duration of psychotherapy
(short vs. long) are independent variables, there is one main effect of type and
another main effect of duration. The
main effect of type is the difference between the average score for the
cognitive group and the average score for the behavioral group … ignoring
duration. That is, short-duration
subjects and long-duration subjects are combined together in computing these
averages. The main effect of duration is
the difference between the average score for the short-duration group and the
average score for the long-duration group … this time ignoring type. Cognitive-therapy subjects and behavioral-therapy
subjects are combined together in computing these averages.

**Main Effects in Design Tables**

Imagine that the
dependent variable in the psychotherapy study is some measure of improvement,
with higher scores indicating more improvement.
Let us assume for simplicity that there are only three subjects per
condition, so we can write their improvement scores directly into the design
table (in place of the sample sizes; see below.) To see the main effect of the type of
psychotherapy, all we need to do is compare the average score in the behavioral
condition with the average score in the cognitive condition. We compute both of these averages *across* subjects in the long and short
duration conditions. We see that the six
subjects in the cognitive conditions scored three points higher on average than
the six subjects in the behavioral conditions.
This is the main effect of the type of psychotherapy. To see the main effect of the duration of
psychotherapy, we compare the average score in the short condition with the
average score in the long condition, now computing these averages *across* subjects in the cognitive and
behavioral conditions. We see that the
six subjects in the long conditions scored three points higher on average than
the six subjects in the short conditions.
This is the main effect of the duration of psychotherapy.

**Main
Effects in Graphs**

Below are the same results plotted in the form of a bar
graph, which is probably the best way to display them. The main effect of type is indicated by the
fact that the two cognitive bars are higher on average than the two behavioral
bars. The main effect of duration is
indicated by the fact that the two long-duration (dark) bars are higher on
average than the two short-duration (light) bars.

Below are some results (for a different experiment)
presented in the form of a line graph. It is a line graph because the independent
variable on the x-axis is quantitative with a small number of values. Note that if you were to “average” the two
lines, the result would be a line sloping downward, showing a negative effect
of noise on concentration. This is the
main effect of noise because it combines the extroverts and the
introverts. To see the main effect of
extroversion, note that extroverts tended to have higher scores regardless of
the noise level. The extrovert line is
above the introvert line.

**Interactions**

An __interaction__ is a special kind of effect that can
be observed in factorial experiments. You
have an interaction whenever the effect of one independent variable *depends* on the level of the other. This is actually a fairly easy idea. Here are some examples.

1) If cognitive psychotherapy is better than behavioral
psychotherapy when the therapy is short but not when the therapy is long, then
there is an interaction between type and duration of therapy. 2) If the negative effect of noise level on
concentration is greater for introverts than for extroverts, then there is an
interaction between these two independent variables. 3) If the boost in intelligence judgments due
to smiling is greater for male stimulus persons than for female stimulus
persons, then there is an interaction between smiling and sex. 4) If drawing a smiley face on checks
increases tips for female servers but not for male servers, then there is an
interaction between drawing smiley faces (or not) and sex of the server.

There is no interaction when the effect of one variable is essentially
the same regardless of the level of the other.
One example we have seen is that a smile boosts perceptions of a
stimulus person about the same amount regardless of whether that person is
attractive or unattractive.

A particularly interesting kind of interaction is a __crossover
interaction__. In a crossover
interaction, the effect of one independent variable is not only different
across levels of the second independent variable, it actually reverses. Imagine, for example, that introverts’
concentration levels started high and then dropped as the noise level
increased, but extroverts’ concentration level started low and then increased
as the noise level increased. This would
be a crossover interaction. (Why do you
think it is called that?)

**The
Relationship Between Main Effects and Interactions**

In a 2x2 factorial experiment, there are two main effects
(one for each independent variable) and one interaction (the one between the
two independent variables). It gets more
complicated with more independent variables.
An experiment with three independent variables would have three main
effects (again, one for each independent variable) and four interactions. There is an interaction between IV’s 1 and 2,
2 and 3, and 1 and 3. There is also
something called a three-way interaction, which has to do with whether the
interaction between two variables depends on the level of the third. But do not worry about this. Until you understand simple factorial
designs, there is no way you will understand more complicated ones.

The important point here is that these effects are all
independent of each other. A 2x2
factorial experiment might result in no main effects and no interaction, one
main effect and no interaction, two main effects and no interaction, no main
effects and an interaction, one main effect and an interaction, or two main
effects and an interaction. Your job now
is to get good at looking at results presented in a design table or (more
importantly) a graph, and interpreting what happened
in terms of main effects and interactions.