A pharmacology graduate student
working on his thesis wanted to
find whether a new chemical,
DOP-Y, which has been shown to
elevate dopamine levels in the
brain, may be beneficial to
depressive patients. He was also
interested to see if electroshock
has an effect on these patients
when combined with DOP-Y.
He randomly selected 20
depressive patients, and randomly
assigned them to 4 groups:
electroshock - DOP-Y,
electroshock-no DOP-Y
no-electroshock - DOP-Y,
no-electroshock-no DOP-Y
The layout of the pharmacology experiment
The data he recorded are given in
the next table.
The data of the pharmacology experiment
High numbers indicate improvement.
The data of the pharmacology experiment
THE PHARMACOLOGY EXPERIMENT
ANOVA SUMMARY TABLE
In this table we see that A, B, and
AxB are significant.
Significance in A means that
electroshock benefited the
depressive patients.
Significance in B means that drug
benefited the depressive patients.
Significance in AxB means that
there was an interaction between electroshock and drug.
Not clear, you say,
You are correct.
Let us look at the graph of the
interaction.
First, we observe that the two lines,
shock and no shock, are not
parallel. Every time we have an
interaction, the two lines are not
parallel.
How about getting to understand
interaction at the gut level, not just
with words? you say.
Let’s do it. Look at the graph
above (previous page).
First, we will visualize the graph
without the effects of the drug. In
that graph the two lines would be
parallel.
Now visualize the effect of drug as
a force pushing the lines up.
Logically we would expect to see
both lines pushed up while
maintaining the distance between
them, i.e., the two lines may move
higher on the graph, but they
should remain parallel. However,
in the present experiment we saw
that the drug has pushed the no
electroshock line
disproportionately higher.
This is the concept of interaction.
Understanding the 2x2 factorial ANOVA summary table
A
Looking at the layout tables above, we see that factor A is gender. Factor B is drug. Our calculations gave a p value <0.05 meaning that factor A, gender, gave a significant difference. In other words, there is a difference in emotionality between male and female
B
Looking at the layout tables above, we see that factor B is Drug. Our calculations gave a p value <0.05, meaning that factor B, drug, gave a significant difference. In other words, there is a difference in emotionality between subjects that received drug 1 as compared to subjects that received drug 2.
AxB
This is the interaction term. Definition of the interaction. What is interaction in factorial designs? Interaction is present if one level of one factor has a disproportionate effect on one level of the other factor.