Module 12- Two-Factor ANOVA
12.1 Two-Factor ANOVA
One-Factor vs Two-Factor Differences
Expanding ANOVA from one factor to two factor introduces some complexities
Explanation of Two-factor ANOVA
A two-factor analysis of variance table lets us ask three different kinds of questions:
1.
Is there an effect of Factor A?
Known as ‘main effects Factor A’
For example, if we average across of cells (or in this case diet effect)
These are questions called main effect questions and has to do with
where there’s an overall effect of different levels within the drug factor
2.
Is there an effect of Factor B?
Known as ‘main effects Factor B’
3.
Does the response to Factor A depend on Factor B
Known as interaction between A and B
Practice Question
1.
An investigator randomly assigns 30 college students into three equal size study groups
(early-morning, afternoon, late-night) to determine if the period of the day at which
people study has an effect on theory retention. What type of test is most appropriate for
this study?
o
Two-Sample t-test
o
Correlation
o
Regression
o
Singe-factor ANOVA
o
Two-factor ANOVA

2.
Which of the following statements is TRUE about a 2 X 2 factorial design?

Two-factor ANOVA Visualization
Graphing along a single factor makes it difficult to see the main effects and interaction
Better to graph an interaction plot: boxplot moved to interaction plot
In interaction plot
o
One factor is shown along the x axis and then the other factor
is shown using different symbols or lines to represent the
other levels in the factor
o
X-axis is one factor, symbols or lines are the other
Building a Interaction Plot
On the x axis we have just the insect treatment, either absent or
present
First dot is insect absent and toads absent
The second one is insects present and toads absent

Connect the two with the line that represents toad absence
Another dot for insects absents and toads present
Then another point where both the insects and the toads
are present
The two new blue dots are joined with a solid line that
represent the toads are present
Then the interaction plot is created
It is the same information as out box plot, but its organized
into the different factors that’s easier to see the main
effects of the factors in the interaction
Questions to ask about the Interaction Plot
1.
Main effects of insects
o
Is there a difference if the insects are absent verses
present on tadpole mass?
o
Key thing to remember for this question is we’re averaging across what the toads
are doing
o
Orange dot added to the interaction plot for insects absent and for insect’s present
o
You then are able to look to see if there is a difference between the orange dots in
the absence or the presence of insects
2.
Main effects of toads
o
Involves taking the average across the treatment groups
o