Exam 3 information:
Morling
Chapter 11 and chapter 12
Agresti
Chapter 9, chapter 10 (except sub-paragraph “Comparing Proportions with Dependent
Samples, p. 501-502, sub-paragraph “Confidence Interval Comparing Proportions with
Matched-Pairs Data”, p. 502-503, and 10.5) and chapter 11
Chapter 12 - Experiments with More than One Independent Variable (Morling)
Experiments with Two Independent Variables can Show Interactions
Adding an additional independent variable, allows researchers to look for an
interaction effect. An interaction effect is when the original independent variable depends on
another level of another independent variable. By researching the distraction from a
smartphone while driving, researchers might also consider whether age, or driving experience
can influence or interact with the independent variable.
Intuitive Interactions
Sometimes an interaction effect can be considered to be a crossover interaction. The
results can be described as “it depends”. For example, if people are asked if they like their
food hot or cold, you might also want to consider what the product is they’re judging. Unless
you’re one of the evil pricks that waits until the ice cream is completely melted, you might
like your ice cream cold, but your noodles warm. Another interaction effect might be a
spreading effect. It can be described with the phrase “only when..”. Children might behave if
you tell them to, but they will only behave when they get a reward for behaving.
Figure 8.1.1 Example of a crossover interaction Figure 8.1.2 Example of a spreading effect
Factorial Designs Study Two Independent Variables
When researchers want to test for interactions, they do so with factorial designs. A
factorial design is one in which there are two or more independent variables (also referred to
a factors). In the most common factorial design, researchers cross the two independent
,variables, they study each possible combination of the independent variables. To cross two
independent variables, they overlay one independent variable on top of another. This overlay
process creates unique conditions (known as cells).
Using Factorial Designs to study Manipulated Variables or Participant Variables
A participant variable is a variable whose levels are selected (so, measures) and not
manipulated. But because they are not manipulated, they are not truly independent variables,
but are called so for the sake of simplicity.
A Form of External Validity
Researchers conduct studies with factorial designs to test whether an independent
variable affects different kinds of people, or people in different situations, in the same way.
This goal of testing limits is related to external validity. When researchers test an independent
variable in more than one group at once, they are testing whether the effect generalizes. In
other cases, groups might respond differently to an independent variable.
Interactions Show Moderators and can Test Theories
The process of using a factorial design to test limits is sometimes called testing for
moderators. A moderator is a variable that changes the relationship between two other
variables. In factorial design language, a moderator is an independent variable that changes
the relationship between another independent variable and a dependent variable. Thus, a
moderator results in an interaction, because the effect of one independent variable depends on
(or is moderated by) the level of another independent variable.
A factorial design can also test theories. The best way to study how variables interact
is to combine them in a factorial design and measure whether the results are consistent with
the theory. Because when you test a hypothesis, this is derived from theories.
Interpreting Factorial Results: Main Effects and Interactions
To analyze the results in a design with two independent variables, you need to inspect
three results; two main effects and one interaction effect. The main effect is the overall effect
of one independent variable on the dependent variable, averaging over the levels of the other
independent variable. In other words, a main effect is a simple difference. In a factorial
design, there are two main effects. Marginal means are the arithmetic means for each level
of an independent variable, averaging over levels of the other independent variable. If the
sample size in each cell is exactly equal, marginal means are a simple average. If the sample
size is unequal, the marginal means will be computed using the weighted average, counting
the larger sample more. Researchers look at the marginal means to inspect the main effects in
a factorial design, and they use statistics to find out whether the difference in the marginal
means is statistically significant. Sometimes statistical significance tests indicate that a main
effect is statistically significant. The term main effect is misleading, it it not the most
important effect in a study. When a study’s results show an interaction, the interaction is the
most important effect. Think of a main effect as an overall effect- the overall effect of one
independent variable at a time. The interaction is almost always the most important result in a
study, because even though there may be real differences in the marginal means, the most
, accurate story is the interaction.
Interactions: is there a Difference in Differences?
In a factorial design with two independent variables, the third effect you have to
analyze is the interaction effect. The interaction effect is the difference in differences. If you
have differences in reaction time with different pictures (let’s say, in condition 1 it’s 11ms
and in condition 2 it’s 7ms, then the difference is 11-7=4ms) and another difference in neutral
and negative words (negative words have a reaction time of 5ms and neutral words a reaction
time of 6ms then the difference is 5-6=-1ms). Then you have two different differences (5ms
and -1ms), one is negative, one is positive. Statistical tests may have told the researchers that
the difference is statistically significant, therefore, you can conclude that there is an
interaction in the factorial study. Look back at the graphs in the beginning of this chapter.
The lines don’t have to cross to indicate an interaction, they simply have to be nonparallel. If
you have a bar graph with two bars, draw an imaginary line from the same coloured bars (or
the bars with the same name, let’s say the two conditions A and the two conditions B) and if
these are nonparallel, they have an interaction. A foolproof way to describe an interaction is
to start with one level of the first independent variable (that is, the first category on the
x-axis), explain what’s happening with the second variable, then move to the next level of the
first independent variable and do the same thing. Another way to describe interactions
involve key phrases. Some interactions can be described using the phrase “it depends”. Other
interactions can be described using the phrase “especially for”.
Factorial Variations
1) Independent-Groups Factorial Designs
In an independent-groups factorial design (or between-subjects factorial) both
independent variables are studied as independent-groups. Therefore, if the design is 2x2 there
are four different groups of participants in the experiment.
2) Within-Groups Factorial Designs
In a within groups factorial design (or repeated measures factorial) both
independent variables are manipulated as within-groups. There is only one group of
participant, but they participate in all cell of the design. A within-groups factorial design
requires fewer participants.
3) Mixed Factorial Designs
In a mixed factorial design one independent variable is manipulated as
independent-groups and the other is manipulated as within-groups.
4) Three-way Design
A 2x2x2 design is called a three-way design. There are two levels of the first
independent, two levels of the second and two levels of the third. This design would create
eight cells.
