Chapter 10 – Complex Experimental Design
Increasing the Number of Levels of an Independent Variable
• In the simplest experimental design there are only two levels of the independent
• However, a researcher may want to design an experiment with three or more
levels for several reasons:
1. A design with only two levels cannot provide very much info about the
exact relationship. Eg look at example 10.1 on page 187. It illustrates
how a relationship can go from a positive linear relationship to a
monotonic positive relationship by adding levels.
2. an experimental design with only two levels of the independent variable
cannot detect curvilinear relationships (recall form chapter 4 – in a
curvilinear relationship the relationship between variables changes and
sot he graph changes direction at least once). If a curvilinear
relationship is predicted, at least three levels must be used. For example,
the relationship between fear arousal and performance – may such
relationship exist in psychology!
3. Researchers are often interested in comparing more than two groups.
For example, when comparing the effect of playing with animals on
elderly people, they may want to test the difference between playing
with a dog, playing with a cat, playing with a bird, or playing with no
animal at all.
Increasing the Number of Independent Variables: Factorial Designs
• Researchers often more than one independent variable in a single experiment, -
typically 2 or 3 independent variables are operating simultaneously, which is a
closer approximation of real-world conditions in which independent variables do
not exist by themselves
• In any given situation a number of variables are operating to affect behaviour – eg
the experiment in which both the crowding and the windows were effecting the
cognitive performance of participants
• It is possible to design an experiment with more than one independent variable
• Factorial Designs are designs with more than one independent variable or factor
• In a factorial design, all levels of each independent variable are combined with all
levels of the other independent variables
• In the simplest factorial design, known as a 2 x 2 (two by two) factorial design –
there are two independent variables each with two levels
• In a study by Ellesworth, a 2 x 2 design was used. They studied the effects of
asking misleading questions on the accuracy of eyewitness testimony. The second
independent variable was the questioner’s knowledge of the crime: either they were
knowledgeable or naïve. This 2 x 2 design resulted in 4 experimental conditions:
1. knowledgeable questioner – misleading questions
2. knowledgeable questioner – honest questions
3. naïve questioner – misleading questions
4. naïve questioner – honest questions • the general format for describing a factorial design is:
Nuber of levels x Number of levels x Number of levels
of first IV of second IV of third IV
and so on
• a design with three two independent variables, one with two levels and one with
three levels would have a 2 x 3 factorial design. There are therefore six conditions
in the design.
Interpretation of Factorial Designs
• Factorial designed yield two types of info:
1. the effect of each independent variable taken by itself. This is known as the
main effect of an independent variable. In a design with two independent
variables, there are two main effects, one for each independent variable
2. interaction – if there is interaction between two independent variables, the
effect of one independent variable depends of the particular level of the
other variable. In other words, the effect that one independent variable has
on a dependent variable depends on the level of the other independent
variable. To illustrate main effect and interaction, look at table 10.1 on
page 190 which illustrates a common method of presenting both outcomes –
the number in each cell is the mean percent of errors made in the four
conditions of the experiment
• the main effect is the effect each variable has by itself.
• The main effect of each independent variable is the overall relationship between the
independent variable and the dependent variable.
• Good explanation of chart 10.1 on pg 190
• These main effects tell us that overall there are more errors when the questioner is
knowledgeable and when the questions are misleading, but there is also the
possibility that an interaction exists; if so, the main effects of the independent
variables must be qualified because an interaction between independent variables
indicated that the effect of one independent variable is different at different at
different levels of the other independent variable
• That is, an interaction tells us that the effect of one independent variable depends
on the particular level of another
• We can see an interaction in the Ellsworthy study: the effect of the type of question
is different depending on whether the questioner is knowledgeable or not
• Thus, the relationship between type of question and recall error is best understood
by looking at both independent variebles.
• Interactions can be seen easily when the means for all conditions are presented in
a graph • The concept of interaction is a simple one that we use often, for example, when we
say “it depends” because “it depends” on some other variable.
• When graphing the experimental results, the dependent variable is always on the
vertical (y) axis and one independent variable is placed on the horizontal (x) axis.
Bars are then drawn (and usually colour coded) to represent each of the levels of
the other independent variable.
Factorial Designs with Manipulated and Non-manipulated Variables
• one common type of factorial design includes both experimental (manipulated) and
non-experimental (measured or non-manipulated) variables
• they are often called IV x PV designs (independent variable by participant
variable) and they allow researchers to investigate how different types of
individuals/participants respond to the same manipulated variable.
• Theses participant variables are personal attributes of the participants, such as age,
gender, ethnicity, personality characteristics, etc. They are sometimes called subject
variables or attribute variables
• The simplest IV X PV design includes one manipulated independent variable with
at least 2 levels and one participant variable that has at least 2 levels (eg two age
• Peterson conducted an experiment in which he found that the degree to which we
are able to focus/pay attention when we are trying to read when there are