Factorial Designs in Experiments
Factorial Designs
Chapter 11
Class Temperature & learning
Add a second factor (gender)
What about another factor (test
level)?
Factorial designs
Allow experiments to have
more than one
independent
variable.
Example
Example
•
This example has
two levels
for the alcohol
factor ( factor A) and
three levels
for the
caffeine factor ( factor B), and can be
described as a
2X3
( read as “ two by three”)
factorial design
•
The total number of treatment conditions
can
be determined by multiplying the levels for
each factor.
Main effect
The mean differences among the levels of
one
factor
are called the main effect of that factor.
Example 1- Main effect
Interaction
An interaction between factors ( or simply an
interaction) occurs whenever
two factors, acting
together
, produce mean differences that are not
explained by the main effects of the two factors.
Example 1- Main effect only
+25
+25
+25
+25
Example 2 - Interaction
+10
+40
+10
+40
Alternative Definitions of an
Interaction
When the
effects of one factor depend
on the
different levels of a second factor, then there is
an interaction between the factors.
A second alternative definition of an interaction
focuses on the pattern that is produced when
the means from a two- factor study are
presented in a
graph
.
When the results of a two- factor study are graphed, the existence of
nonparallel lines
( lines that cross or converge) is an indication of an
interaction between the two factors. ( Note that a statistical test is needed to
determine whether the interaction is significant.)
=
Interaction
≠
sample
Possible
outcomes
Main effect Factor A
Not B
Main effect for A & B
No main effect
Interaction A&B
Important
If the analysis results in a significant interaction, then the main
effects, whether significant or not,
may present a distorted view
of the actual outcome.
5 Types of Mixed Designs
A factorial study that combines two different research
designs is called a mixed design.
1.
Both Experimental – Both between
2.
Both Experimental –Both within
3.
Both Experimental - One
between
- subjects factor and one
within
- subjects factor.
4.
Both
factors are
non-manipulated
(pre existing)
5.
One
experimental
& one
non-experimental
Example
(between/Within)
•
The graph shows the pattern of results obtained by Clark and Teasdale ( 1985).
The researchers showed participants a list containing a mixture of pleasant and
unpleasant words to create a
within- subjects factor ( pleasant/ unpleasant
). The
researchers manipulated mood by dividing the participants into two groups and
having one group listen to happy music and the other group listen to sad music,
creating a
between- subjects factor ( happy/ sad
). Finally, the researchers tested
memory for each type of word.
music
Quasi- independent variables
It also is possible to construct a factorial study
for which
all the factors
are
non-manipulated
,
quasi- independent variables.
Example
One Experimental one non-experimental
In the behavioral sciences, it is common for a
factorial design to use an
experimental strategy
for one factor and a quasi- experimental or
non-
experimental
strategy for another factor.
Example
Pre-existing
Manipulate
Higher- Order Factorial Designs
•
The basic concepts of a two- factor research
design can be extended to more complex
designs involving
three or more factors
; such
designs are referred to as higher- order
factorial designs. A three- factor design, for
example, might look at academic performance
scores for two different
teaching methods
(
factor A), for
boys versus girls
( factor B), and
for
first- grade versus second- grade
classes (
factor C).
Factorial designs in experiments allow researchers to study the effects of multiple independent variables simultaneously. This type of design enables the examination of main effects and interactions between factors, providing a comprehensive understanding of the research variables. Main effects refer to the differences in means across levels of one factor, while interactions occur when the effects of one factor depend on different levels of another factor. By utilizing factorial designs, researchers can gain valuable insights into complex relationships within their studies.
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Presentation Transcript
Factorial Designs Chapter 11
Class Temperature & learning Temperature Exam Score High 80 Low 80
Add a second factor (gender) Chart Title 86 84 82 80 78 76 74 72 70 Male Female High Low
What about another factor (test level)?
Factorial designs Allow experiments to have more than one independent variable.
Example This example has two levels for the alcohol factor ( factor A) and three levels for the caffeine factor ( factor B), and can be described as a 2X3 ( read as two by three ) factorial design The total number of treatment conditions can be determined by multiplying the levels for each factor.
Main effect The mean differences among the levels of one factor are called the main effect of that factor.
Interaction An interaction between factors ( or simply an interaction) occurs whenever two factors, acting together, produce mean differences that are not explained by the main effects of the two factors.
+25 +25 +50 +50 +50 +25 +25 Example 1- Main effect only
+10 +10 +20 +80 +50 +40 +40 Example 2 - Interaction
Alternative Definitions of an Interaction When the effects of one factor depend on the different levels of a second factor, then there is an interaction between the factors. A second alternative definition of an interaction focuses on the pattern that is produced when the means from a two- factor study are presented in a graph.
When the results of a two- factor study are graphed, the existence of nonparallel lines ( lines that cross or converge) is an indication of an interaction between the two factors. ( Note that a statistical test is needed to determine whether the interaction is significant.)
Main effect Factor A Not B sample Possible outcomes Main effect for A & B No main effect Interaction A&B
Important If the analysis results in a significant interaction, then the main effects, whether significant or not, may present a distorted view of the actual outcome.
5 Types of Mixed Designs A factorial study that combines two different research designs is called a mixed design. 1. Both Experimental Both between 2. Both Experimental Both within 3. Both Experimental - Onebetween- subjects factor and one within- subjects factor. 4. Both factors are non-manipulated (pre existing) 5. One experimental & one non-experimental
Example (between/Within) music The graph shows the pattern of results obtained by Clark and Teasdale ( 1985). The researchers showed participants a list containing a mixture of pleasant and unpleasant words to create a within- subjects factor ( pleasant/ unpleasant). The researchers manipulated mood by dividing the participants into two groups and having one group listen to happy music and the other group listen to sad music, creating a between- subjects factor ( happy/ sad). Finally, the researchers tested memory for each type of word.
Quasi- independent variables It also is possible to construct a factorial study for which all the factors are non-manipulated, quasi- independent variables.
Example Factor B Psychology 6 20 History 19 5 Male Female Memory Scores Factor A 25 20 15 Male Female 10 5 0 Psychology History
One Experimental one non-experimental In the behavioral sciences, it is common for a factorial design to use an experimental strategy for one factor and a quasi- experimental or non- experimental strategy for another factor.
Example Manipulate Pre-existing
Higher- Order Factorial Designs The basic concepts of a two- factor research design can be extended to more complex designs involving three or more factors; such designs are referred to as higher- order factorial designs. A three- factor design, for example, might look at academic performance scores for two different teaching methods ( factor A), for boys versus girls ( factor B), and for first- grade versus second- grade classes ( factor C).
