Simple Effects
And
Factorial Design Hypotheses
Outline of Today’s Discussion
1. Simple Effects
2. Hypotheses for Factorial Designs
Part 1
Simple Effects
Simple Effects
1. Once we have found a significant
interaction in a complex design, we must
locate the source of the interaction using
“simple effects”…
2. Simple Effect - The effect of one IV at one
level of the second IV.
3. Sometimes these are called ‘simple main
effects’.
4. Example: The simple effect of Factor A, at
level B1.
Simple Effects
Example of Simple Effect
From Shaughnessy, Zechmeister & Zechmeister
http://en.wikipedia.org/wiki/Locus_of_control
Would someone please describe the
dimensionality of this experiment?
Simple Effects
Example of Simple Effect
From Shaughnessy, Zechmeister & Zechmeister
Let’s see if we have an interaction…
would someone please walk us through the
“subtraction method” ?
Simple Effects
1. In the sessions to come, we’ll have a more formal
way of identifying an interaction (i.e., an ANOVA
that tests the statistical significance of the
interaction.)
2. For now, we’ll assume on the basis of the
subtraction method that we have a significant
interaction. Work with me here. :-)
3. In our 3 by 2 design, there are five simple
effects…
Simple Effects
When there is a significant interaction,
look at simple effects.
From Shaughnessy, Zechmeister & Zechmeister
There is a simple effect of Accident (factor A)
at each level of Depression (factor B).
So, that’s 3 of the 5 simple effects.
Simple Effects
When there is a significant interaction,
look at simple effects.
From Shaughnessy, Zechmeister & Zechmeister
Which of these simple effects
do you suspect would be statistically significant,
and why?
Simple Effects
When there is a significant interaction,
look at simple effects.
From Shaughnessy, Zechmeister & Zechmeister
There is also a simple effect of Depression (factor B)
at each level of Accident (factor A).
So, that’s 2 of the 5 simple effects.
Simple Effects
When there is a significant interaction,
look at simple effects.
From Shaughnessy, Zechmeister & Zechmeister
Which of these simple effects
do you suspect would be statistically significant,
and why?
Simple Effects
When there is a significant interaction,
look at simple effects.
From Shaughnessy, Zechmeister & Zechmeister
Note: Since there are three depression levels
at each accident type, we would need some
post-hoc (Scheffe or Tukey or Dunnet) tests to determine
which pairs differ from each other.
Simple Effects
1. Let’s consider “the big picture”…
2. That is, when you are beginning to analyze data
from your complex design, it helps to have a
plan for your analysis…
Simple Effects
Modified From Shaughnessy, Zechmeister & Zechmeister
Post Hoc
Tests
Post Hoc
Tests
Decision Tree for Analyzing Complex Designs
Post hoc tests e.g., Scheffe, Tukey, Dunnet, Bonferroni.
Simple Effects
1. Potential Pop Quiz Question: What is the
simplest possible complex design?
2. Potential Pop Quiz Question: In your own
words, explain what is meant by the phrase
“natural groups design”.
3. Potential Pop Quiz Question: In your own
words, explain how researchers could use
complex designs to test a theory of why
natural groups differ.
Part 2
Hypotheses For Factorial Designs
Hypotheses For Factorial Designs
• In the population, the means will be the
same across all levels of Factor A.
• In the population, the means will be the
same across all levels of Factor B.
• In the population, differences among the
levels of Factor A will be the same at each
level of Factor B.
Hypotheses For Factorial Designs
• Consider a study in which a story is presented.
The story contains either 0, 1, 2, or 3 violations
of physical laws (e.g., gravity is suspended).
• Participants rate the plausibility of the story.
• The researcher investigates whether
plausibility ratings depend on (A) the number
of violations, and (B) the extent to which the
participant is “manic”.
Hypotheses For Factorial Designs
• In the population, mean plausibility ratings will
be equal across number-of-violations.
• In the population, mean plausibility ratings will
be equal across “mania” levels.
• In the population, differences among the means
for number-of-violations will be the same at
each level of mania.
Hypotheses For Factorial Designs
3-Way Interaction
• In the population, the interaction between
Factor A and Factor B will be the same at each
level of factor C.
• In the population, the interaction between
number-of-violations and mania will be the
same at each level of Gender.
Analysis of Complex Designs
Probability of
Finding Spouse
Interactions Obscure
Main Effects
0.8
0.6
0.4
0.2
0
Young
Old
Male
Female
Gender
Shaughnessy,JJ, Shaughnessy, EB, and Zechmesiter, JS.
Research Methods
Psychology,
Hill.
What’sin“wrong”
withMcGraw
this graph?