factorial designs - university of dayton · 2015. 11. 17. · 3 naming of factorial designs...
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Factorial Designs
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Outline
Factorial designs
Conditions vs. levels
Naming
Why use them
Main effects
InteractionsSimple main effect
Graphical definition
Additivity definition
Factorial designs
Independent samples
Repeated measures
Mixed
Higher order interactions
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Definition
Condition – one level of each IV paired together
A factorial design
has at least two IVs
has all possible conditions
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IV # 1
Level 1
Level 2
Level 3
IV # 2
Level 1
Level 2
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Factorial Example
A person acts as if he has a heart attack
this happens in front of either 1, 3, or 5 other people
the person can appear either drunk or elderly
The time it takes for one of the people to summon help is recorded
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Factorial Example
What conditions were used?
1. Drunk, 1 other person
2. Drunk, 3 other people
3. Drunk, 5 other people
4. Elderly, 1 other person
5. Elderly, 3 other people
6. Elderly, 5 other people
If all conditions are present, the study is a factorial design.
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What Conditions Are Used?
What are the conditions in the following factorial design?
Factor#1 – Males vs. females
IV#2 – Pictures of clothing vs. cars
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Naming of Factorial Designs
Factorial designs are given a name which tells how many IVs are being used and the number of levels of each IV
m X n X o X …m = number of levels of first IV
n = number of levels of second IV
…
What is the name of the number of bystanders (1 vs. 3 vs. 5) and appearance (drunk vs. elderly) study?
What is the name of the sex (male vs. female) and object (car vs. clothing) study?
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Number of Conditions
How many conditions are their in an m X n X o X … design?
Do the multiplication!
The number of conditions in the number of bystanders (1 vs. 3 vs. 5) and appearance (drunk vs. elderly) study is 3 X 2 = 6
How many conditions are their in the sex (male vs. female) and object (car vs. clothing) study?
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X
Why Use a Factorial Design?
Researchers often want to know if more than one IV influences the DV
Is helping behavior influenced by the number of bystanders?
Is helping behavior influenced by the appearance of the person needing help?
The effect of each individual IV on the DV is called a main effect
There can be as many main effects as there are IVs
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Main Effects
A main effect occurs when the value of a DV is sufficiently different for different levels of an IV
H0: 0 = 1 = … = m
H1: not H0
Main effects are worded with a single IV
As the number of bystanders increases, the time to help increases
People are more quick to help when a person appears elderly as compared to appearing drunk
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Main Effects
A main effect occurs if the average value of the DV for all the conditions at one level of an IV is sufficiently different from the average value of the DV for all the conditions at some other level of the IV
The following example assumes equal sample size in each condition
Balanced designs are good!
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Main Effects
Appearance
Drunk Elderly
# of
bystanders
1 25 15
5 45 35
Mean 35 25
Effect -10
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The effect tells us
that when we
move from the
drunk level to the
elderly level,
there is, on
average, a 10
second decrement
in the time it
takes someone to
help
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Main Effects
The larger the effect is, the more likely the main effect is to be statistically significant
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Main Effects
Appearance
Drunk Elderly Mean Effect
# of
bystanders
1 25 15 20
205 45 35 40
Mean 35 25
Effect -10
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Main Effects
The effect tells us that when we move from the 1 bystander level to the 5 bystanders level, there is, on average, a 20 second increment in the time it takes someone to help
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Main Effects
Main effects can be estimated graphically
Find the mean value of all conditions at each level of an IV
The more different the means are, the more likely the main effect is statistically reliable
The following example assumes equal sample sizes in each condition
0
10
20
30
40
0 2 4 6
# of Bystanders
Tim
e t
o H
elp
(s)
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Elderly
Drunk
Main Effect of # of Bystanders
Find the mean value of all conditions at each level of an IV
0
10
20
30
40
0 2 4 6
# of Bystanders
Tim
e t
o H
elp
(s)
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Elderly
Drunk
– Mean value of 3
bystanders = (25 + 15) / 2
= 20
– Mean value of 5
bystanders = (35 + 10) / 2
= 22.5
– Mean value of 1 bystander
= (20 + 15) / 2 = 17.5
Main Effects
The more different the means are from each other, the more likely the main effect is to be statistically reliable and the more likely there is to be a main effect of the number of bystanders
0
10
20
30
40
0 2 4 6
# of Bystanders
Tim
e t
o H
elp
(s)
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Elderly
Drunk
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Main Effect of Appearance
Find the mean value of all conditions at each level of an IV
0
10
20
30
40
0 2 4 6
# of Bystanders
Tim
e t
o H
elp
(s)
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Elderly
Drunk
– Mean value of drunk =
(15 + 25 + 35) / 3 = 25
– Mean value of elderly =
(20 + 15 + 10) / 3 = 15
The more different the means
are from each other (15 vs 25),
the more likely there is to be a
main effect of appearance
Are Main Effects Likely?20
0
5
10
15
20
25
30
Low High
Word Frequency
# o
f It
em
s R
etr
ieved
Recognition
Recall
0
1
2
3
4
5
6
7
8
Introvert Extravert
Personality
Lik
ing
Rati
ng
Cat
s
Cat
sDogs
Dogs
Why Use a Factorial Design?
The hypothesized existence of a main effect is not a sufficient reason to use a factorial design
We could perform two, single factor studies, one with one of the IVs and the other with the other IV
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Why Use a Factorial Design?
Factorial designs also tell us whether the effect of each IV on the DV is independent of the effects of the other IVs
Does the effect of the number of bystanders depend on the appearance of the person who needs help?
Such an effect is called an interaction effect
H0: There is no interaction
H1: There is an interaction
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Interactions
Interactions are important because they
tell us that we cannot generalize our results to all situations
the effect of one IV depends on the level of another IV
limit our ability to make simple statements
main effects do not fully describe the effect
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Definitions of Interactions
An interaction occurs when
the simple main effect of an IV depend on the level of one or more other IVs
the lines on a graph of the results of an experiment are not statistically parallel
the effect of two or more IVs are not additive
All three definitions are logically equivalent to each other
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Definition of Interaction
The simple main effect of an IV depends on the level of one or more other IVs
If no interaction exists:As the number of bystanders increases, helping behavior decreases
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• If an interaction exists:– As the number of
bystanders increases, helping behavior decreases if the person appears drunk, otherwise it increases if the person appears elderly
Examples
Is an interaction likely?High frequency words are easier to recall than low frequency words. Low frequency words are easier to recognize than high frequency words
Relative to silence, listening to Mozart improves spatial abilities equally in both men and women
People who wear thick glasses are more introverted than people who do not wear glasses, but this is true only if the person is less than 25 years of age
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Definitions of Interaction
An interaction occurs when the lines on a graph of the results of an experiment are not statistically parallel
The greater the difference in the slopes of the lines, the more likely the interaction is present
0
20
40
60
80
1 3 5
# of Bystanders
Tim
e t
o H
elp
(s)
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Drunk
Elderly
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Examples
Are interactions likely?
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0
20
40
60
80
1 3 5
# of Bystanders
Tim
e t
o H
elp
(s)
Elderly
Drunk
0
20
40
60
80
1 3 5
# of Bystanders
Tim
e t
o H
elp
(s)
Elderly
Drunk
Definitions of Interaction
An interaction occurs when the effect of two or more IVs are not additive
That is, you cannot add the simple effects of each IV together to predict what will happen when both treatments are simultaneously present
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Definitions of Interaction
Appearance
Drunk Elderly Mean Effect
# of
bystanders
1 15 30 22.5
-2.55 20 20 20.0
Mean 17.5 25.0
Effect 7.5
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Are the Effects Additive?
If the effects of the IVs are additive, we should be able to predict the mean value of n - 1 conditions given the effect sizes and 1 condition
n = number of conditions
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Factorial Designs
Factorial designs can occur in three varieties
Independent samples designs
Repeated measures designs
Mixed designs
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Independent Samples, Factorial Designs
An independent samples, factorial design
has all of its IVs manipulated as independent samples IVs
each person participates in a single condition
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1
Person
5
People
Drunk
Elderly
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Independent Samples, Factorial Designs
Independent samples designs
should be used when sequence effects are likely to occur in all IVs
eliminate the possibility of carry-over effects
have low statistical power
hard to reject H0 when H0 is false
can be offset by increasing sample size
must have block random assignment or matching for all IVs
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Repeated Measures, Factorial Designs
A repeated measures, factorial design
has all of its IVs manipulated as repeated measures IVs
each person participates in every condition
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1
Person
5
People
Drunk
Elderly
Repeated Measures, Factorial Designs
Repeated measures designs
should be used when sequence effects are not likely to occur in any IV
have high statistical power
easier to reject H0 when H0 is false
can have a smaller sample size
must have counterbalancing for all IVs
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Mixed, Factorial Designs
A mixed, factorial design
has at least one of its IVs manipulated as an independent samples IV and at least one IV manipulated as a repeated measures IV
each person participates in all levels of the repeated measures IVs, but only one level of the independent samples IV
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1
Person
5
People
Drunk
Elderly
Mixed Factorial Designs
Mixed designsshould be used when sequence effects are likely to occur in some, but not all IVs
IVs with potential sequence effects are made independent samples IVs, and IVs with little potential of sequence effects are made repeated measures IVs
have intermediate statistical powermust have counterbalancing for all repeated measures IVsmust have block random assignment or matching for all independent samples IVs
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More Than Two IVs
When there are more than two IVs in an experiment, there can be
As many main effects as there are IVs
Multiple two way interactions
Two way interaction = interaction of two IVs
One or more higher order interaction(s)
Higher order interaction = interactions of n – 1 IVs are different at different levels of nth IV
n!/(r! (n – r)!) n = number of IVs r = level of interaction
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More Than Two IVs
Number of
IVs
# of 2 Way
Interactions
# of 3 Way
Interactions
# of 4 Way
Interactions
# of 5 Way
Interactions
# of 6 Way
Interactions
3 3 1
4 6 4 1
5 10 10 5 1
6 15 20 15 6 1
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No 3 Way Interaction41
3 Way Interaction42
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Abstract
The APA abstract is a summary of the entire manuscript
Problem under investigation
Brief description of participants
Essential methodology
Basic findings
Conclusions
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Abstract
Always page 2
Level 1 heading “Abstract”
Written as a single paragraph
Never indented
Word count limit – 150 for us
Keywords: centered at bottom, followed by keywords for the manuscript
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