Chapter 9 – Factorial Designs

Factorial Design -- definition
– Two or more IVs
– every level of one IV
• combined with every level of other IV
– IVs -- called factors
Example: memory for words
List A
key
tree
door
hair
wood
pan
sink
wall
dirt
ball
List B
computer
microwave
elevator
telephone
stereo
spatula
camera
cabinet
waterfall
basketball
List C
walk
jump
read
drink
eat
touch
talk
sit
write
dance
List D
remember
liberate
jeopordize
violate
sanitize
stimulate
dominate
prosecute
hypnotize
calculate
Factors


word type (noun or verb)
word length (short or long)
Numerical notation

Denotes:
– Number of IVs (factors)
– Number of levels of each factor

e.g. 2 x 2 design
e.g., 4 x 3 design

Factorial Table
One factor rows – Other factor columns
 Each column / row corresponds to a level of its factor
 Each cell represents a specific condition
 Combination of specific levels of each factor
 note: #conditions = levels x levels

Word Length
Short
Word
Type
Noun
Verb
Long
Alternative labeling scheme



word type = factor A
length = factor B)
4 Conditions
– noun / short: A1B1
– noun / long: A1B2
– verb / short: A2B1
– verb / long: A2B2
Results of Factorials:


Main effects & Interactions
Main Effect
– effect of one IV independent of other IV
– collapse across levels of other IV
– compute and compare marginal means
Word Length
Word
Type
Short
Long
Noun
7.5
5.5
6.5
Verb
6
4
5
6.75
4.75
Results of Factorials

Interaction between factors (IVs)
– Ask: does effect of on IV depend on the level of the other IV?
– If the answer is “yes” – you have an interaction
– easiest way to see interaction -- in a line graph
8
7
6
5
Noun
Verb
4
3
2
1
0
Short
Long
Results of Factorials

Can plot either way -- same interpretation
8
7
6
5
Short
Long
4
3
2
1
0
Noun
Verb
Example 2:

Effect of violent media on 6th grade children

IV1: Comic book content (violent vs. nonviolent)
IV2: Sex of subject (male vs. female)
DV: Measure of aggressiveness (response to scenario)


Comic Book
Sex
Violent
NonViolent
Girl
3
2.5
2.75
Boy
8
4
6
6.5
3.25
Interaction
9
8
7
6
5
Girl
Boy
4
3
2
1
0
Violent


Nonviolent
Does type of comic book have effect? -- it depends
Does sex matter? -- it depends
Interaction
9
8
7
6
5
Violent
Nonviolent
4
3
2
1
0
Girl

Can plot either way
Boy
Possible patterns
can get any possible combination of main effects and
interactions
 main effects but no interactions
 interactions but no main effects
 main effect of one factor, but not the other


**INTERPRETATION:
– INTERACTION SUPERCEDES MAIN EFFECTS
Comic Book
Sex
Violent
NonViolent
Girl
3
3
3
Boy
8
8
8
5.5
5.5
9
8
7
6
5
Girl
Boy
4
3
2
1
0
Violent
Nonviolent
Comic Book
Sex
Violent
NonViolent
Girl
8
3
5.5
Boy
8
3
5.5
8
3
9
8
7
6
5
Girl
Boy
4
3
2
1
0
Violent
Nonviolent
Comic Book
Sex
Violent
NonViolent
Girl
3
3
3
Boy
3
3
3
3
3
9
8
7
6
5
Girl
Boy
4
3
2
1
0
Violent
Nonviolent
Comic Book
Sex
Violent
NonViolent
Girl
2
4
3
Boy
8
6
7
5
5
9
8
7
6
5
Girl
Boy
4
3
2
1
0
Violent
Nonviolent
Comic Book
Sex
Violent
NonViolent
Girl
4
8
6
Boy
8
4
6
6
6
9
8
7
6
5
Girl
Boy
4
3
2
1
0
Violent
Nonviolent
Anxiety Level
Test
Difficulty
Low
Medium
High
Easy
90
85
90
Hard
80
75
50
100
90
80
Easy
Hard
70
60
50
40
Low
Medium
High
Types of Factorials

Between Subject Factorials
 Within Subject (Repeated Measures) Factorials
 Mixed Factorials
 IV x PV Factorials
Between Subjects Factorial



all factors(IV) are manipulated between subjects
e.g., study material by material generation (2x2 between
subject design)
– study material – outline vs. questions
– material generation – self vs. instructor
– four conditions: four different groups of subjects
concerns: begin with equivalent groups
– random assignment
– matching
Within Subjects Factorial

all factors(IV) are manipulated within subject

e.g., effect of sex and age of approacher on personal space
(2x3 within sub design)
– 2 levels of sex (f vs. m)
– 3 levels of age (20’s, 40’s, 60’s)
• 6 different conditions (6 different people approaching
concerns: sequence or carryover effects
– complete counterbalancing
– partial counterbalancing (Latin Square)


Mixed Factorial Designs







at least one factor (IV) manipulated between
at least one manipulted within
e.g., add the factor of mood into above design
– (3x2x3 mixed factorial design)
sex and age are manipulated within subject
perform a between subject mood manipulation:
– Positive, Neutral, or Negative
concerns: equivalence for between subject factors
concerns: carryover effects for within subject factors
IV x PV designs







At least one manipulated IV
At least one subject variable
e.g., Personality Type (Type A or Type B) x competition (hi or
low)
DV -- problem solving task
Main Effect of PV -- effect of person type
Main effect IV -- task/situation effect
Interaction -- task/situation differences depend on person type
– ** Must be careful in interpreting subject variables (as
always)
Higher order designs
Three or more factors (IVs)
 Each level crossed with every other
 Each factor – may produce main effect
 May have interaction between any combination of factors

Higher Order Designs



2x3x2 Design
Personality Type x Caffeine level x Sex
DV: Problem solving speed
Males
Personality
Type
Caffeine Level
Low
Medium
High
A
40
30
20
B
40
50
60
Females
Personality
Type
Caffeine Level
Low
Medium
High
A
30
30
30
B
50
50
50
Higher Order Designs

Main Effect of Sex
Males
Personality
Type
Caffeine Level
Low
Medium
High
A
40
30
20
B
40
50
60
Females
Personality
Type
Caffeine Level
Low
Medium
High
A
30
30
30
B
50
50
50
Higher Order Designs

Main Effect of Caffeine Level
Males
Personality
Type
Caffeine Level
Low
Medium
High
A
40
30
20
B
40
50
60
Females
Personality
Type
Caffeine Level
Low
Medium
High
A
30
30
30
B
50
50
50
Higher Order Designs

Main Effect of Personality Type
Males
Personality
Type
Caffeine Level
Low
Medium
High
A
40
30
20
B
40
50
60
Females
Personality
Type
Caffeine Level
Low
Medium
High
A
30
30
30
B
50
50
50
Interactions

Two Way Interactions
– Personality Type x Caffeine Level
• (average across sex)
– Personality Type x Sex
• (average across caffeine level)
– Caffeine Level x Sex
• (average across personality type)

Three Way Interaction
– Two-way interaction DEPENDS on level of other
variable
Three Way Interaction
Females
Males
70
60
60
50
50
40
40
Type A
Type B
Type A 30
Type B
30
20
20
10
10
0
0
Low
Medium
High
Low
Medium
High