Chapter 9 – Factorial Designs

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 Long

Word

Type

Noun

Verb

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

4.756.75

5

6.5Word

Type

Word Length

46Verb

5.57.5Noun

LongShort

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

0

1

2

3

4

5

6

7

8

Short Long

NounVerb

Results of Factorials Can plot either way -- same interpretation

0

1

2

3

4

5

6

7

8

Noun Verb

ShortLong

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)

3.256.5

6

2.75Sex

Comic Book

48Boy

2.53Girl

NonViolentViolent

Interaction

Does type of comic book have effect? -- it depends Does sex matter? -- it depends

0

1

2

3

4

5

6

7

8

9

Violent Nonviolent

GirlBoy

Interaction

Can plot either way

0

1

2

3

4

5

6

7

8

9

Girl Boy

ViolentNonviolent

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

0

1

2

3

4

5

6

7

8

9

Violent Nonviolent

GirlBoy

5.55.5

8

3Sex

Comic Book

88Boy

33Girl

NonViolentViolent

0

1

2

3

4

5

6

7

8

9

Violent Nonviolent

GirlBoy

38

5.5

5.5Sex

Comic Book

38Boy

38Girl

NonViolentViolent

0

1

2

3

4

5

6

7

8

9

Violent Nonviolent

GirlBoy

33

3

3Sex

Comic Book

33Boy

33Girl

NonViolentViolent

0

1

2

3

4

5

6

7

8

9

Violent Nonviolent

GirlBoy

55

7

3Sex

Comic Book

68Boy

42Girl

NonViolentViolent

0

1

2

3

4

5

6

7

8

9

Violent Nonviolent

GirlBoy

66

6

6Sex

Comic Book

48Boy

84Girl

NonViolentViolent

40

50

60

70

80

90

100

Low Medium High

EasyHard

Anxiety Level

Low Medium High

Test Difficulty

Easy 90 85 90

Hard 80 75 50

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

Males Caffeine Level

Low Medium High

Personality Type

A 40 30 20

B 40 50 60

Females Caffeine Level

Low Medium High

Personality Type

A 30 30 30

B 50 50 50

Higher Order Designs 2x3x2 Design Personality Type x Caffeine level x Sex DV: Problem solving speed

Males Caffeine Level

Low Medium High

Personality Type

A 40 30 20

B 40 50 60

Females Caffeine Level

Low Medium High

Personality Type

A 30 30 30

B 50 50 50

Higher Order Designs Main Effect of Sex

Males Caffeine Level

Low Medium High

Personality Type

A 40 30 20

B 40 50 60

Females Caffeine Level

Low Medium High

Personality Type

A 30 30 30

B 50 50 50

Higher Order Designs Main Effect of Caffeine Level

Males Caffeine Level

Low Medium High

Personality Type

A 40 30 20

B 40 50 60

Females Caffeine Level

Low Medium High

Personality Type

A 30 30 30

B 50 50 50

Higher Order Designs Main Effect of Personality Type

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

0

10

20

30

40

50

60

70

Low Medium High

Type AType B

Males

0

10

20

30

40

50

60

Low Medium High

Type AType B

Females