FACTORIAL DESIGNS

Terms for Factorials Types of Factorial Designs Notation for Factorials Types of Effects Looking at Tables of Means Looking at Graphs of Means

Terms for Factorials

level: value of an IV condition: combination of levels of two or

more IV’s factor: another name for IV

Factor A

Factor B

Level 1 Level 2

Level 1

Level 2

Level 3

condition condition condition

condition condition condition

Types of Factorial Designs

between subjects within subjects mixed

Between Subjects

B

1

2

A1 2

Subjects1-10

Subjects11-20

Subjects31-40

Subjects21-30

Within Subjects

B

1

2

A1 2

Subjects1-40

Subjects1-40

Subjects1-40

Subjects1-40

Mixed (A Between, B Within)

B

1

2

A1 2

Subjects1-20

Subjects1-20

Subjects21-40

Subjects21-40

Notation for Factorials The number of numbers tells you how

many i.v.’s The numbers tell you how many levels A factorial with two i.v.’s which each have

two levels is a 2 x 2

Notation for Factorials

2x2 2x3 3x4How many i.v.’s?How many d.v.’s?How many conditions?

Types of Effects

Main Effect: the overall effect of one IV, averaging over the levels of the other IV

Interaction: the effect of one IV changes depending on the level of the other IV

Drug

Therapy

1 2

1

2

40 60

60 40

meanrecoveryscore

No main effect of therapyNo main effect of drugBUT the effect of the therapy depends on which drug is being taken

Why Factorials?

Reduce amount of non-systematic variance Ability to measure interaction Main effects can be misleading without

considering the interaction

Looking at Means Tables For main effects:

– find marginal means (means of levels)– if marginal means are different, there is a main

effect

Looking at Means Tables For interaction:

– find simple effects (effects of one variable for each level of other variable)

– If simple effects change, there is an interaction

A

B

1 2

1

2

40 60

40 60

main effect of A

50

50

40 60

+20

+20

A

B

1 2

1

2

40 60

40 80

40 70

A

B

1 2

1

2

40 30

50 20

A

B

1 2

1

2

3

20

20

20

20

50

80

Looking at Graphs of Means

main effects: – visually estimate marginal means– if they are at different heights, there is a main

effect

Looking at Graphs of Means

interaction:– parallel lines mean no interaction– non-parallel lines mean an interaction

d.v.

10203040506070

0

A1 2

B1

B2x

xx x

main effect of B

d.v.

10203040506070

0

A1 2

B1

B2

d.v.

10203040506070

0

A1 2

B1

B2

d.v.

10203040506070

0

A1 2

B1

B2

d.v.

10203040506070

0

A

1 3

B1

B2

2