Factorial Designs

Brian J. Piper, Ph.D.

Goals

• Main Effect(s)

• Interaction

• graph & statistics comparison

Terminology

• ceiling effects:

• floor effects:

• factorial design: more than 1 independent variable– 2 x 3

– 3 x 4

– 2 x 5 mixed (2 between group, 5 within groups)

• factorial matrix (2 x 2) with 4 cells (conditions)

• main effect: overall effect of an IV (sex or drug)

Males Females

Drug 1st 2nd

Placebo 4th 3rd

Terminology

• Ceiling effects: mean score near maximum

• Floor effects: mean score near minimum

• factorial design: more than 1 independent variable– 2 x 3

– 3 x 4

– 2 x 5 mixed (2 between group, 5 within groups)

• factorial matrix (2 x 2) with 4 cells (conditions)

• main effect: overall effect of an IV (sex or drug)

Males (A1) Females (A2)

Drug (B1) 1st 2nd

Placebo (B2) 4th 3rd

Main Effect (Intuition)

Main Effect of Type of Training Main Effect of Presentation rate

Examining Main Effects

• Main Effects (continued)

– Calculations row and column means

– For hypothetical data:

• Row mean #1 mean of 17 and 23 (= 20)

• Row mean #2 mean of 12 and 18 (= 15)

• Column mean #1 mean of 17 and 12 (= 14.5)

• Column mean #2 mean of 23 and 18 (= 20.5)

Main Effects

• Male and Female college students (N=89) were assigned to different encoding intervals (3, 6, 9, 12, or 15) with the Novel Faces and Places (NFAP) test.

• This design is _____ x _____

Main Effects: Intuitive

Main Effects: Statistical

Main Effects: Statistical

• Between Groups degrees of freedom = #groups - 1

More Main Effects

• Attractiveness rating at different times among bar patrons

Mickey Gilley (1 min): http://www.youtube.com/watch?v=2e2qsnHVAo4&feature=fvst

More Main Effects

• Attractiveness rating at different times among bar patrons

Mickey Gilley (1 min): http://www.youtube.com/watch?v=2e2qsnHVAo4&feature=fvst

Interaction

• The effect of one IV (A) depends on the level of another IV (B)

• Possibilities:

A B A x B

- - -

- - +

++

--

-+

+ + -

- + -

-+

++

++

Interaction (but no main effect) Example #1

• Interactions

– IVs course emphasis and student major

– No main effects (row and column means all equal 75)

Guideline

• Parallel Lines: main effect

• Non-parallel lines: interaction

Self-Test

• Rats were exposed to MDMA or Saline during adolescence (age 35 to 60) and locomotoractivity tested at age 65

• Time Main Effect: ?

• Drug Main Effect: ?

• Interaction: ?

Piper et al. (2007) Developmental Psychobiology, 47, 145-157.

Example

• Rats were exposed to MDMA or Saline during adolescence (age 35 to 60) and locomotoractivity tested at age 65

• Time Main Effect: Yes

• Drug Main Effect: No

• Interaction: Yes

Piper et al. (2007) Developmental Psychobiology, 47, 145-157.

Emotional Labeling

• Participants (N=32) are asked to label emotions of faces

Anger Fear

Direct

Averted

Adams & Kleck (2003) Psychological Science, 14, 644-647.

Emotional Labeling

• Participants (N=32) are asked to label emotions of faces

• Response time recorded (ms)Anger Fear

Direct 862.3 (23.5) 944.5 (27.5)

Averted 914.1 (25.6) 891.2 (24.4)

Adams & Kleck (2003) Psychological Science, 14, 644-647.

Guess

• Main effect of direction: ?

• Main effect of expression: ?

• Interaction: ?

Guess

• Main effect of direction: No

• Main effect of expression: Yes

• Interaction: ?

Adams & Kleck (2003) Psychological Science, 14, 644-647.

Guess

• Main effect of direction: No

• Main effect of expression: Yes

• Interaction: Yes

Adams & Kleck (2003) Psychological Science, 14, 644-647.

Statistical Output

Further Factorial Example (12 min): http://www.youtube.com/watch?v=EgVmfryCAkU

Decision Times

A Main Effect of Sex: Main Effect of Type:Sex x Type Interaction:

Waller & Linn (2012) J Student Research.

Decision Times

A

Waller & Linn (2012) J Student Research.

A: X axisB: red versus blue groups

Data Collection Guidelines

• Be early

• Be organized

• Pilot (including coding data)

• Be consistent

• Be appreciative

• Be conservative