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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. Factors. word type (noun or verb) word length (short or long). Numerical notation. Denotes:

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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
factors
Factors
  • word type (noun or verb)
  • word length (short or long)
numerical notation
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
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
alternative labeling scheme
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
Results of Factorials:

Word Length

Short

Long

Word

Type

Noun

7.5

5.5

6.5

Verb

6

4

5

6.75

4.75

  • Main effects & Interactions
  • Main Effect
    • effect of one IV independent of other IV
    • collapse across levels of other IV
    • compute and compare marginal means
results of factorials1
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
results of factorials2
Results of Factorials
  • Can plot either way -- same interpretation
example 2
Example 2:

Comic Book

Violent

NonViolent

Sex

Girl

3

2.5

2.75

Boy

8

4

6

6.5

3.25

  • 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)
interaction
Interaction
  • Does type of comic book have effect? -- it depends
  • Does sex matter? -- it depends
interaction1
Interaction
  • Can plot either way
possible patterns
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
slide14

Comic Book

Violent

NonViolent

Sex

Girl

3

3

3

Boy

8

8

8

5.5

5.5

slide15

Comic Book

Violent

NonViolent

Sex

Girl

8

3

5.5

Boy

8

3

5.5

8

3

slide16

Comic Book

Violent

NonViolent

Sex

Girl

3

3

3

Boy

3

3

3

3

3

slide17

Comic Book

Violent

NonViolent

Sex

Girl

2

4

3

Boy

8

6

7

5

5

slide18

Comic Book

Violent

NonViolent

Sex

Girl

4

8

6

Boy

8

4

6

6

6

types of factorials
Types of Factorials
  • Between Subject Factorials
  • Within Subject (Repeated Measures) Factorials
  • Mixed Factorials
  • IV x PV Factorials
between subjects factorial
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
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
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
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
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 designs1
Higher Order Designs
  • 2x3x2 Design
  • Personality Type x Caffeine level x Sex
  • DV: Problem solving speed
higher order designs2
Higher Order Designs
  • Main Effect of Sex
higher order designs3
Higher Order Designs
  • Main Effect of Caffeine Level
higher order designs4
Higher Order Designs
  • Main Effect of Personality Type
interactions
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
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