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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


Comic Book

Violent

NonViolent

Sex

Girl

3

3

3

Boy

8

8

8

5.5

5.5


Comic Book

Violent

NonViolent

Sex

Girl

8

3

5.5

Boy

8

3

5.5

8

3


Comic Book

Violent

NonViolent

Sex

Girl

3

3

3

Boy

3

3

3

3

3


Comic Book

Violent

NonViolent

Sex

Girl

2

4

3

Boy

8

6

7

5

5


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


Three way interaction
Three Way Interaction

Females

Males


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