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# Chapter 9 – Factorial Designs - PowerPoint PPT Presentation

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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• Factorial Design -- definition

• Two or more IVs

• every level of one IV

• combined with every level of other IV

• IVs -- called factors

• word type (noun or verb)

• word length (short or long)

• Denotes:

• Number of IVs (factors)

• Number of levels of each factor

• e.g. 2 x 2 design

• e.g., 4 x 3 design

• 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 type = factor A

• length = factor B)

• 4 Conditions

• noun / short: A1B1

• noun / long: A1B2

• verb / short: A2B1

• verb / long: A2B2

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

• 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

• Can plot either way -- same interpretation

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)

• Does type of comic book have effect? -- it depends

• Does sex matter? -- it depends

• Can plot either way

• 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

Violent

NonViolent

Sex

Girl

3

3

3

Boy

8

8

8

5.5

5.5

Violent

NonViolent

Sex

Girl

8

3

5.5

Boy

8

3

5.5

8

3

Violent

NonViolent

Sex

Girl

3

3

3

Boy

3

3

3

3

3

Violent

NonViolent

Sex

Girl

2

4

3

Boy

8

6

7

5

5

Violent

NonViolent

Sex

Girl

4

8

6

Boy

8

4

6

6

6

• Between Subject Factorials

• Within Subject (Repeated Measures) Factorials

• Mixed Factorials

• IV x PV Factorials

• 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

• 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)

• 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

• 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)

• 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

• 2x3x2 Design

• Personality Type x Caffeine level x Sex

• DV: Problem solving speed

• Main Effect of Sex

• Main Effect of Caffeine Level

• Main Effect of Personality Type

• 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

Females

Males