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 List A key tree door hair wood pan sink wall dirt ball List B computer microwave elevator telephone stereo spatula camera cabinet waterfall basketball List C walk jump read drink eat touch talk sit write dance List D remember liberate jeopordize violate sanitize stimulate dominate prosecute hypnotize calculate

Factors word type (noun or verb) word length (short or long)

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 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 Length ShortLong Word Type Noun Verb

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: Main effects & Interactions Main Effect –effect of one IV independent of other IV –collapse across levels of other IV –compute and compare marginal means Word Type Word Length 46Verb Noun LongShort

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 Factorials Can plot either way -- same interpretation

Example 2: 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) Sex Comic Book 48Boy 2.53Girl NonViolentViolent

Interaction Does type of comic book have effect? -- it depends Does sex matter? -- it depends

Interaction Can plot either way

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

Sex Comic Book 88Boy 33Girl NonViolentViolent

Sex Comic Book 38Boy 38Girl NonViolentViolent

Sex Comic Book 33Boy 33Girl NonViolentViolent

Sex Comic Book 68Boy 42Girl NonViolentViolent

Sex Comic Book 48Boy 84Girl NonViolentViolent

Anxiety Level LowMediumHigh Test Difficulty Easy Hard807550

Types of Factorials Between Subject Factorials Within Subject (Repeated Measures) Factorials Mixed Factorials IV x PV Factorials

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 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 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 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 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

MalesCaffeine Level LowMediumHigh Personality Type A B FemalesCaffeine Level LowMediumHigh Personality Type A30 B50 Higher Order Designs 2x3x2 Design Personality Type x Caffeine level x Sex DV: Problem solving speed

MalesCaffeine Level LowMediumHigh Personality Type A B FemalesCaffeine Level LowMediumHigh Personality Type A30 B50 Higher Order Designs Main Effect of Sex

MalesCaffeine Level LowMediumHigh Personality Type A B FemalesCaffeine Level LowMediumHigh Personality Type A30 B50 Higher Order Designs Main Effect of Caffeine Level

MalesCaffeine Level LowMediumHigh Personality Type A B FemalesCaffeine Level LowMediumHigh Personality Type A30 B50 Higher Order Designs Main Effect of Personality Type

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 Males Females