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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. 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

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  1. 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

  2. Example: memory for words

  3. Factors • word type (noun or verb) • word length (short or long)

  4. 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

  5. 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

  6. Alternative labeling scheme • word type = factor A • length = factor B) • 4 Conditions • noun / short: A1B1 • noun / long: A1B2 • verb / short: A2B1 • verb / long: A2B2

  7. 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

  8. 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

  9. Results of Factorials • Can plot either way -- same interpretation

  10. 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)

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

  12. Interaction • Can plot either way

  13. 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

  14. Comic Book Violent NonViolent Sex Girl 3 3 3 Boy 8 8 8 5.5 5.5

  15. Comic Book Violent NonViolent Sex Girl 8 3 5.5 Boy 8 3 5.5 8 3

  16. Comic Book Violent NonViolent Sex Girl 3 3 3 Boy 3 3 3 3 3

  17. Comic Book Violent NonViolent Sex Girl 2 4 3 Boy 8 6 7 5 5

  18. Comic Book Violent NonViolent Sex Girl 4 8 6 Boy 8 4 6 6 6

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

  20. 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

  21. 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)

  22. 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

  23. 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)

  24. 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

  25. Higher Order Designs • 2x3x2 Design • Personality Type x Caffeine level x Sex • DV: Problem solving speed

  26. Higher Order Designs • Main Effect of Sex

  27. Higher Order Designs • Main Effect of Caffeine Level

  28. Higher Order Designs • Main Effect of Personality Type

  29. 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

  30. Three Way Interaction Females Males

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