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FACTORIAL DESIGNS

FACTORIAL DESIGNS. Terms for Factorials Types of Factorial Designs Notation for Factorials Types of Effects Looking at Tables of Means Looking at Graphs of Means. Terms for Factorials. level: value of an IV condition: combination of levels of two or more IV’s

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FACTORIAL DESIGNS

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  1. FACTORIAL DESIGNS • Terms for Factorials • Types of Factorial Designs • Notation for Factorials • Types of Effects • Looking at Tables of Means • Looking at Graphs of Means

  2. Terms for Factorials • level: value of an IV • condition: combination of levels of two or more IV’s • factor: another name for IV

  3. Factor A Level 1 Level 2 Level 3 condition Level 1 condition condition Factor B condition condition condition Level 2

  4. Types of Factorial Designs • between subjects • within subjects • mixed

  5. Between Subjects A 1 2 Subjects 1-10 Subjects 21-30 1 B Subjects 11-20 Subjects 31-40 2

  6. Within Subjects A 1 2 Subjects 1-40 Subjects 1-40 1 B Subjects 1-40 Subjects 1-40 2

  7. Mixed (A Between, B Within) A 1 2 Subjects 1-20 Subjects 21-40 1 B Subjects 1-20 Subjects 21-40 2

  8. Notation for Factorials • The number of numbers tells you how many i.v.’s • The numbers tell you how many levels • A factorial with two i.v.’s which each have two levels is a 2 x 2

  9. Notation for Factorials • 2x2 2x3 3x4 • How many i.v.’s? • How many d.v.’s? • How many conditions?

  10. Types of Effects • Main Effect: the overall effect of one IV, averaging over the levels of the other IV • Interaction: the effect of one IV changes depending on the level of the other IV

  11. Drug 1 2 60 mean recovery score 1 40 Therapy 40 2 60 No main effect of therapy No main effect of drug BUT the effect of the therapy depends on which drug is being taken

  12. Why Factorials? • Reduce amount of non-systematic variance • Ability to measure interaction • Main effects can be misleading without considering the interaction

  13. Looking at Means Tables • For main effects: • find marginal means (means of levels) • if marginal means are different, there is a main effect

  14. Looking at Means Tables • For interaction: • find simple effects (effects of one variable for each level of other variable) • If simple effects change, there is an interaction

  15. A 1 2 60 1 40 50 +20 B 60 2 40 50 +20 40 60 main effect of A

  16. A 1 2 60 1 40 B 80 2 40 40 70

  17. A 1 2 30 1 40 B 20 2 50

  18. A 1 3 2 1 B 2 20 20 50 20 20 80

  19. Looking at Graphs of Means • main effects: • visually estimate marginal means • if they are at different heights, there is a main effect

  20. Looking at Graphs of Means • interaction: • parallel lines mean no interaction • non-parallel lines mean an interaction

  21. 70 60 50 B2 x 40 d.v. 30 x x B1 20 x 10 0 1 2 A main effect of B

  22. 70 B2 60 50 40 B1 d.v. 30 20 10 0 1 2 A

  23. B2 70 60 50 40 d.v. 30 B1 20 10 0 1 2 A

  24. 70 60 B2 50 40 d.v. 30 B1 20 10 0 1 2 A

  25. 70 60 50 B2 40 d.v. 30 B1 20 10 0 3 1 2 A

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