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Introduction to Factorial Designs

Introduction to Factorial Designs. Lawrence R. Gordon. EXTENSIONS FROM TWO-LEVEL DESIGNS…. … to more than 2 groups or levels of a single factor (multiple-level) brief review . QUICK REVIEW. Multiple-level single factor (IV) designs: Independent groups * [between-Ss]

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Introduction to Factorial Designs

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  1. Introduction to Factorial Designs Lawrence R. Gordon

  2. EXTENSIONS FROM TWO-LEVEL DESIGNS… • … to more than 2 groups or levels of a single factor (multiple-level) • brief review 

  3. QUICK REVIEW • Multiple-level single factor (IV) designs: • Independent groups * [between-Ss] • Matched groups ** [between-Ss; blocks] • Nonequivalent groups * [between-Ss] • Repeated measures ** [within-Ss; blocks] • * use simple one-way ANOVA (between-Ss) • ** use one-way ANOVA for within-Ss (or blocks)

  4. EXTENSIONS FROM TWO-LEVEL DESIGNS… • … to more than 2 groups or levels of a single factor (multiple-level) • brief review  • …to more than one IV • this class and the next

  5. NEW: FACTORIAL DESIGNS... • …extend single factor (1 IV) designs to 2 (or more) IVs… • 2+ IVs (“factors”), each with 2+ levels • Factors may be of any type we’ve discussed already: independent, matched, selected, or repeated-measures; “between-” or “within-Ss” • Overview of factorial designs 

  6. BUILDING BLOCK EXAMPLE • Suppose you are interested in the effects of the delay of reward and of the amount of reward on problem solving (anagrams, say) Oneway: Effect of Delay of Reward on Anagram Solving

  7. BUILDING BLOCK EXAMPLE • Suppose you are interested in the effects of the delay of reward and of the amount of reward on problem solving (anagrams, say) Oneway: Effect of Amount of Reward on Anagram Solvg

  8. BUILDING-BLOCK EXAMPLE • But, can study both effects of timing and amount of reward in a single study • Nomenclature • 1st IV (A) has two levels of reward timing • 2nd IV (B) has four levels of reward amount • AxB = 2 x 4 = 8 cells (“conditions,” “treatment combinations”), with different Ss in each • “a 2x4 between-Ss factorial design” • …next

  9. BUILDING-BLOCK EXAMPLE • Analysis • Descriptive statistics: means, sds, ns • In cells • “Marginal means” -- for each DV

  10. BUILDING BLOCK EXAMPLE Example: Effect of Delay X Amount of Reward on Anagram Solving

  11. BUILDING-BLOCK EXAMPLE • Analysis • Descriptive statistics: means, sds, ns • In cells • “Marginal means” -- for each DV • Graph of cell means

  12. BUILDING BLOCK EXAMPLE

  13. BUILDING-BLOCK EXAMPLE • Analysis • Descriptive statistics: means, sds, ns • In cells • “Marginal means” -- for each DV • Graph of cell means • Inferential: “Two-way ANOVA, Between-Ss” • Summary table • Main effects (each IV ignoring other): A, B • Interaction: A x B or AB (more next class)

  14. BUILDING BLOCK EXAMPLE

  15. NO INTERACTION EXAMPLE • Rats running a maze: • 3 strains: maze dull, mixed, maze bright • 2 rearing environments: basic, enriched • a “P”E design (ok, “R”E) • Results • Both main effects significant (p<.05) • Interaction is not (F<1)

  16. NO INTERACTION EXAMPLE

  17. NO INTERACTION EXAMPLE

  18. NO INTERACTION EXAMPLE

  19. NO INTERACTION EXAMPLE • Rats running a maze: • 3 strains: maze dull, mixed, maze bright • 2 rearing environments: basic, enriched • a “P”E design (ok, “R”E) • Results • Both main effects significant (p<.05) • Interaction is not (F<1) • Q: “What does this mean?” • A: “Let me tell you…”

  20. Further example -- • “Memory2002” in-class experiment • MORE THAN 2 IVs • OVERALL design: • 3 conditions of encoding (between-Ss, manip) • 2 sex of respondents (between-Ss, selected) • 3 periods of recall (“thirds”) (within-Ss) • 2 trials of the above (within-Ss) • A “3 x 2 x 3 x 2 mixed factorial design”

  21. Further example -- cont’d • “Memory2002” in-class experiment • Example for one trial, ignoring sex of Ss (3x3 “mixed” between/within design)

  22. MEMORY 2002: “2-way factorial” (quick peek)

  23. Further example -- cont’d • “Memory2002” in-class experiment • Example for one trial, ignoring sex of Ss (3x3 “mixed” between/within design) • Example of full design (4 IVs: 2 between-Ss and 2 within-Ss): 3x2x3x2 “mixed” factorial • 4 main effects • 11 interactions! (6 2-ways, 4 3-ways, 1 “dreaded” 4-way) • A quick peek at all this!

  24. MEMORY 2002: “4-way factorial” (quick peek)

  25. MEMORY 2002 --- “4-way factorial” THIRDS * Condition * TRIALS p=.555, ns

  26. MEMORY 2002 --- “4-way factorial” THIRDS * Condition * Sex p=.262, ns.

  27. PREVIEW - Next class • Interaction -- our last “new” concept • Definition • Examples with and without significant interactions, emphasizing interpretation • Wrapup on factorial designs • PLEASE DO ASSIGNED READING -- more explanation and examples

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