1 / 27

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]

tallulah-alston
Download Presentation

Introduction to Factorial Designs

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  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

More Related