Introduction to Factorial Designs Lawrence R. Gordon

EXTENSIONS FROM TWO- LEVEL DESIGNS… 4 … to more than 2 groups or levels of a single factor (multiple-level) –brief review 

QUICK REVIEW 4 Multiple-level single factor (IV) designs: –Independent groups * [between-Ss] –Matched groups ** [between-Ss; blocks] –Nonequivalent groups * [between-Ss] –Repeated measures ** [within-Ss; blocks] 4 * use simple one-way ANOVA (between-Ss) 4 ** use one-way ANOVA for within-Ss (or blocks)

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

NEW: FACTORIAL DESIGNS... 4 …extend single factor (1 IV) designs to 2 (or more) IVs… 4 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” 4 Overview of factorial designs 

BUILDING BLOCK EXAMPLE 4 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

BUILDING BLOCK EXAMPLE 4 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

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

BUILDING-BLOCK EXAMPLE 4 Analysis 4 Descriptive statistics: means, sds, ns In cells “Marginal means” -- for each DV

BUILDING BLOCK EXAMPLE 4 Example: Effect of Delay X Amount of Reward on Anagram Solving

BUILDING-BLOCK EXAMPLE 4 Analysis 4 Descriptive statistics: means, sds, ns In cells “Marginal means” -- for each DV 4 Graph of cell means

BUILDING BLOCK EXAMPLE

BUILDING-BLOCK EXAMPLE 4 Analysis 4 Descriptive statistics: means, sds, ns In cells “Marginal means” -- for each DV 4 Graph of cell means 4 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)

BUILDING BLOCK EXAMPLE

NO INTERACTION EXAMPLE 4 Rats running a maze: –3 strains: maze dull, mixed, maze bright –2 rearing environments: basic, enriched –a “P”  E design (ok, “R”  E) 4 Results –Both main effects significant (p<.05) –Interaction is not (F<1)

NO INTERACTION EXAMPLE

4 Rats running a maze: –3 strains: maze dull, mixed, maze bright –2 rearing environments: basic, enriched –a “P”  E design (ok, “R”  E) 4 Results –Both main effects significant (p<.05) –Interaction is not (F<1) –Q: “What does this mean?” –A: “Let me tell you…”

Further example -- 4 “Memory2002” in-class experiment 4 MORE THAN 2 IVs 4 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”

Further example -- cont’d 4 “Memory2002” in-class experiment 4 Example for one trial, ignoring sex of Ss (3x3 “mixed” between/within design)

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

Further example -- cont’d 4 “Memory2002” in-class experiment 4 Example for one trial, ignoring sex of Ss (3x3 “mixed” between/within design) 4 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) 4 A quick peek at all this!

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

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

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

PREVIEW - Next class 4 Interaction -- our last “new” concept –Definition –Examples with and without significant interactions, emphasizing interpretation –Wrapup on factorial designs 4 PLEASE DO ASSIGNED READING -- more explanation and examples