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FACTORIAL DESIGNS: Identifying and Understanding Interactions

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FACTORIAL DESIGNS:Identifying and Understanding Interactions

Lawrence R. Gordon

- “Effects of timing and amount of reward on problem solving”
- 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”

- Analysis
- Descriptives: means, sds, ns
- In cells
- Marginals -- for each DV

- Graph of cell means
- Inferential: “Two-way ANOVA, Between-Ss”
- Summary table
- Main effects (each IV ignoring other): A, B

- Descriptives: means, sds, ns

Significant effects: Delay main effect, Reward main effect,

and Delay by Reward interaction effect: “F(3,32)=3.68, p<.05”

- Analysis
- Descriptives: means, sds, ns
- In cells
- Marginals -- 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 -- is significant; what does this mean? First, let’s quickly review a study without a significant interaction!

- Descriptives: means, sds, ns

- 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
- Interaction is not
- Q: “What does this mean?”
- A: “Let me tell you…”

- Cooper & Zubeck (1958), studied “genotype - environment interaction” (PxE again -- oops, “R” by E)
- “R” -- maze-bright vs. maze-dull rats
- E -- Restricted, Intermediate, Stimulating
- What happened? “IT DEPENDS…” -- there were marked performance differences only in the Intermediate environment

INTERACTION OR NOT? What did they look at?

- Graphs of an interaction: (overhead)
- No interaction --- parallel line segments
- Interaction --- non-parallel line segments
- No lines perfectly so, must use statistical test

- What is the null hypothesis? How is interaction measured?
- Testing after finding an interaction is different than when only main effects are significant.

- Q: “What do these mean?”
- A: “It depends…”
- “Blunder” (Aronson et al., 1966)

- Ps heard audiotape of student said to be a candidate for the “College Quiz Bowl.” An interview asked difficult questions.
- Four tapes:
- Candidate “nearly perfect,” no blunder
- Candidate “nearly perfect,” blunder (coffee spill)
- Candidate “average,” no blunder
- Candidate “average,” blunder

- Asked to rate “liking” of the candidate

ANOVA table

- Results:

Graph of the interaction

Graph of the interaction

- Q: “What do these mean?”
- A: “It depends…”
- “Blunder” (Aronson et al., 1966)
- “Stroop (1935),” reconstrued

- Did two experiments:
- RCNb vs RCNd (no difference)
- NC vs NCWd (“Stroop effect”)

- Could consider as two factors:
- Control vs. Different
- Read color vs. Name color

- Q: “What do these mean?”
- A: “It depends…”
- “Blunder” (Aronson et al., 1966)
- “Stroop (1935),” reconstrued
- “Underwater” (Godden &Baddeley, 1975)

- Interested in the match between the conditions of encoding and the conditions of retrieval on recall
- Four conditions:
- Learn on land -- recall on land
- Learn on land -- recall under water
- Learn under water -- recall on land
- Learn under water -- recall under water

- All divers eventually participated in all four conditions, making this a repeated-measures factorial design.
- DV is number of words recalled per list
- A reference: Goodwin, pp. 254-255. Graph

Where They Learned

- “Dr. Jones” in-class experiment (done Fall 1999)
- Written scenarios varied two factors:
- Gender of “Dr. Jones”: He vs. She
- Time teaching since PhD: “since that time,” 10, or 30 yrs.

- DV was a “Teaching Evaluation” scale (8 items)
- Design: 2 x 3 Between-Ss randomized experiment

- Written scenarios varied two factors:
- Summary: “The main effects of Sex and Time were not significant; there was a significant Sex By Time interaction, F(2,96)=3.86, p=.024.”

Dr. Jones Experiment F99

Main effects (I.e., on marginal means)

Dr. Jones Experiment F99

Interaction effect (…but what’s it mean?)

- Summary: “The main effects of Sex and Time were not significant; there was, however, a significant Sex By Time interaction, F(2,96) = 3.86, p =.024. Although there was no sex difference in attributed teaching performance at 10 yrs post-PhD, there was a sex difference at 30 yrs post-PhD, with females seen as improving over the 10 yr mark, and males seen as declining under the 10 yr mark. The vague “since that time” control was better than the ten-yr result for both, but had a nonsignificant sex difference.”

- NO INTERACTION: main effects are unqualified; generalizes from one factor over the other(s) [often the goal of a PE design]. “Let me tell you…”
- INTERACTION: main effects ignored or qualified; does not generalize [especially if a PE design]. “It depends…” This may lead to theory revision if not already predicted.

- To more than 2 groups or levels of a single factor (multiple-level)
- Previously covered

- To more than one factor (IVs) (“factorial” designs)
- Today: interactions & examples

- Is there another extension from the simple 2-level experiment?
- YES -- to multiple simultaneous DVs!
- Will we study? NO - quite advanced!