FACTORIAL DESIGNS: Identifying and Understanding Interactions

1
FACTORIAL DESIGNSIdentifying and Understanding
Interactions

• Lawrence R. Gordon

2
BUILDING-BLOCK EXAMPLE, REVISITED

• 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

3
Layout / Nomenclature
4
BUILDING-BLOCK EXAMPLE, contd..

• 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

5
ANOVA SUMMARY TABLE
Significant effects Delay main effect, Reward
main effect, and Delay by Reward interaction
effect F(3,32)3.68, plt.05
6
INTERPRETATION Reward Descriptive Statistics
7
BUILDING-BLOCK EXAMPLE, contd..

• 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, lets quickly review a
  study without a significant interaction!

8
NO INTERACTION EXAMPLEReview Rosenzweig Tryon
(1950)

• 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

9
NO INTERACTION EXAMPLE
10
NO INTERACTION EXAMPLE
11
BUTReplicate and Extend ?

• 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 ?

12
INTERACTION OR NOT? What did they look at?
13
INTERACTIONS our last new concept

• 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.

14
YES, INTERACTION, EXAMPLES

• Q What do these mean?
• A It depends
• Blunder (Aronson et al., 1966)

15
Aronson et al. (1966)The effect of a pratfall on
increasing interpersonal attractiveness.

• 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

16
Aronson (1966) continued
ANOVA table ?
17
Aronson (1966) continued

• Results

Graph of the interaction ?
18
Aronson (1966) continued
Graph of the interaction ?
19
Aronson et al., Person x Blunder Interaction
20
YES, INTERACTION, EXAMPLES

• Q What do these mean?
• A It depends
• Blunder (Aronson et al., 1966)
• Stroop (1935), reconstrued

21
Stroop (1935), reconsideredRef. Goodwin, Box
7.1, p. 219

• 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

22
YES, INTERACTION, EXAMPLES

• Q What do these mean?
• A It depends
• Blunder (Aronson et al., 1966)
• Stroop (1935), reconstrued
• Underwater (Godden Baddeley, 1975)

23
Godden Baddeley, 1975 Encoding Specificity

• 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?

24
Godden Baddeley (1975)Encoding ? Retrieval
Interaction
Where They Learned
25
Further Example

• 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
• 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.

26
Dr. Jones Experiment F99
Main effects (I.e., on marginal means)

27
Dr. Jones Experiment F99
Interaction effect (but whats it mean?)
28
Further Example

• 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.

29
Wrapup

• NO INTERACTION main effects are unqualified
  generalizes from one factor over the other(s)
  often the goal of a P?E design. Let me tell
  you
• INTERACTION main effects ignored or qualified
  does not generalize especially if a P?E design.
  It depends This may lead to theory revision
  if not already predicted.

30
EXTENSIONS FROM TWO-LEVEL DESIGNS, next?

• 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!