Introduction to Factorial Designs

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Introduction to Factorial Designs

• Lawrence R. Gordon

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EXTENSIONS FROM TWO-LEVEL DESIGNS

• to more than 2 groups or levels of a single
  factor (multiple-level)
• brief review ?

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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)

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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

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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 weve discussed
  already independent, matched, selected, or
  repeated-measures between- or within-Ss
• Overview of factorial designs ?

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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
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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
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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

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BUILDING-BLOCK EXAMPLE

• Analysis
• Descriptive statistics means, sds, ns
• In cells
• Marginal means -- for each DV

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BUILDING BLOCK EXAMPLE

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

• Analysis
• Descriptive statistics means, sds, ns
• In cells
• Marginal means -- for each DV
• Graph of cell means

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BUILDING BLOCK EXAMPLE
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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)

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BUILDING BLOCK EXAMPLE
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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 (plt.05)
• Interaction is not (Flt1)

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NO INTERACTION EXAMPLE
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NO INTERACTION EXAMPLE
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NO INTERACTION EXAMPLE
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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 (plt.05)
• Interaction is not (Flt1)
• Q What does this mean?
• A Let me tell you

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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

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Further example -- contd

• Memory2002 in-class experiment
• Example for one trial, ignoring sex of Ss (3x3
  mixed between/within design)

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MEMORY 2002 2-way factorial (quick peek)
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Further example -- contd

• 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!

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MEMORY 2002 4-way factorial (quick peek)
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MEMORY 2002 --- 4-way factorial
THIRDS Condition TRIALS p.555, ns
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MEMORY 2002 --- 4-way factorial
THIRDS Condition Sex p.262, ns.
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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