Psych 611 Lecture 6

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Psych 611Lecture 6

• Repeated Measures, Mixed Designs
• Chapters 13,14

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Starters

• Exam 1 copies come during my office hours if you
  want to go over your exam
• Presentations and Exam 2 next week!
• Presenters announced after lecture today

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Three-way ANOVA

• You now have
• Three main effects
• Three two-way (first-order) interactions
• One three-way (second-order) interaction
• Same assumptions to think about
• Independence of observations
• Normality of DV
• Homogeneity of variance

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Three-way ANOVA

• For blocking, heres what you need to know
• If an IV that has an effect on the DV can be
  added to your research design, it might increase
  power
• The reason is that it helps to move error
  variance from the denominator into the numerator
• Must be careful not to lower n per cell too much

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High Heat Setting
Low Heat Setting
http//www.ecoharmony.com/thesis/PhDch3.htm
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Repeated Measures ANOVA

• So far, all of our ANOVAs have been
  between-subjects
• Different units of measurement in each cell
  (i.e., different people, rats, organizations,
  etc.)
• Lets now call cells conditions
• Often this has to be the case
• Once a person has experienced one condition,
  they are spoiled for the others
• Logistically it would be too hard or impossible
  to get people to be in multiple conditions

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Repeated Measures ANOVA

• But sometimes you want the same units of
  measurement to appear in all your conditions
• Longitudinal designs in which individuals are
  repeatedly tested over time, and time is an IV
• You want each person to give opinions about
  multiple products or candidates or whatever
• These are repeated measures designs

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GREEN

RED
Kello, Plaut, MacWhinney (2000)
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http//www.psychosocial.com/IJPR_8/Coping_in_Schiz
ophrenia.html
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One-Way Repeated Measures

• Like a two-way ANOVA, except that subject is one
  of the IVs
• Subjects are more generally units of
  observation
• Each individual unit is a level of the IV
• Note this is NOT what it looks like in an SPSS
  spreadsheet

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Fixed vs Random Effects

• Fixed effects are IVs whose levels are limited to
  the ones measured
• Random effects are IVs whose levels are sampled
  from a potentially infinite number of levels
• Subjects is a random effect

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Additive vs Non-Additive Model

• Recall the SS structural model for two-way ANOVA
• We can now build a similar model for repeated
  measures ANOVA, except in terms of raw scores
  instead of SS

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Additive vs Non-Additive Model

• Additive model
• Non-additive model

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Additive vs Non-Additive Model

• Non-additive is usually more appropriate
• IVs may have different effects on different units
  of measurement (subjects)
• This is an interaction between subjects and your
  IV
• In this case, the model includes the interaction
  between subjects and your IV

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Advantages of Repeated Measures

• Fewer units of measurement needed
• They get reused across levels of your IV
• Increased power because of reduced error variance

Individualdifferences
MeasurementError
Between-Groups
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Advantages of Repeated Measures

• Fewer units of measurement needed
• They get reused across levels of your IV
• Increased power because of reduced error variance

X
Individualdifferences
MeasurementError
Repeated Measures
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Randomization of Conditions

• Unless time is one of the repeated measures, the
  order of conditions should be randomized to
  minimize effects of time
• Practice, fatigue
• Decreased power, but usually necessary

18

GREEN

RED
Kello, Plaut, MacWhinney (2000)
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Issues with the Non-Additive Model

• Including the subjects interaction decreases
  power
• But probably still better than between-groups
• We now have to deal with a new assumption
  Sphericity
• Difference scores for all pairs of IV levels
• SPSS has a test of sphericity (Mauchly), and a
  correction for it (Greenhouse-Geiser)
• Randomization helps to meet this assumption

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Multifactor Repeated Measures

• Subjects is always a random effect
• For other IVs, one must decide fixed or random
  effects for each
• Random effects enable generalization beyond
  arbitrarily chosen levels

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Random Effects Examples

• Is happiness related to ones place of birth?
• Are some faces easier to remember than others?
• Are some commercials more persuasive than others?
• Holding obvious factors constant like length,
  exposure, and product being advertised

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Mixed Designs

• When you have multiple IVs, and some are
  between-groups and some are repeated measures

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http//www.psychosocial.com/IJPR_8/Coping_in_Schiz
ophrenia.html
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http//www.internationalbreastfeedingjournal.com/c
ontent/2/1/9/figure/F6
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Mixed Designs

• Contrasts, trends, simple effects, power, and
  effect sizes are all available in repeated
  measures and mixed designs
• Calculations and logic behind them become more
  complicated, but let SPSS handle it
• Pre-post designs are often mixed
• E.g., effect of instruction is between-groups,
  but pre-post effect is a repeated measure

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For Lab on Monday

• Collect data for a mixed design
• One between-groups IV
• One repeated measures IV, not including subjects
  themselves
• At least 10 units of observation (subjects) at
  each level of your between-groups IV