Repeated-Measures ANOVA

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Repeated-Measures ANOVA
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Repeated-Measures ANOVA

• Used if we have groups that are not independent
  from one another
• Yolked groups
• Participants measures on 2 time points
• Data from multiple family members (i.e. a wife
  and son group) on a variable influenced by the
  common family environment
• and if we have an IV with 2 levels

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Repeated-Measures ANOVA

• Have both a within-subjects variable and
  between-subjects variable(s)
• Within subjects variable the IV for which
  subjects appear in multiple groups (in most cases
  Time)
• Between subjects variable the IV, as we have
  traditionally thought of it

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Repeated-Measures ANOVA

• Repeated-measures ANOVAs test at least these two
  types of IVs and their interaction
• Time x IV interaction indicates that rate of
  change in the DV over Time differs between the IV
  subgroups (levels)
• I.e. a treatment vs. control group we would
  predict no change in the control and increase (in
  benefit) or decrease (in risk or symptoms) in
  scores in the treatment group

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Repeated-Measures ANOVA

• Assumptions
• Normally distributed data
• Homoscedasticity
• Sphericity
• Refers to differences between variances in levels
  of the repeated-measures factor (Time)
• Only applies if you have 3 levels (time points
  of assessment)
• Assumes that all of these differences are roughly
  equal
• Robust to violates of 1 and/or 2, but not 3
• If 3 violated, various corrections exist that
  are readily provided by SPSS

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Assumptions

• Detecting violations of assumptions
• Normality
• Homoscedasticity
• Same as all other ANOVAs
• Sphericity
• Mauchlys W test provided by SPSS
• Significant results indicate violations of
  sphericity
• But very underpowered (i.e. w/ small ns, it will
  never properly detect violations of sphericity
• Unless your n is large, use corrections
  regardless of results of Mauchlys W

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Assumptions

• Corrections for violations of sphericity
• Greenhouse-Geisser
• Adjusts the df downward for increasing violations
  in sphericity
• Very conservative adjustment small violations
  of sphericity ? very difficult to find anything
  significant
• Huyuh-Feldt
• Similar to Greenhouse-Geisser correction, adjusts
  df downward, but not as much
• Lower Bound
• Even more conservative than Greenhouse-Geisser

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Repeated-Measures ANOVA

• Calculations
• Once again, dont worry about them

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Mixed-Model ANOVAs

• Mixed-Model ANOVA
• ANOVA with both (1 or more) fixed and random
  factors
• Within-subjects factor in repeated-measures
  almost always a random factor
• Theoretically, there is an infinite number of
  time points we could use choice of which to use
  depends on conclusions we wish to draw
• Since we dont use all possible levels of the
  within subjects factor (Time i.e. we randomly
  sample levels), it is a random factor

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Mixed-Model ANOVAs

• Between subjects factor frequently a fixed factor
• I.e. IV Treatment, Levels Present (Tx Grp) or
  Absent (Control Grp) This is an exhaustive
  sample the contains all possible values of
  treatment its either there or its not
• Therefore, most repeated-measures ANOVAs mixed
  model ANOVAs