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Repeated-Measures ANOVA

Repeated-Measures ANOVA. 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

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Repeated-Measures ANOVA

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  1. Repeated-Measures ANOVA

  2. 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

  3. 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

  4. Repeated-Measures ANOVA • Repeated-measures ANOVA’s test at least these two types of IV’s 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

  5. 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

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

  7. 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

  8. Repeated-Measures ANOVA • Calculations • Once again, don’t worry about them

  9. 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 don’t use all possible levels of the within subjects factor (Time; i.e. we “randomly” sample levels), it is a random factor

  10. 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” – it’s either there or it’s not • Therefore, most repeated-measures ANOVAs = mixed model ANOVAs

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