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