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 …and if we have an IV with 2+ levels

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

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

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

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

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

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

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

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