# Dealing with Score Dependency in Repeated Measures ANOVA

#### statsgirl87

##### New Member
I am writing a report for my company looking at the impact of a relationship education curriculum on participants. Prior to the class, immediately after the class, and 30 days after the class, participants completed surveys on their relationship satisfaction, communication skills, and commitment. When I received this dataset (I wasn't involved in data collection), I thought repeated measures ANOVAs would be a good way to look at the data and see if improvement occurred over time in these areas.

However, I've discovered an issue with the dataset I'm not sure how to deal with. About a fourth of the participants attended the class with their romantic partner. Although I have individual scores from all participants, I'm sure the couples' scores are related to each other. I think this violates the basic assumption for repeated measures ANOVA that there is no dependency in the scores between participants.

Does this mean that repeated measures ANOVA is out as a viable option, or would it still be permitted since a minority of the scores are related to each other? If repeated measures ANOVA is not appropriate here, what would be an alternative analysis that would allow me to look at change in scores across the three time points?

#### mmercker

##### Member
Hi, you are right, a simple repeated measures ANOVA is not possible here, since you have a more complex dependency structure: Measurements are nested within persons (that means measurements of the same person are related to each other) and persons possibly are nested within couples. What you can do is: Beside the ID variable, you can additionally create a factor variable called "Couple". In this variable you give an individual number for each "single" person and in case you have a couple, you give them the same number. Thus, this variable stores the information if data are only related to one person or to a couple. Finally, you use a "linear mixed model = hierarchical model = multilevel model" which is the generalization of an ANOVA. Here, you can define the hierarchical structure of the data.

E.g., if you use R, this could be the following code:

library(arm)

model <- lmer(Outcome ~ Timepoint + (1|Couple/ID), data=data, REML=TRUE)

summary(model)

The term "(1|Couple/ID)" specifies your dependency structure and says that "ID" is nested within the variable "Couple"

#### statsgirl87

##### New Member
Thank you! I don't have much experience with linear mixed models. Is there anyplace online I could learn the basics that you would recommend?

#### mmercker

##### Member
Hi, which statistical software do you use? Before learning the ropes of multilevel models you should probably look/google if your software provides the possibility to consider your nested design with an ANOVA.

Here

http://conjugateprior.org/2013/01/formulae-in-r-anova/

you find a short and nice explanation of mixed ANOVA versus multilevel Models