## Repeated measures ANOVA with R (functions and tutorials)

Repeated measures ANOVA is a common task for the data analyst.

There are (at least) two ways of performing “repeated measures ANOVA” using R but none is really trivial, and each way has it’s own complication/pitfalls (explanation/solution to which I was usually able to find through searching in the R-help mailing list).

So for future reference, I am starting this page to document links I find to tutorials, explanations (and troubleshooting) of “repeated measure ANOVA” done with R

### Functions and packages

(I suggest using the tutorials supplied bellow for how to use these functions)

• aov {stats} – offers SS type I repeated measures anova, by a call to lm for each stratum. A short example is given in the ?aov help file
• Anova {car} – Calculates type-II or type-III analysis-of-variance tables for model objects produced by lm, and for various other object. The ?Anova help file offers an example for how to use this for repeated measures
• ezANOVA {ez} – This function provides easy analysis of data from factorial experiments, including purely within-Ss designs (a.k.a. “repeated measures”), purely between-Ss designs, and mixed within-and-between-Ss designs, yielding ANOVA results and assumption checks. It is a wrapper of the Anova {car} function, and is easier to use. The ez package also offers the functions ezPlot and ezStats to give plot and statistics of the ANOVA analysis. The ?ezANOVA help file gives a good demonstration for the functions use (My thanks goes to Matthew Finkbe for letting me know about this cool package)
• friedman.test {stats} – Performs a Friedman rank sum test with unreplicated blocked data. That is, a non-parametric one-way repeated measures anova. I also wrote a wrapper function to perform and plot a post-hoc analysis on the friedman test results
• Non parametric multi way repeated measures anova – I believe such a function could be developed based on the Proportional Odds Model, maybe using the {repolr} or the {ordinal} packages. But I still didn’t come across any function that implements these models (if you do – please let me know in the comments).
• Repeated measures, non-parametric, multivariate analysis of variance – as far as I know, such a method is not currently available in R.  There is, however, the Analysis of similarities (ANOSIM) analysis which provides a way to test statistically whether there is a signiﬁcantdifference between two or more groups of sampling units.  Is is available in the {vegan} package through the “anosim” function.  There is also a tutorial and a relevant published paper.

### Troubelshooting

Unbalanced design
Unbalanced design doesn’t work when doing repeated measures ANOVA with aov, it just doesn’t. This situation occurs if there are missing values in the data or that the data is not from a fully balanced design. The way this will show up in your output is that you will see the between subject section showing withing subject variables.

A solution for this might be to use the Anova function from library car with parameter type=”III”. But before doing that, first make sure you understand the difference between SS type I, II and III. Here is a good tutorial for helping you out with that.
By the way, these links are also useful in case you want to do a simple two way ANOVA for unbalanced design

I will “later” add R-help mailing list discussions that I found helpful on the subject.