Is a two-way repeated measures ANOVA appropriate for my study? I have 20 students, but consider them as 10 pairs.
They will be doing six different activities, where the aim is to find which of the activities produce the most spoken output in the pairs. Independent variables of the study which make up the six activities:


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*2 modes of communication (online and offline)

*3 different activity types


In other words, there are both an online and offline version for each of the three activity types. This makes up the six activities that the students will undertake. I am interested in finding if either mode of communication or task type has an affect on spoken output.
From what I have read so far, this seems to point towards a two-way repeated measures ANOVA.
Can anyone confirm?
 A: You are definitively on the right track. Now a balanced repeated measures ANOVA assumes Gaussian errors with constant variance. Since you are analyzing counts, both assumptions will probably be clearly invalidated. There are different options how you can deal with this:


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*Take the log of the count as response and go with your repeated measures ANOVA. This is easy but you are not anymore comparing mean counts but mean log counts (which may or may not be useful). Diagnostic tools will reveal if taking the logs was helpful.

*Use a fancy Poisson mixed effects ANOVA (counts tend to have Poisson distribution) e.g. with communication and activity as fixed effects and crossed random effects (which is a bit tricky to figure out). 

*Use a non-parametric repeated measures ANOVA. A good reference is [1], which is e.g. implemented in R's library nparLD. As in Method 1, you are not comparing means anymore (but something called "relative treatment effects").


Methods 2 and 3 would also work if you have random drop outs. 
[1] Brunner, E., Domhof, S., and Langer, F. (2002). Nonparametric Analysis of Longitudinal Data in Factorial Experiments, Wiley, New York.
