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Suppose I have multiple responses from each subject in three different conditions (A, B, C). If I would decide to run a repeated measures ANOVA, I would first average over the repetitions from each subject and then run the analysis on these averages (one average per subject per condition).

However, am I still right to run a repeated measures ANOVA if, for instance, condition C has less repetitions per subject than the other two conditions? The straightforward solution would be to use linear mixed models, but I would still like to know if it is "legit" to use repeated measures ANOVA.

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To answer your question, you can still use a repeated measures ANOVA when you have missing data, but you're likely to run into problems that might encourage you to take another approach. In general, the design doesn't handle these situations well. While data from each subject is not required, cases with missing data are dropped from the analysis which can lead to biases (e.g. sampling bias) in the results.

For a reference see:

Gueorguieva R, Krystal JH. Move over ANOVA: progress in analyzing repeated-measures data and its refelection in papers published in the Archives of General PSychiatry. Arch Gen Psychiatry 2004; 61:310-7. http://www.ncbi.nlm.nih.gov/pubmed/14993119

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