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I have a rather simple design, but I am unsure how best to (properly) handle the data analysis.

I have an experiment with two between-subjects factors and one within-subjects factor. I will use, as an example Gender(Male v Female) and Training(Noob vs Pro) for the between, and Shapes(Red and Blue) for the within.

My problem: the Shapes factor has unequal trials based on the Training condition, where Noob sees 5 Red and 6 Blue, while Pro sees 6 Red and 5 Blue trials. What I care about is "accuracy in correctly detecting the colour of a the shape".

Now, I have no idea how to analyze this data. If I just input the data in long form, with Trial as a factor, would a MEM in R analyze the data based on AVERAGES (due to the difference in trial number) or SUMS (which would be wrong)?

I also assume that there are differences in the scores people given to specific trials, so i need to have this as a random effect.

Any advice is appreciated.

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  • $\begingroup$ Are differences such as 5R/6B vs 6R/5B random, or systematic? Do number of IDs always sum to 11, or does the number of IDs also vary? $\endgroup$
    – BruceET
    Commented Jul 30, 2019 at 19:29
  • $\begingroup$ The differences are systematic. There are always 5R/6B in one condition and 6R/5B in the other. So yes, at the end, the trials sum to 11 per each participant. $\endgroup$
    – Hubris555
    Commented Jul 31, 2019 at 11:49

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I (kinda) figured out what nlme and/or lme4 are doing when runing such a study. By entering the raw data (i.e. all the trials for each participant, without any pre-processing, e.g., sums, or means), the final results show that it is indeed calculating the scores for each factor and sub-factor by calculating averages. Namely, it is taking into account the unequal trials when analyzing the results. (yey).

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