It is sometimes claimed that ANOVA requires averaging across multiple tokens of the same measure (e.g., the trials in an experiment). As an alternative to that, one could factor in the identifier of these different repetitions - trial ID. Do you know if the latter practice is well accepted?
Many thanks
(Please note that I cannot resort to mixed effects models because I need to test the difference between levels of the same factor through contrasts)
That wouldn't be valid; the whole point of averaging across observations within a participant is that those observations are related in a way that other observations aren't (i.e., that they come from the same participant). If you treat every token as having its own unique ID then you've lost the relatedness among tokens that come from the same participant.
Needing to compare levels of a factor doesn't preclude you from using mixed models; it's still entirely possible in a mixed model.
Thank you for your reply!!
That's right. I was ambiguous in my explanation (because trial number was also relevant to me earlier). Certainly, the lumping factor would be participant ID.
I'm surprised! Would you please let me know how to compare levels of a factor statistically within a mixed model - or point me to some reference? Can it be done with custom contrasts, too? Not that I haven't sought this -- LMM manuals don't seem to cover it.
Not only are contrasts possible, they're mandatory. In ANOVA you can test a 'main effect', but in regression coefficients you have to explicitly code the contrasts (the main effect you get from model comparison instead of coefficients). The default scheme in R is dummy coding, but there are many other possibilities as well.
http://www.ats.ucla.edu/stat/r/library/contrast_coding.htm
In my case, I'm doing a consecutive modeling based on likelihood ratio, so I don't need to specify within-factor contrasts. Besides, I've tried entering custom contrasts but it doesn't work. Still, falling back on the simpler ANOVA for that one comparison is not too bad, I hope -- as long as the ID is right! :D
Thank you so much
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