Whenever I read about repeated measures or within-subjects design in different books and on webpages, the example that always is brought up is some kind of longitudinal or repeated measures design (e.g. people are measured on the same scale several times during the day). For my experiment, I have showed people a number of different pictures in random order, and then grouped these pictures into different categories. Is this an example of a repeated measures or within-subjects design, that is, can I use a repeated measures (within-subjects) ANOVA on my data (given that it satisfies all the basic assumptions)?

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    $\begingroup$ You appear to have TWO forms of dependence here: By person and by category. So you probably need a multilevel model to account for both $\endgroup$ – Peter Flom - Reinstate Monica Mar 3 '12 at 15:36

Traditionally, yes, your design can be treated as a repeated-measures design where you treat person as a unit of repeated observation and you treat the pictures in each category as homogenous replications of one another, collapsing them to a mean and treating category as a within-Ss variable.

However, as Peter Flom notes, it's possible (likely?) that the intra-category variability in your pictures is worth accounting for, in which case you will want to move to a mixed effects modelling context where you will treat category as a fixed effect and both person and category token as crossed random effects. See Baayen et al 2008 for explanation.

  • $\begingroup$ Thanks for the reference! I've printed it out and will sink my teeth into it tonight. $\endgroup$ – Speldosa Mar 3 '12 at 16:25
  • $\begingroup$ Now that is a good reference. Particularly helpful since your factors are also crossed. Gelman and Hill 2007 Part 2 if you want a slower exposition. $\endgroup$ – conjugateprior Mar 3 '12 at 17:43
  • $\begingroup$ @Mike Lawrence So, when you take a mixed effect modelling approach, you don't collapse your data (in this case for subject and category) to a single mean but rather use all the observations? I'm taking a signal detection approach for some of my data, and you obviouslty can't talk about concepts such as "hit rate minus false alarm rate" for single observations. Also, in the paper, they mention that this model is robust against violations against sphericity and homoscadasticity. Does this mean I can cancel my upcomming question about alternatives to RM-ANOVA in cases of non-sphericity of data? $\endgroup$ – Speldosa Mar 4 '12 at 17:50
  • $\begingroup$ @Spledosa, Indeed, when using mixed effects models you want to keep your data in its raw, trial-by-trial format. This is especially the case when the raw data are binomial in nature (see: sciencedirect.com/science/article/pii/S0749596X07001283), as implied by the fact that you refer to signal detection theory in your comment. $\endgroup$ – Mike Lawrence Mar 5 '12 at 12:05
  • $\begingroup$ @Spledosa, With regards to SDT in mixed effects models, see springerlink.com/content/71p13107473qh842, which explains that if you have a mixed effects model with response as the DV, effects that interact with reality as a IV reflect effects on d' whereas effects that do not involve reality reflect effects on criterion. $\endgroup$ – Mike Lawrence Mar 5 '12 at 12:07

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