What statistical test should I use with count data? In my experiment, participants are shown 4 images (A, B, C, D) that they have to rate on a 5 point scale. So my data looks like this:
particpant1: A 5, B 3, C 3, D 1
p2: A 4, B 3, C 2, D 4
p3: A 4, B 3, C 2, D 4
etc...
I want to see if A and B are rated higher by participants, but I am not sure how to do this. I thought I could use a poisson regression, because I have count data. But I'm not sure and wouòd appreciate help.
 A: Interesting thread!  Demetri suggested one possibility for analyzing your data. But I wonder if something like what I outline below might get you closer to what you want?
It seems like you would like to see if A and B are rated higher than C and D. So why not compute the average rating given by each participant to the A and B images and the average rating given by that participant to the C and D images? (Computing average ratings from ordinal ratings is not ideal, but beggars can't be choosers.)
Then, you would end up with two response observations for each participant. For example, your first participant would have an average rating across images A and B of (5 + 3)/2 = 4 and an average rating across images C and D of (3 + 1)/2 = 2.
Then you could use a linear mixed effects model to model the average rating. The response variable in this model would be average rating across a 2-image set. The predictor variable would be image set, which is a dummy variable set to 1 for the set of images consisting of A and B and 0 for the set of images consisting of C and D.  Your model would also include a random intercept for participant and, if necessary, a random slope for image set.
This model would allow you to investigate if the set of images consisting of A and B has tends to have higher average ratings than the set of images consisting of C and D.
A: The unfortunate fact is that this can not likely be done with an easy statistical test like a chi-square or t test.  That you've chosen an ordinal outcome (not a count, as you say) and have experimental subjects rank multiple images will require us to use an ordinal mixed effects model.
Thankfully, the ordinal package in R can do this.  However, the model will not give you the exact answer you are looking for.  It will answer if there is a change in the probability of choosing A or B over some reference group (C,D, or E).  That is to say, it won't tell if A or B are chosen more over C, D, or E, it will tell you how the probability of choosing a 5 changes when you show someone img B over img A.
