Variables which sum to a constant - ANOVA, MANOVA or none of these?

I asked a group of subjects to make a series of 12 binary choices regarding preferences.

Let's say for arguments sake, these were between ugly (ug), attractive (att), and neutral (neut) faces. Hence, we have 4 ug vs att, 4 ug vs neut and 4 att vs neut choices. For each subject I summed the number of times each face was chosen. Hence, I have a 3 column table comprising a score (max 8) for Att, Ug and Neut for each subject. Each row sums to 12 hence the variables are negatively correlated.

My questions:

• Are attractive faces preferred to ugly and if so:
• Is this driven by an attraction to att or an aversion to ug or both? - this is why we have choices with the neutral faces.

I originally thought to do a repeated measures ANOVA followed by post hoc tests to look for differences in ratings but i'm wondering if the fact that the DVs all sum to a constant is problematic because in essence the third variable - say $neut = 12-(ug+att)$. If so, is MANOVA the way to go, or how about chi-square?

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Neither ANOVA nor MANOVA would work here because of the fact that your variables are dependent. Though I would say that the way you set up your variables seems a bit unusual for trying to solve this problem. My recommendation would be to, instead of summing up the number of times each participant selected the each type of face in general, count the number of times each participant chose the "more attractive option" in each decision and then use a chi-square test to compare the counts in the ug vs. neut decisions to the counts in the neut vs. att decisions, conditioned on the count of the ug vs. att decision (somewhat similar to a Cochran–Mantel–Haenszel test with a series of tables of ug vs. neut and neut vs. att counts indexed by the ug vs. att count).

If you need clarification, I'll be willing to work some more on this problem.

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 Thanks and yes I would appreciate your help here. I'm not sure going with the "more attractive option" works because that presupposes my treatment worked (the stimuli were abstract symbols which underwent various procedures). I could analyze each choice type on its own using a 1*2 chi-sq but if I sum the counts over subjects does that mean its a fixed effects analysis or is it considered random effects? Also subjects could contribute to both boxes here and im not sure if this is ok? – alps Jun 10 '12 at 11:42 First, could you elaborate on what you mean by "subjects could contributes to both boxes"? Do you mean that the questions weren't two-alternative forced choice questions? Second, I would expect that you didn't assign objects to "att", "neut", and "ug" groups without some reasoning behind it. That being said, counting the number of responses that show preference to the more attractive option shouldn't presuppose anything about your treatment (i.e. If a subject made 4 choices in the ug vs. att condition, they could have chosen "ug" 4 times, which is the same as choosing "att" 0 times). – Jonathan Thiele Jun 12 '12 at 21:02