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
neut and 4
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
Neut for each subject. Each row sums to 12 hence the variables are negatively correlated.
- Are attractive faces preferred to ugly and if so:
- Is this driven by an attraction to
attor an aversion to
ugor 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?