Easy and common way to separate latent classes from Likert-scale survey? Let say, there are two 5-points Likert-scale questions "How do you like a flavor?" applied for two product samples. That is, each respondent tries two samples and evaluate them on Likert scale.
Obviously, there are two basic options: one sample is always superior to another; or there are two latent groups: one prefers first one and dislike another; and vice versa.
H0 is "There are no distinct groups. The flavor is one type. Probably just one better than another. Mean measure would be sufficient to understand."
What is the best and possibly common way to demonstrate existing of these groups and strength of this?
 A: If you want to test whether the data are consistent with two distinct groups of "aggree" on both flavours" or "strongly disagree", then you need to model that situation. You could take $|A-B|$, as the absolute value of the difference. You have now transformed your two dimensional data into one dimension, but it's the dimension that pinpoints the difference you care about. At this point, I would plot a histogram of the data with density function overlayed and gawk at it. If the effect is pronounced (there really are two groups), you should see two good peaks -- one at 0 and one positive, with a trough between them. If there's nothing to see, it's doubtful that a statistical test will reveal anything. 
If you do need a test, I think you need to go back to first principles and design something. If you assume your original responses are normal, then |A-B| is a folded normal. You want to fit a mixture of folded normals where one comes from a mean 0 distribution. The other has a mean to be determined. You could presumably write down a likelihood for this and compare to the likelihood obtained from one folded normal. You would have to set up the optimization yourself and it would involve an iterative process. When fitting the mixture distribution, you have to estimate which group each observation belongs to. The usual standard methods probably don't apply to your specific research question. 
