Q:

How to analyze preference / comparison on a likert scale

User participants experienced method A and then method B of a computer interface. Afterwards, we asked them to indicate which method they preferred regarding certain aspects. For example, for ease of use, which do you prefer, A or B, from 1 to 7 (Likert scale), where 1 = definitely method A, 4 = Neutral, and 7 = definitely method B.
Here are my questions:

Since we are directly asking them to compare methods on this Likert scale and thus receive only 1 response, does it make sense to do a statistical analysis? I guess we cannot compare the participants' answers based on different methods because there is only 1 response.
If the answer to #1 is no, then do we simply aggregate the data and see how many users prefer A vs. B?
If the answer to #1 is yes, then do we statistically analyze if the responses vary from some "neutral" distribution? What's the best method/way to analyze this?

A:

I believe this is an instance of having 0 independent variables and thus we should use the one-sample median test, a.k.a. the Wilcoxon signed rank test (see this table). This is what I ended up using.

