I'm going to use a hypothetical example to explain my question.
I want to know whether people prefer riding a bike to work or taking the bus. I want to survey the same group of people four times during a year: August, November, February, and May.
Bike: Alternative constant ($0)
Crowdedness: High, medium, low
Length of ride: Shorter than biking, Longer than biking
I want to know how time of year affects choices. I predict that people will be more likely to bike in August and May (due to daylight and weather). In November and February though, I think bus crowdedness will have higher importance than it does in August and May.
So a few questions around this kind of scenario...
A) How can I compare the importance of bus crowdedness in August to bus the importance of bus crowdedness in February? Could I test the the two importance proportions (McNemar's or Cochran's Q)? Or would it be better to compare the utility estimate of a single level at both time points via t-test?
B) I'm lost as to a minimum acceptable sample size. I've read the sections you have on this topic - I know it depends on the design complexity, etc. But I'm interested in this time of year comparison most of all, which is a slightly different question than usually addressed with CBC. For feasibility/budget purposes, I'm interested in getting that number as low as possible.