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I don't see that A/B/X inherently asks such a question.
The only thing it asks is to identify X as either A or B. It places no specific demands on how the listener comes to that identification and does not force a "same/different" paradigm.A listener may switch between A and B and choose one or the other based purely on preference. Once they've done that, then they can do the same between their preference and X, again going purely by preference. And once that's done, then the identification of X takes care of itself by way of simple logic. For example, let's say the listener prefers A to B. If, when comparing between A and X they prefer A to X, then logic says that X is B. If they find they have no preference between A and X, then logic says that X is A. So again, I don't see that A/B/X inherently demands any sort of same/different paradigm. k |

But it does force some very unnatural question, and you have yourself laid out the tortured logic it takes to reach a very simple conclusion, namely, what do you like better?

Just say "No" to A/B/X. Instead, play two samples for the listeners, and ask the natural question ("which do you like better"), which has 4 answers:

Now suppose you have two pieces of equipment (or cables, or digital files), A and B.

- I prefer the first sample.
- I prefer the second sample.
- I hear no difference between the the two samples.
- I hear a difference, but have no preference.

You constitiue the first sample, and then the second sample, randomly as follows:

I am trying at present to work out the correct statistical tests given the four possible answers above, not pooling over subjects, using "play the winner sampling", and the optimum way to assign the random weights to the four test conditions above, and working on an academic paper ... but this is not my day job, so it is a slow go. Sorry.

- A then B
- B then A
- A then A (swindle)
- B then B (swindle)

The idea is to avoid a number of subtle response bias problems that sensory tests suffer from, especially those in groups with leaders of the test at the front of the room (some folks try to please them, some try to foil them, both are bad).