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This question is about terminology.

Assume the following scenario. A research participant is asked to choose one out of four options: products A and B in packagings X and Y. That is, the choice (denote it as O) is the combination A&X, A&Y, B&X, B&Y.

The researcher wants to find out if the choice of the product is independent of the choice of the packaging. That is, $H_0: P(A| X) = P(A | Y)$

Is it a "between-subject" or a "within-subject" design?

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I would think it falls under a Simultaneous Within-Subjects Design (still looking for literature in this particular topic myself) - or under a discrete choice experiment with 4 alternatives to choose from.

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