Eight different binary attributes form the underlying basis of the hypothetical product mix. Respondents were asked to rate each binary attribute on a 1-5 scale, and to then rank the relative importance of each attribute. These data constitute the alternative model test.

In addition, a fractionated factorial design was used to select 16 unique combinations of the attributes from the 2 to the eighth or 256 total possible combinations. The eight respondents in the test ranked these combinations in a manner identical to the classic conjoint data gathering exercise.

Together with the alternative model, these data constitute the full test data set for the small validity study.

An individual differences conjoint model was fit to each subject's rank or derived preference score for the alternative model and the overall average for the product combination. These scores were monotonically transformed with a quadratic monotone spline transformation, and a single knot was specified at the median. The classification variables in the model (i.e., the eight attributes that define the conjoint profile) are optimally scored in an additive model with a mean of zero.

While only the sixteen combinations included in the fractionated factorial design could be tested for the classic conjoint model, the mathematical transformations of the alternative model make it possible to test all of the possible combinations in the theoretical design. This was done for this test. Throughout this discussion, however, only the comparable pairs across the two models are used.