Me again. I commented above on the psychometric technique of Semantic Differential rating scales, which is the primary technique I use in assessing perception because it is easy for participants to use and it differentiates products along multiple dimensions simultaneously. However, I have also used another psychometric technique, which is based upon similarity judgements. It strikes me that this touches upon the issue of AB and ABX testing. I collect similarity data either by having participants in my studies rate the degree of perceived similarity between pairs of items, or with a "triad" method in which items are presented three at a time and the participant selects the one that seems most different. Each triad provides input to three cells of a (dis)similarity matrix. Cells for the two items that weren't chosen as being "different" are coded "0" for minimum dissimilarity and cells for the two pairings involving the "different" item are coded "1" for maximum dissimilarity. I sum the matrices for individual participants and analyze it using Multidimensional Scaling to map all items within a multidimensional perceptual space.
The rating method provides what is essentially a continuous metric for the AB comparison and the triad method provides something that is functionally similar to ABX except with three different items and the question being reversed, i.e., not which two are the same, but which one is most different? The two items remaining after the odd-man-out become the "same" items in ABX.
Although many psychometricians assume that the similarity judgments and Semantic Differential ratings produce equivalent results, I find that is usually not the case. In my experience, the Semantic Differentials (using Factor Analysis) differentiate a larger number of independent perceptual dimensions whereas the similarity comparisons (using Multidimensional Scaling) sometimes reveal higher order perceptual qualities that are not easily described with words. Either way, the emphasis is on identifying the number of different ways that things vary. Perception is always multidimensional unless you intentionally restrict the range of variation. Ironically, that is exactly what happens when you compare only two or a small number of items.
The rating method provides what is essentially a continuous metric for the AB comparison and the triad method provides something that is functionally similar to ABX except with three different items and the question being reversed, i.e., not which two are the same, but which one is most different? The two items remaining after the odd-man-out become the "same" items in ABX.
Although many psychometricians assume that the similarity judgments and Semantic Differential ratings produce equivalent results, I find that is usually not the case. In my experience, the Semantic Differentials (using Factor Analysis) differentiate a larger number of independent perceptual dimensions whereas the similarity comparisons (using Multidimensional Scaling) sometimes reveal higher order perceptual qualities that are not easily described with words. Either way, the emphasis is on identifying the number of different ways that things vary. Perception is always multidimensional unless you intentionally restrict the range of variation. Ironically, that is exactly what happens when you compare only two or a small number of items.