Abstract:

 

An important example of a paradox in the sensory field is The paradox of discriminatory nondiscriminators discussed by Gridgeman1 in 1970. A paradox is an apparent contradiction where apparent means appears to be as opposed to obvious. This paradox involved a large observed difference between the choice proportions for the triangular method and the three-alternative forced choice (3-AFC) method involving the same stimuli. Gridgeman called this result a paradox because, unlike a contradiction, he thought that reconciliation was possible. He proposed that the triangular method was a “psychosensorily confusing task.” A more insightful resolution was published by Frijters in 1979 and this insight was truly a watershed in the field because it led to an expansion of conventional thinking about the role of perceptual variance in decision making. Frijters explained the result by showing that the two methods agreed extremely well at the level of scaled sensory intensity and that the results from the methods differed because different decision rules were used in the presence of noise. That insight ushered in a whole new vein of research into Thurstonian models that provided a scientific basis for the methodology used in sensory and consumer science. Model predictions could be tested. The now commonly used tetrad method arose out of the implications of that theory.

 

Equivalence claims are based on a binary choice between two products and involve two bounds set at 45% and 55%. Within these bounds, two products are equivalent. Superiority claims are established when a choice probability (usually preference) exceeds 50%. Unsurpassed claims are made when the choice probability exceeds 45%. An unsurpassed claim combines the concept of equivalence, with a 45% lower bound, and superiority, which has an upper bound of 100%. When an equivalence claim can be supported, there is also support for an unsurpassed claim since equivalence implies that the two products are mutually unsurpassed. The reverse is, however, not true.

 

The various editions of the Standard Guide for Sensory Claim Substantiation (Claims Guide) have always been replete with paradoxes. In a previous technical report we discussed a paradox that an advertiser could claim to be equivalent to a competitor and the competitor could claim superiority over the advertiser with the same data. As with Gridgeman’s paradox, this paradox can be explained because different standards are used in the two cases and therefore the two claims are not contradictory. If the Guide were updated to include a consumer-relevant action standard that corresponds to the upper limit for equivalence, then partial or complete elimination of the paradox would occur. It is not necessary, however, to eliminate a paradox, it is just necessary to understand and explain it. In this report, a paradox involving equivalence and unsurpassed claims is explored.