Multiplicative versus Ratio Comparisons
Ennis, J. M. and Ennis, D. M. (2009). IFPress, 12(2) 2-3.
Claims such as “Our product whitens teeth twice as well as product X!” abound in advertising. Such claims have traditionally been viewed as statements regarding ratios of product performances and have been treated accordingly. In previous technical reports, we have both reviewed and extended traditional ratio based statistical methods used to evaluate such claims. In this report we offer a new perspective, one that is both more natural and more powerful. In particular, we propose a shift away from ratio based comparisons towards what we term multiplicative comparisons. This means that instead of viewing the above claim as a statement that our product’s performance divided by the performance of product X is at least two, we instead consider whether the efficacy of our product is at least twice the efficacy of product X. This change might seem trivial, but we show below that this change is both more generally applicable and is more powerful than a ratio based approach. In what follows, we review our recent statistical work on a multiplicative approach to evaluate product claims and we compare this multiplicative approach to the ratio based approaches that follow in the classical tradition.
Figure 1. d' values distributions for the two test products