Conditional Ratio Statements
Ennis, J. M. and Ennis, D. M. (2008). IFPress, 11(2) 2-3.
“Our product is 5 times more effective at reducing malodor than Brand X!” is a ratio statement with powerful consumer take-away. More generally, a ratio claim involves any statement meant to indicate that one product is superior to another by a multiplicative factor. The statement given above and a statement such as “Shown in studies to be 33% stronger than the leading brand!” are both examples of ratio claims. In a previous technical report we showed that ratios estimated from experiments have error associated with them and that this variation needs to be considered in order to avoid exaggerating a claim of superiority. Typically ratio statements a reused to compare improvements on some interval scale. Until recently all methods for producing meaningful ratio statements have assumed that these improvements are positive and no approach has allowed for the possibility that the products involved could have deleterious effects. In this report we revisit the topic of ratios and present a generalization of the existing methods.
Figure 2. Results of Monte Carlo simulations showing 95% of the ratios of d´’s above 3.04 when simulated runs with negative competitor performance are excluded.