Extension of Critical Difference for Product Comparison. Application to Tobacco Products

The differences or equivalence of products depend on various sources of variability like analytical methods, manufacturing processes, agricultural practices and environmental conditions. In addition, the capacity to compare and discriminate accurately two products is impacted by the number of characteristics considered for the comparison. Previously, it has been shown that a comparison of two products can be performed using the critical difference (CD), because it takes into consideration both the variability of measurements and laboratories. However, some additional sources of variability need to be added in the comparison when products were not manufactured at the same period of time or in the same factory. Here, an extended critical difference is proposed including manufacturing process variability according to the number of samples and batches collected for each product. The general formula and specific cases corresponding to different situations (one vs two labs, short vs long periods of time, same vs different periods of time, one vs several batches) are given.