Construction and evaluation of confidence ellipses applied at sensory data

The sensory evaluation of products by a panel of experts or consumers involves qualitative data (in sorting task description), quantitative variables structured by groups (in napping or in free choice profiling), quantitative and qualitative data (in sorted napping). Whatever the nature of data, a mean configuration of products is built and it is crucial to assess its stability, especially when the judges are untrained. Unfortunately, most of the confidence ellipses constructed around the position of the products do not give a confidence area in the sense that two products are significantly different when their ellipses do not overlap. Indeed, most ellipses proposed in the literature are too small and lead the user to misinterpretations since they are too optimistic. Here we propose to use truncated total bootstrap to build confidence ellipses that can be actually interpreted as confidence areas. The ellipses are evaluated from simulations and real examples and the evaluation shows that the methodology is adequate for all methods.

► We explain why the confidence ellipses usually used are too small and do not represent a confidence area.
► We propose a new bootstrap method to construct confidence ellipses in sensory data analysis.
► The method to construct confidence ellipses are efficient for holistic approaches.
► The method is also efficient for QDA.