One citation, one vote! A new approach for analysing check-all-that-apply (CATA) data using L1-norm methods

A unified framework is provided for analysing check-all-that-apply (CATA) product data following the "one citation, one vote" principle. CATA data arise from studies where A assessors evaluate P products by describing samples by checking all of the T terms that apply. Giving every citation the same weight, regardless of the assessor, product, or term, leads to analyses based on the L1 norm where the median absolute deviation is the measure of dispersion. Five permutation tests are proposed to answer the following questions. Do any products differ? For which terms do products differ? Within each of the terms, which products differ? Which product pairs differ? On which terms does each product pair differ? Additionally, we show how products and terms can be clustered following the "one citation, one vote" principle and how principal component analysis using the L1-norm (L1-PCA) can be applied to visualise CATA results in few dimensions. Together, the permutation tests, clustering methods, and L1-PCA provide a unified approach that provides robust results measured in citation percentages. The proposed methods are illustrated using a data set in which 100 consumers evaluated 11 products using 34 CATA terms. R code is provided to perform the analyses.