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

TL;DR

This paper introduces a unified L1-norm based framework for analyzing check-all-that-apply (CATA) data, including permutation tests, clustering, and visualization, to provide robust insights into product differences and term associations.

Contribution

It presents a novel L1-norm approach for CATA data analysis, incorporating permutation tests, clustering, and PCA for robust and interpretable results.

Findings

Permutation tests identify significant product and term differences.

Clustering reveals groups of similar products and terms.

L1-PCA visualizes CATA data in reduced dimensions.

Abstract

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 visualize 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.