Resumen de Independence test for compositional tables

Vera Pawlowsky Glahn , Montserrat Planes Pedra, Juan José Egozcue Rubí

• Contingency tables can be decomposed in independence and interaction tables. Given a sample of compositional tables, the need for a test arises to answer the question whether the mean table is an independent table, or, on the contrary, there are significant interactions. With this purpose we develop a bootstrap test to check the hypothesis that the interaction table is the neutral element, that is, that all entries of the interaction table are equal. It is based on the idea (a) to generate via bootstrap a sample of independent tables, (b) to compute for each independent table its Aitchison norm, (c) to build the empirical distribution of the norms, and (d) to compare the norm of the original table with the obtained distribution. Survey data, corresponding to 145 undergraduate students (76% females, 24% males) asked to evaluate three protective measures in 10 different situations, and annual mortality rates in some European countries are used for illustration.