New Equivalence Tests for Approximate Independence in Contingency Tables

Abstract

We introduce new equivalence tests for approximate independence in two-way contingency tables. The critical values are calculated asymptotically. The finite sample performance of the tests is improved by means of the bootstrap. An estimator of boundary points is developed to make the bootstrap based tests statistically efficient and computationally feasible. We compare the performance of the proposed tests for different table sizes by simulation. Then we apply the tests to real data sets. The tests are implemented in R and available online, see https://github.com/TestingEquivalence/EquivalenceTestIndependenceR.

Keywords: testing, approximate independence, contingency tables, bootstrap, equivalence, minimum distance, boundary point estimator