🤖 AI Summary
Traditional chi-square tests can only assess exact independence between variables in contingency tables and are ill-suited for capturing the approximate independence commonly encountered in practice. This work proposes an equivalence testing framework tailored for two-dimensional contingency tables, which employs a boundary-point estimator combined with asymptotic critical values and Bootstrap resampling to enhance performance in small samples while maintaining statistical efficiency. The method is the first to be systematically applicable across contingency tables of varying dimensions, offering both theoretical rigor and computational feasibility. Extensive simulations demonstrate its superior performance across diverse table sizes, and its practical utility is further corroborated through real-data applications. The accompanying implementation code has been made publicly available.
📝 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].