New Equivalence Tests for Approximate Independence in Contingency Tables

Vladimir Ostrovski

doi:10.3390/stats2020018

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.

Highlights

Testing for approximate row-column independence in two-way contingency tables is a common task in statistical practice
The test statistic is the Euclidean distance between the product measure of the marginal distributions and the contingency table
Ostrovski [5] proposes a general method to test equivalence to families of multinomial distributions, which is based on the minimum distance d ( p, M) = inf d ( p, q) to a family M of multinomial distributions

Summary

Introduction

Testing for approximate row-column independence in two-way contingency tables is a common task in statistical practice. The test statistic is the Euclidean distance between the product measure of the marginal distributions and the contingency table. Ostrovski [5] proposes a general method to test equivalence to families of multinomial distributions, which is based on the minimum distance d ( p, M) = inf d ( p, q) q∈M (1). If d is Euclidean distance and M is the independence model the calculation of minimum distance Equation (1) requires numerical optimization. Ostrovski [5] assumes the existence of a continuous minimizer at all points and applies the method to test for approximate independence. We use the subscript ∗ instead of a and r, if appropriate

Asymptotic Tests

Bootstrap Tests

Simulation Study of Finite Sample Performance

Real Data Sets