Improving the power of hypothesis tests in sparse contingency tables

When analyzing data in contingency tables it is frequent to deal with sparse data, particularly when the sample size is small relative to the number of cells. Most analyses of this kind are interpreted in an exploratory manner and even if tests are performed, little attention is paid to statistical power. This paper proposes a method we call redundant procedure, which is based on the union–intersection principle and increases test power by focusing on specific components of the hypothesis. This method is particularly helpful when the hypothesis to be tested can be expressed as the intersections of simpler models, such that at least some of them pertain to smaller table marginals. This situation leads to working on tables that are naturally denser. One advantage of this method is its direct application to (chain) graphical models. We illustrate the proposal through simulations and suggest strategies to increase the power of tests in sparse tables. Finally, we demonstrate an application to the EU-SILC dataset.