An interpretable, finite sample valid alternative to Pearson's X2 for scientific discovery

Abstract

Contingency tables, data represented as counts matrices, are ubiquitous across quantitative research and data-science applications. Existing statistical tests are insufficient however, as none are simultaneously computationally efficient and statistically valid for a finite number of observations. In this work, motivated by a recent application in reference-free genomic inference (1), we develop OASIS (Optimized Adaptive Statistic for Inferring Structure), a family of statistical tests for contingency tables. OASIS constructs a test-statistic which is linear in the normalized data matrix, providing closed form p-value bounds through classical concentration inequalities. In the process, OASIS provides a decomposition of the table, lending interpretability to its rejection of the null. We derive the asymptotic distribution of the OASIS test statistic, showing that these finitesample bounds correctly characterize the test statistics p-value up to a variance term. Experiments on genomic sequencing data highlight the power and interpretability of OASIS. The same method based on OASIS significance calls detects SARS-CoV-2 and Mycobacterium Tuberculosis strains de novo, which cannot be achieved with current approaches. We demonstrate in simulations that OASIS is robust to overdispersion, a common feature in genomic data like single cell RNA-sequencing, where under accepted noise models OASIS still provides good control of the false discovery rate, while Pearsons X2 test consistently rejects the null. Additionally, we show on synthetic data that OASIS is more powerful than Pearsons X2 test in certain regimes, including for some important two group alternatives, which we corroborate with approximate power calculations. Significance StatementContingency tables are pervasive across quantitative research and data-science applications. Existing statistical tests fall short, however; none provide robust, computationally efficient inference and control Type I error. In this work, motivated by a recent advance in reference-free inference for genomics, we propose a family of tests on contingency tables called OASIS. OASIS utilizes a linear test-statistic, enabling the computation of closed form p-value bounds, as well as a standard asymptotic normality result. OASIS provides a partitioning of the table for rejected hypotheses, lending interpretability to its rejection of the null. In genomic applications, OASIS performs reference-free and metadata-free variant detection in SARS-CoV-2 and M. Tuberculosis, and demonstrates robust performance for single cell RNA-sequencing, all tasks without existing solutions.