A Geometry-Based Multiple Testing Correction for Contingency Tables by Truncated Normal Distribution

Abstract

Inference procedure is a critical step of experimental researches to draw scientific conclusions especially in multiple testing. The false positive rate increases unless the unadjusted marginal p-values are corrected. Therefore, a multiple testing correction is necessary to adjust the p-values based on the number of tests to control type I error. We propose a multiple testing correction of MAX-test for a contingency table, where multiple χ2-tests are applied based on a truncated normal distribution (TND) estimation method by Botev. The table and tests are defined geometrically by contour hyperplanes in the degrees of freedom (df) dimensional space. A linear algebraic method called spherization transforms the shape of the space, defined by the contour hyperplanes of the distribution of tables sharing the same marginal counts. So, the stochastic distributions of these tables are transformed into a standard multivariate normal distribution in df-dimensional space. Geometrically, the p-value is defined by a convex polytope consisted of truncating hyperplanes of test’s contour lines in df-dimensional space. The TND approach of the Botev method was used to estimate the corrected p. Finally, the features of our approach were extracted using a real GWAS data.