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Multiple Testing in Large-Scale Contingency Tables:



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Multiple Testing in Large Scale Contingency Tables Inferring Pair Wise Amino Acid Patterns in Sheets Seoung Bum Kim and Kwok Leung Tsui School of Industrial and Systems Engineering Georgia Institute of Technology Atlanta GA 30332 USA E mail sbkim isye gatech edu E mail ktsui isye gatech edu Mark Borodovsky Schools of Biology and Biomedical Engineering Georgia Institute of Technology Atlanta GA 30332 USA E mail mb56 mail gatech edu July 12 2005 ABSTRACT One of the most common test procedures using two way contingency tables is a test of independence between two categorizations Current significant tests such as 2 tests or likelihood ratio tests provide overall independency but bring limited information about the nature of the association in the contingency tables This study examines the feasibility of using multiple testing procedures for an inference of independence of categories in each cell in contingency tables In the simulation study we compare the performance of various multiple testing procedures in a contingency table setup and demonstrate the relationship among the proportion of true null hypothesis type I error power and false discovery rate Finally we apply the proposed methodology to identify the patterns of pair wise associations of amino acids involved in sheet bridges in proteins We identify a number of amino acid pairs that exhibit either strong or weak association These patterns provide useful information for algorithms for predicting the secondary as well as tertiary structure of proteins Keywords strands Contingency table False discovery rate Multiple testing 1 1 Introduction One of the most common test procedures applied to two way contingency tables is a test of independence or association between two categorizations In general the test of independence uses 2 tests or likelihood ratio tests that can be called globally significant tests The basic idea of these tests is as follows If the sum of all the differences between observed and expected



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