Date of Award:

5-2014

Document Type:

Dissertation

Degree Name:

Doctor of Philosophy (PhD)

Department:

Mathematics and Statistics

Department name when degree awarded

Mathematics

Committee Chair(s)

John R. Stevens

Committee

John R. Stevens

Abstract

One of the great aims of statistics, the science of collecting, analyzing, and interpreting data, is to protect against the probability of falsely rejecting an accepted claim, or hypothesis, given observed data stemming from some experiment. This is generally known as protecting against a Type I Error, or controlling the Type I Error rate. The extension of this protection against Type I Errors to the situation where thousands upon thousands of hypotheses are examined simultaneously is known as multiple hypothesis testing. This dissertation presents an improvement to an existing multiple hypothesis testing approach, the Focus Level method, specific to gene set testing (a branch of genomics) on Gene Ontology graphs. This improvement resolves a long standing computational difficulty of the Focus Level method, providing more than a 15.000-fold increase in computational efficiency. This dissertation also presents a solution to a multiple testing problem in genetics where a specific approach to mapping genes underlying quantitative traits of interest requires a multiplicity adjustment approach that both corrects for the number of tests while also ensuring logical consistency. The power advantage of the solution is demonstrated over the current standard approach to the problem. A side issue of this model framework led to the development of a new bivariate approach to quantitative trait marker detection, which is presented herein. The overall contribution of this dissertation to the statistics literature is that it provides novel solutions that meet real needs of practitioners in genetics and genomics with the aim of ensuring both that truth is discovered and that discoveries are actually true.

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