Hypothesis testing procedures for two sample means with applications to gene expression data
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In Bioinformatics, the number of available variables for a few tens of subjects, is usually in the order of tens of thousands. As an example is the case of gene expression data, where usually two groups of subjects exist, cases and controls or subjects with disease and subjects without disease. The detection of differentially expressed genes between the two groups takes place using many 2 independent samples (Welch) t-tests, one test for each variable (probeset). Motivated by this, the present research examines the empirical and exponential empirical likelihood, asymptotically, and provides some useful results revealing their relationship with the James's and Welch t-test. By exploiting this relationship, a simple calibration based on the t distribution, applicable to both techniques, is proposed. Then, this calibration is compared to the classical Welch t-test. A third, more famous, non parametric test subject to comparison is the Wilcoxn-Mann-Whitney test. As an extra step, bootstrap calibration of the aforementioned tests is performed and the exact p-value of the Wilcoxn-Mann-Whitney test is computed. The main goal is to examine the size and the power behaviour of these testing procedures, when applied on small to medium sized datasets. Based on extensive simulation studies we provide strong evidence for the Welch t-test. We show, numerically, that the Welch t-test has the same power abilities with all other testing procedures. It outperforms them though in terms of attaining the type I error. Further, it is computationally extremely efficient.
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