Abstract
It is shown that the most popular posterior distribution for the mean of the normal distribution is obtained by deriving the distribution of the ratio X/Y when X and Y are normal and Student’s t random variables distributed independently of each other. Tabulations of the associated percentage points are given along with a computer program for generating them.
Highlights
A central problem in microarray data analysis is identification of differentially expressed genes, i.e., those genes whose expression intensities are significantly associated with the group label or covariate (Simon et al, 2004)
Upon examination of the results presented in this Table, we may draw the conclusion that for small sample sizes, the bio-weight test is vastly superior to the t-test
We have suggested a modification of the classical t-test designed to enhance sensitivity of detection of differentially expressed genes in microarray data analysis
Summary
A central problem in microarray data analysis is identification of differentially expressed genes, i.e., those genes whose expression intensities are significantly associated with the group label or covariate (Simon et al, 2004). Classical statistics usually deals with the situation when the number of parameters to be estimated is smaller, or even substantially smaller, than the number of subjects in the study This is not the case in microarray data analysis where the expression profiles of many thousands of genes are usually estimated from experiments with only several dozen subjects. This new statistical paradigm, often referred to as “curse of dimensionality” (Donoho, 2000), stimulated p-values development of a wide range of innovative ideas whose pros and cons are currently being assessed to determine their practical usability (Efron et al, 2001; Kerr et al, 2000). To reconcile conflicting meanings of significance suggested by the smallest p-values and the largest fold changes, we introduce a new test statistic that we call “bio-weight.”. We introduce the bio-weight test statistic in a more formal way and present the results of comprehensive simulation study comparing its power with the power of the classical t-test
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