A new efficient statistical test for detecting variability in the gene expression data

DNA microarray technology allows researchers to monitor the expressions of thousands of genes under different conditions. The detection of differential gene expression under two different conditions is very important in microarray studies. Microarray experiments are multi-step procedures and each step is a potential source of variance. This makes the measurement of variability difficult because approach based on gene-by-gene estimation of variance will have few degrees of freedom. It is highly possible that the assumption of equal variance for all the expression levels may not hold. Also, the assumption of normality of gene expressions may not hold. Thus it is essential to have a statistical procedure which is not based on the normality assumption and also it can detect genes with differential variance efficiently. The detection of differential gene expression variance will allow us to identify experimental variables that affect different biological processes and accuracy of DNA microarray measurements.In this article, a new nonparametric test for scale is developed based on the arctangent of the ratio of two expression levels. Most of the tests available in literature require the assumption of normal distribution, which makes them inapplicable in many situations, and it is also hard to verify the suitability of the normal distribution assumption for the given data set. The proposed test does not require the assumption of the distribution for the underlying population and hence makes it more practical and widely applicable. The asymptotic relative efficiency is calculated under different distributions, which show that the proposed test is very powerful when the assumption of normality breaks down. Monte Carlo simulation studies are performed to compare the power of the proposed test with some of the existing procedures. It is found that the proposed test is more powerful than commonly used tests under almost all the distributions considered in the study. A microarray data is used to illustrate the working of the proposed test. Results indicate that the proposed test is very powerful in detecting the smallest change in differential expression variance with high degree of confidence than some of its competitors.