DNA microarray technology is a powerful tool for analyzing patterns in gene expression data for thousands of genes. Due to a number of systematic variations in microarray experiments, the raw gene expression data is often obfuscated by undesirable technical noises. Various normalization techniques were designed in an attempt to remove these non-biological errors prior to any statistical analysis. One of the reasons for normalizing data is the need for recovering the covariance matrix used in gene network analysis. We introduce and demonstrate a novel normalization technique, called the covariance shift (C-SHIFT) method. We prove that under certain conditions applying quantile normalization prior to performing Welch’s t-test can increase the value of the test statistics. We discuss the probabilistic monotonicity property of covariance graph models through a set of mean and correlation inequalities. Our analysis suggests that for two diﬀerent studies, comprising healthy and cervical cancer patients, underlying biological networks largely follow the probabilistic monotonicity property.