Genes that show differential variability between conditions are important for complementing a systems biology understanding of the molecular players involved in a biological process. Under the dominant paradigm for modeling RNA-Seq gene counts using the negative binomial model, tests of differential variability are challenging to develop, owing to dependence of the variance on the mean. The limited availability of methods for detecting genes with differential variability means that researchers often omit differential variability as an analytical step in RNA-Seq data analysis. Here, we describe clrDV, a statistical method for detecting genes that show differential variability between two populations. clrDV is based on a compositional data analysis framework. We present the skew-normal distribution for modeling gene-wise null distribution of centered log-ratio transformation of compositional RNA-seq data. Simulation results show that clrDV has false discovery rate and Type II error that are on par with or superior to existing methodologies. In addition, its run time is faster than the closest competitor's, and remains relatively constant for increasing sample size per group. Analysis of a large neurodegenerative disease RNA-Seq dataset using clrDV recovers multiple gene candidates that have been reported to be associated with Alzheimer's disease. Additionally, we find that the majority of genes with differential variability have smaller relative gene expression variance in the Alzheimer's disease population compared to the control population.