The question: Is there an appropriate statistical test of a change in dispersion across a large number of variables as a result of experimental manipulation?
Background: A manipulation has been made to a regulatory 'error-checking' gene and RNA-sequencing has generated count values for the level of expression of thousands of other genes, where counts are generally considered to originate from a Poisson distribution. Thus, the data is m-genes by n-samples, with n = 2 groups (control, treatment) times 3 replicates for each group. The standard approach with these data is a gene- or row-wise GLM to test for a difference in the number of counts with treatment.
The problem: I suspect that my treatment might also disrupt the stability of expression across replicates for any given gene with some probability. Thus, I want to test for a group level difference in dispersion itself with treatment. I would naively consider computing the dispersion for each gene and treatment, possibly as Shannon entropy on row-wise probabilities, then testing if the expected dispersion for treatment is statistically greater than that of control using a non-parametric test, but I am not sure if this is valid or whether there are established tests for this.
