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Confusion regarding Euclidean distance measures of dissimilarity

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Dear All, I have a data set  (attached), this is an RNA seq experiment to compare treated Vs control group in several breeds of animals. In each breed, I want to see how is the extent of the sepration between treatment vs control groups based on 18.000 genes being DE between the two groups. In another word, in which breed was the effect of treatment the greatest ?. Usually one visualize this using MDS plot, but I can not estimate this visually. In my MDS analyses (either the one that run from inside edgeR or the one run on the CPM TMM normalized counts) I could see sepration between treated vs control groups in two breeds.

The question is 1) How can I estimate numerically the divergence of the two groups in each breed so that I can tell the difference in treatment effect in among breeds. I have actually tried calculating the Euclidean distance among control and treated individuals within each breed, but it gave a distance number between each individual within each group in a pairwise manner, so what is the best method to show an overall dissimilarity between control and treatment given the distance between each pairs of individuals of the groups. I also thought about correlation coefficient, but it gave strange results.

I have another question: Are there any relation between the common dispersion (estimated during the DE analyses in EdgeR) among genes in one breed and the number of sig DE genes identified in this breed and the degree of sepration between the two groups in the same breed ? in another word, Is this right that if for instance I found that in breed A the two groups have greater dissimilarity than in breed B, Should I expect higher dispersion for the genes or higher number of sig DE genes in breed A than in B ?

Any comment would be helpfull

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