Simulation exploring the behavior of MAD in relation to alternative measures of dispersion. Each panel is a simulation of sequence data on a balanced phylogeny of 20-(A, C, E, and G) and 100-tips (B, D, F, and H). A and B total tree length scaled to 0.10. C and D total tree length scaled to 0.25. E and F total tree length scaled to 0.50. G and H total tree length scaled to 2.00. Saturation was assessed by descriptors of dispersion on the one-dimensional Euclidean distance between the raw pair-wise sequence distances (uncorrected distance) and those corrected according to a Jukes-Cantor model of molecular substitution (corrected distance). Our simulations demonstrated that the use of the non-parametric median absolute deviation (MAD) had several advantages of detecting saturation over alternative measures of dispersion based on the sample mean (i.e. mean square error, MSE; root mean square, RMSE).