This is an interesting, difficult, and potentially controversial question. I think the most likely explanation for your example is that you are surveying two (or more) populations experiencing different levels of risk. If a large sub-population were improving slowly while a small sub-population were worsening rapidly then you might see stagnant GAM with increasing SAM. The case of a seemingly normally distributed population made of a number of smaller and different distributed (either normally distributed with different means and SDs or non-normal) is known as a "finite mixture" and has been part of the statistical / mathematical framework of evolutionary theory over a century. See: Weldon WFR, On Certain Correlated Variations in Carcinus maenas, Proceedings of the Royal Society of London, 54:318–329 (1893) Pearson K, Contributions to the Mathematical Theory of Evolution, Philosophical Transactions of the Royal Society of London A, 185:71-110 (1894) The Weldon (1893) paper has a great illustration of how two normal distributions combine to give a "fat-tailed" distribution (as with your example): [img]http://www.brixtonhealth.com/Weldon.png[/img] This is for measurements of crabs (one species of two?) but the idea holds for human populations. I would like others to comment on this because what I have written above is a little controversial. Plausibility checks based on normality would reject a "fat-tailed" distribution as poor quality data on (in my opinion) shaky and doctrinaire grounds. This is, I think, due to a confusion between the normal distribution as a frequently useful model (a common view and my view) and the normal distribution as something more "real" than that (I think this is the SMART view). We often see GAM by MUAC and GAM by W/H yielding very different results. This is, in large part, a body shape issue. WHZ underestimates GAM in short-limbed, long-trunked, broad chested, cold climate, high altitude populations and overestimates GAM in long-limbed, short-trunked, narrow chested, hot climate, low altitude, milk-consuming populations. This accounts, in large part, for the poor prognostic value of W/H. In extreme cases it is possible (e.g.) that W/H will select healthier and older children. My advice is (as always) to stick with MUAC. BTW ... Thank you for your kind comments.

Someone sent me this link: [url]http://bit-player.org/2010/disentangling-gaussians[/url] in which refers to the papers I referenced and has some methodological discussion and some illustrations.