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The control was plain water. That seems like the sort of methodological flaw that would preclude a study from publication in a journal like PNAS.
It’s so bizarre that you wouldn’t have other sweeteners in other experimental groups and, especially, an experimental group that was actual sugar.
Can you elaborate why do you think that water is improper control?
They’re providing a sweetener at all times. That alone would have some affect, so I’d think you’d want another sweetenere like sucrose, glucose, some other artificial sweetener, in addition to a water treatment. Alternatively, a dose response could be informative. They did have different doses of aspartame, but in both groups of mice (male and female), the dose response was opposite what you’d expect; the lower dose had a larger effect.