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    it would be terrible design if they exercised one group and not the other

I second Odder somewhat on this... Every study of starvation shows that as calories are reduced, voluntary motion reduces too.

We know exercise is correlated with calories consumed in animals. This study does not control for both total calories and total energy expenditure, so it isn't correct to say the result is due to one and not the other.

Diet studies are super hard because it's impossible to change only one thing and the sheer number of variables is massive.