I've been measuring my weight and ketosis daily for over three months now, while on-and-off sticking to a low carb diet. So the ketosis has been going on and off.
There has been plenty of argument amongst nutrition researchers whether or not low-carb and/or ketosis has any relevant to weight loss. This n=1 data suggests that for people like me it certainly does.
Did I ever mention that I'm an engineer? So I know a bit about statistical analysis.
Taking the current data I have weight and ketone readings..
The data is noisy with day to day ups and downs. A 5 day, anticausal, moving average smooths this nicely while retaining the underlaying shape of the curves. The argument that I'm trying to show or refute is whether ketosis is associated with weight loss. Don't confuse this with absolute weight or with ketosis causing weight loss. All my data can show is an association.
So to show the weight loss/gain rather than absolute weight, we take the difference each day, turn it upside down (so higher = more loss) and normalize the mid point to 1.6 so it lines up vertically, then apply a five day moving average to smooth it out. So here is a 5 day moving average smoothed weight loss vs. ketosis over three months.
Are they associated? They certainly look like it. If you shuffle the graphs in time, the strongest correlation between them is at a 5 day offset, with the correlation R=0.547, which is pretty strong correlation.
Can we argue that this association could happen by chance? Let's try a chi-square goodness of fit test to see what the odds are. The probability of getting this close a match by chance is P=0.00000040203, or less than one in a million.
So yes, ketosis is associated significantly and strongly with weight loss. So if like me you have the kind of metabolic disorder that causes you to slowly gain weight over time and low calorie dieting is counterproductive, my advice is do what is required to get into ketosis and then you can expect to lose weight.