Sum normalization needs clarification or potentially has an issue


I was trying to use the web version of MetaboAnalyst as a guest and got confused at the data processing step.

I submitted my data in the form of metabolite concentrations to the Statistical Analysis (one factor) module.

At the step of data processing, I chose “Sum normalization” while keeping all other transformations as “None”.

The generated results appear counter-intuitive. While I would expect all values reduced making the sum to 1, results turned to be increased by about 50-fold.

I am attaching the figure with metabolite distributions for illustration.

Can you please explain how the resulting values became higher after the normalization than the original values?

Thank you for the question. This is indeed the case (sum is 1000, not 1). The main reason is for numerical stability when divide concentrations by their sums (which could generate very small values and downstream computing could be unstable). The details is clear in the R function (below)