publications - What to do when you are suspicious about numerical results in a submitted manuscript that you are reviewing?

I am currently reviewing a paper and feel suspicious about their numerical results. I feel their results have been slightly modified to exhibit their superiority compare to other comparative methods.

I cannot give an exact mathematical reason why I think their numerical results have been manipulated, but it is so odd that in all 15 scenarios they have been better. Actually, I am pretty sure that their method is better than his benchmarks but not always. Maybe they modified some scenarios.

As I don't have a mathematical reason why I think some of their numbers are altered, should I ask for their computer code and run them myself?

Answer

Complementing the other answers, either in addition to, or apart from, asking for the codes and running them yourself, I don't think it is a bad idea to explicitly ask the authors, something like this:

The standard algorithms for executing (bla bla bla), e.g. as followed in the works of Refs. [1-3] (feed these in), are suggestive of a standard accuracy in typical algorithms. The current work appears to have bettered the same, which is a strong point in favor of publication. However, the authors should include a comment in the manuscript, mentioning what changes have they implemented to the typical algorithms so highly prevalent, which leads to this enhanced accuracy.

My jargon may have to be twisted a bit here, but I think I convey the point.

This being a query in the referee report, the authors shall be obligated to feed in the details, and if there is some manipulation involved, it may end up being exposed.

Hope that helps :)