I have a paper that is accepted and published in a journal. After it was accepted I realized that some of the errors were calculated in a wrong manner and hence they appeared around 1.5 times smaller in the paper (this was due to a wrong advice that my advisor gave me). I was busy at the moment however later, when the paper was published, I managed to recalculate the errors and realize their difference. I told my supervisor about it and sent the new results to him. Although he seems to admit that his advice was wrong he is opposing my idea to send an erratum to the journal. Here is his argument:
- The differences are minimal and do not change the conclusion or the main point of the paper. (Although the actual errors are 1.5 times the reported ones, they are still small because the reported ones are small too)
- We have to change many parts of the paper and not only one place.
- It will put us and the journal in a bad situation.
- I am neither the first person nor the last person who has done a mistake in his paper.
- Our code and dataset are public.
I have had serious arguments with my supervisor in the past. The last time it got to the point that he ordered me to do as he says. This makes me worried if I push him harder I will ruin my relationship with him.
What are your thoughts about this situation? What is the right thing to do in your opinion?