I believe a portion of a paper I am coauthoring is false I have mildly contributed to a research project which is now ready for publication.
However, I am convinced the treatment of the experimental data is wrong. 

I shared my concerns with the PI of this project and shown him why I believe this was not correct. Yet, I only made him doubt and he still wants to publish it as it is. This treatment of the data is not necessary to reach the conclusion of the paper which still holds with more standard data analysis, but it looks less fancy. Now what should I do ?


should I go ahead and work on the publication ?
should I withdraw from this project (which is a side project for me) ?


On the one hand I still believe the conclusion of the paper is true and I could use an additional publication on my CV. On the other hand I feel it is dishonest to publish something which I believe is not true.
You seem to be giving two stories: you note that you 'still believe the conclusion of the paper is true' but you then note that 'it is dishonest to publish something which I believe is not true'.  If the issue is simply the handling of the data analysis (with alternative paths leading to the same conclusions through more or less fancy approaches), I might suggest a compromise. Add a footnote at the presentation of that analysis indicating that conclusions remain even under a more conservative statistical analysis.  If the journal allows, you can elaborate a bit there.  That way, you've solidified that you understand there are multiple approaches, but the conclusion is robust to that. This might be even more convincing.