-1: While I fully agree that fabricating data and selling it as genuine is the worst possible approach, the second part of this answer may seriously backfire. Chances are good that the advisor has a better connection to the department chair than the OP. Also, sending seemingly random emails to journals that their articles are fake is something the department chair certainly won't like either and will escalate. Especially when done either before or in parallel to talking to them. The other side of the story will sound like: The OP cannot finish their PhD in time, now they are panicking.

It sucks that the OP is in this position, but someone has to do this, and they're the one in a position to do so.

You are right that the behavior of the advisor needs to be reported. I'm merely pointing out that according to the OPs self-description, I'm not sure they can handle the associated stress.

@VoodooCode You could be right about that. I've added a paragraph at the end that hopefully addresses any concerns the OP might have (as much as possible). With luck, that'll make it easier to do what needs to be done.

Also consider a switch to a statistically skilled new adviser who can help you with Sebastian Gruber's Bayesian data-analysis idea - which may be all you can salvage from your current results.

@Ray the "spoils system" the problem here. The almost entire academic community is heavily politically influenced, and if our current supervisers are removed, the people who are waiting for that placement would be worse. The current people are doing lot of training to farmers and underpriviledged people which will be stopped. The situation is gradually improving than last few years, that will be dropped. But at this point I feel the only way is to discontinue.

The likelihood of a grad student taking down a professor is nil. Like data falsification, it is a path to career suicide. A single powerless person will have no effect on a powerful one. Joint action might be successful if enough people join, but not a lone student.

@WoJ Exactly. If the whole system is corrupt then 1. Do what you think is right so you respect yourself. 2. Save your a... 3. Later decide if you want to be Erin Brockovich

@Miguel the local education system is a drama. It is heavily politically influenced. Respectable poets literary professors all are bootlicking politicians. The "spoils system" en.m.wikipedia.org/wiki/Spoils_system is so intensely deep, it is more of a political issue than just academic.

@FrustratedBird It is easy to say this from the safety of my tenure, but I really think your self-respect will be much more valuable in the long term than any academic achievement

@Miguel not only me but my parents would feel hurt when they will listen their son is cheating the worlds knowledge base. Cheating is not the way of upbringing my parents and my school teachers offered me back in 90's

How is it worse than selecting data?

I completely agree with point 1. Point 2 must be done in a very sensitive, careful way. This may also be culturally dependent. Is there a way to turn this around, like using 'simulated' data, and admitting it is such, rather than passing off 'fake' data as real? Also, you could possibly finish your Ph.D. with the data you have and add a "future research" section, and have that ready for some other student to pick up. This would then turn a 'bug' into a 'feature' !!!

It is possible that this happens in a country where academics are appointed based on political connections and not on academic achivements.

@gerrit at least within my state or province, yes. However, sometimes reputed research institutes are not far away. Recently a phd student committed suicide in a research institute, and you know what he wrote in his suicide note? that his mentor does not read any research papers. He chosen death before reporting it. It went into news.

@Ray Anonymous reporting is pointless if you're one of very few people (perhaps the only one) who could possibly make a specific set of allegations.

-1 for "Report your supervisors immediately" as completely out of touch with the full reality of the situation. If you are in the middle of an armed bank robbery do you stand up, pull out your cellphone and call the police to report it immediately? Or do you take your personal safety into consideration?

@Frustrated Bird Have you looked at the suggestion of Random PhD Student below ? Is it possible for you do do something like that ? Can you go to the university's statistics advice center and seek advice (privately) there ? If complaints are pointless this might be the only viable way to proceed here. Don't give up the work that you have done, whatever about the work that you'd like to have done.

@uhoh It seems unlikely that the risk in your bank robbery scenario is comparable to whatever risk exists here, but I also have a hard time picturing a department that's so horrible that there's nobody you could report data fabrication to without risk of retaliation, so what do I know? Lacking the information needed to recommend exactly how to solve this problem, I leave my suggestion in place as the optimal solution in an ideal world, and leave it to the OP to decide how close to it they can get in practice (perhaps mavzolej's suggestion of postponing the report until in a better position).

@Ray in an ideal world this kind of supervisors would not exist. The professor themself is an evidence that this kind of people get selected for such dignified posts in spite of consistent track record of publishing in predatory journals, having political influence, not providing enough time and sincerity to department, and lot more red flags. Looks like the various dignified interview panelists blindly obey them without looking actual work and situation of the students.

The risks would exist in real world. however, these malpractices should come into notice especially when a widely respected teacher is allowing, encouraging and even pressurising this malpractice