What is the strongest result that has subsequently been shown to just be a statistical glitch? While reading up on the $g-2$ result, I noticed that the authors stopped short of announcing a definitive result because they only had 4.2 sigma of confidence rather than the 5 that is the standard for confirmation. That got me thinking: Has anyone ever published results anything close to 5 sigma and then had it turn out to be a statistical glitch? (As opposed to for example a systemic error in construction or execution of the experiment.)

Edit:
I ran into a mention of a 3.9 sigma result at the LHC that turned out to be a statistical glitch
 A: There are lots of unexplained >5-sigma results out there, and the only way establish that one of them was a statistical glitch would be to prove that it had no systematic errors. This is impossible. There is a well-known aphorism that "all models are wrong", and all real measurements have inherent systematic errors. We can work hard to keep their effects small, but they can never be eliminated.  When a 5-sigma result is reported that later goes away without explanation, it is always far more likely that it was an unknown systematic effect than a statistical fluctuation.
One can, however, make a statistical argument that 5-sigma statistical glitches have been published.  Several million scientific articles appear every year and the total number of scientific papers ever published is probably of order $10^8$. Not all scientific papers have experimental results, of course, but many report more than one result, so $10^8$ is a conservative guesstimate for a lower bound on the total number of published scientific measurements.  Given that the (2-sided) probability of a 5-sigma fluctuation is about one in two million, one would expect quite a few 5-sigma statistical fluctuations to have appeared in the scientific literature. It is just impossible to distinguish them from the more common 5-sigma unknown systematic errors.
