"Turned out to be not statistically significant" is a very polite way of saying it... they initially said "up to 6 sigma significance", while it was obvious to anyone in the field that the data analysis in the paper was borderline crackpot.
Example of a Gurzadyan takedown. See my comment on OP for more links.
How would you recommend someone to get up to speed on data reduction to the point where they would be able to recognize such errors and know how to tease out a signal without making similar mistakes?
Well I did a PhD in CMB analysis so that is how I know. Not sure if such things will ever be controllable by people who are not researchers in the field (or at least doing similar kind of data analysis). It is a shame the peer review system cannot be relied on more; I hope a revolution happens there (on the line of "N accredited researchers trust/distrust this paper").
Example of a Gurzadyan takedown. See my comment on OP for more links.
https://www.aanda.org/articles/aa/full_html/2012/02/aa17344-...