An example from my own work how difficult the distances to individual objects (galaxies in this case) can be. Blue points are objects I believe to have reasonably well determined distances. X’s are more suspect. Nice relation for the “good” data. Less so for the rest. 
Note that many of the less trustworthy data follow the same relation as the better data. Most of the time one gets it right, albeit with big uncertainties. But there are also some whopper outliers. Note, for example, the group of points that are “too high” at low rotation speed.
If one believes those points as plotted, then there isn’t much of a relation. More of a happenstance. Which happens a lot on astronomy, so maybe that’s the case here. Or maybe there is an intrinsically right relation with a few outliers. That also happens-a lot.Pretty much always
It is very hard to express the distance uncertainty in a statistically meaningful way. Sometimes distances are just plain wrong.
In this case, I suspect deviations from a pure Hubble flow. E.g., galaxies that happen to be near the Virgo cluster could have the same redshift at 2 or even 3 distances. (Trace lines of sight that cross V=1000.) So which is it? Without additional information, we don’t know.
That figure is from Davis & Peebles 1983. Yes, kids, we knew about large scale structure and bull flows when I was still an undergrad and Flashdance was a thing but Deadpool was not.
Now, if we were doing a project using Tully-Fisher as a distance indicator, we’d use that additional information to assign a distance. Put ‘em on the line!
If instead we’re interested in the intrinsic scatter of TF, we don’t have that liberty, as that would be presuming the answer. One must instead use one’s brain to judge the likelihood of whether these are seriously discrepancy points, or mere outliers.
As best I can tell, there is no evidence for much (if any) intrinsic scatter in TF. The scatter is comfortably explained by the known uncertainties, the expected scatter in stellar mass-to-light ratios, and the occasional outlier.
This being astronomy, there are of course published claims to exactly the opposite conclusion, using exactly the same data.
In one case (in Nature Astronomy) a flat 20% prior was imposed on distance uncertainties. This guarantees the wrong answer, as it chops off the extra peaks in a bi(tri)modal PDF. Fancy statistical methods won’t fix a bad choice of prior. They’ll just confirm the mistake.
So: please engage brain before turning crank. Or submitting to Nature, for that matter.
