Seems some are missing the point. Floating a arrow in water is finding the heaviest side of the arrow, thus what is said to the strongest or stiffest part of the arrow.
bf's, spine tester is just that a spine tester. Weak part of the arrow and indicator gives bigger reading. This is not checking for run out.
Now, I posed this to a few knowledgeable archery notables; Stiffest part of the arrow found, which way does it go to the bow, up or down? Answer most given; Doesn't matter so long as it is aligned to the power stroke of the bow string.
Personally, I shoot my arrows. Numbered, any arrow that doesn't impact as the rest is put aside. I'll spin test them if way out they are put aside for casual plinking. I then come back with nock tune to see if it can be made to impact as the others. Here, I index the nock to the next vane and when that's done and no improvement I'll install a new nock and try again. After this and no improvement I'll refletch the arrow. Usually the arrow is corrected.