Ok so I did some testing this weekend.
I measured out table sugar using my precision scale. It's calibrated and certified to be accurate to 0.1g
I then put that sugar into my cleaned dried Hydrometer test tube, and measured the sugar measurement container to make sure it read 0.0g
I then placed the tube and sugar on the scale and added distilled water and measured out the weight. Since Brix is the sucrose percentage of a solution by weight, it was easy to determine what the Brix Value should be, which I then plugged into brewer's friend to provide the correct SG value for that brix value.
I then capped my hand over the end of the tube, and shook it back and forth until all the sugar had dissolved. I then placed my rinsed and dried hydrometer in the solution, and used a pipette to get my sample for the refractometer and placed that on the window and let it sit to match the temp of the refractometer. Refractometer samples were done twice to ensure that the values matched. Readings were taken with daylight.
it would seem that my refractometer reads low by about 3%, and my hydrometer reads about 6% high. and of course if I compare them I get a difference of 9% which is a noticeable difference.
Both were calibrated with distilled water as you can see from the spreadsheet I put together.
I did throw out some of the variance values because they were just wierdly off, and I wanted to get a useful correction value that would be close to accurate across most of the range. Also, I can't rule out some kind of tester error on that.
Moral of the story. Just because your hydrometer or refractometer reads 0 at zero with distilled water, does not mean that it is accurate. Please test it using more than one known value. Also, I'm very disappointed in my hydrometer. It has been lying to me all along. This is very important when mixing and matching readings from different instruments. At least it's a percentage of difference that's reasonably consistent. So as the reading approaches 1.000, then the absolute error gets smaller and smaller. Apparently my beverages have been only about 94% of the alcohol percentage advertised.
The good news from all of this is that my Refractometer at least has an accurate SG and Brix scale, provided that I adjust for the fact that it's low by 3%.
****row 8 of the spreadsheet looks like it's garbage data most likely from an instrument reading perspective, and possibly also from a solution generation perspective