An interesting thing I tested, back some 30-ish years ago, was a comparison between a plain groundglass and a split-image screen. The setup was for a chain studio operation; long roll cameras with a locked-down focus point. Whenever a camera was replaced, a technician would reset the focus using a special "focus tool." The tool was installed in place of the film magazine, and basically included a ground glass with magnifier. Once the lens was focused and locked down, the film magazine was put back on.
Anyway, we had a lot of complaints from techs about the precision of this method, and they were never certain if they had it nailed. So we looked into the possibility of switching to a focus screen with a split-image insert in the center. I oversaw some of the trials, and everyone was thrilled with how precise and positive the new tool was. But there was some corporate resistance to spending the money to retrofit all of the tools.
I set up a test to "prove" how much better the split-image screen was. I had something upwards of a dozen people, semi-randomly borrowed from our lab, and asked them to focus the camera in a test studio. My method was basically to mark the final focus position of the lens for each person, such that I would be able to draw a graph of focus-position vs how many people ended up there, it was essentially a histogram crudely showing a statistical distribution. And they also noted how confident they were that they had it nailed.
The results showed that one tool was clearly superior - the results were much tighter centered. But. . . it was the wrong tool. I figured I had mislabeled my tracking sheets, but . . . this had to be verified. So I got all the same people to come back and refocus. Same results. The plain groundglass was clearly superior to the split-image screen with regard to everyone ending up close to the same position. Although nearly everyone was convinced that they did better with the split-image, the opposite was actually true. I have no idea how to explain the mechanism at work, but after that I was always skeptical about the accuracy of a split image focusing screen. (My purpose, on the job, was to "prove" that it was worthwhile to spend some money, but after failing to do so, we just stayed with the existing tools; there was no justification to investigate further.)
To this day, it's still a question that sits somewhere in the back of my mind, waiting to be explained. But in the meantime, I try to use the plain groundglass part of the screen, even though it "feels" less precise.