I just got around to watching the first 17 minutes of the video. I think I'd have a really fun time working with Bryan on his testing. I've come away with a lot of respect for his methods.
The critically important idea he puts forward is that a 1 MOA rifle will routinely print groups as small as half an inch and as large as an inch and a half with absolutely no change in the rifle, cartridge, shooter, or environmental conditions. That's basic built-in variation. So his next point is that if you shoot a 1" group, and then change your trigger technique and shoot a 1/2" group, you don't know whether it was basic built-in variation or real change in performance. A lot of shooters spend a lot of time chasing random variation. No matter, it's all good practice.
The average of three five-shot groups will let you estimate the long term precision of your rifle within about 25%. To get it much closer than that, you need really big sample sizes.
He does make a subtle statistical error or two, but these are not important to the result. The distribution of group sizes is not normal. It looks like a Normal Distribution that has been pushed to the left, with a long tail to the right. So the 68% rule for plus or minus one standard deviation isn't quite right, but it's also not far off. Also, there is no Central Limit Theorem for any measure of dispersion (range, SD, group size), so collections of data do not tend toward normality.
