When I read it most of the concern was the statistical variance introduced by using a smaller number of shots in the group. It was shown it could be a significant factor when calculating a change. Like the sloppy scope screws, the swing back and forth attempting the narrow the results actually meant you have to shoot more ammo to discover where the sweet spot is.
Since its a math operation issue, then it also affects all the other measurements of data, too. Smaller sample sizes have more error, shooting ten eliminates most of it so that other factors become the variables - seating depth, powders, neck concentricity, etc. If the sample sizes are small enough they create most of the variance, it's hard to see what's causing the differences.
At least that is what I took away from the discussion. My concern is to eliminate creating a variable so that with the tools at hand, the items that are creating group dispersion aren't clouded in the data. Determining accuracy has it's own standard, using accurate measurements and a process to derive an accurate answer. If the "scope screws" are too loose, it's an exercise in frustration.
while evaluating the data this morning I noticed something interesting that has me wondering if there may be some other explanations for why 5 shot groups are notoriously more difficult than 3 shot groups.
We dived off into a lot of discussion about the tools of measurement, the link was to a discussion about the mathematical methodology of analyzing the results. If the method used is creating the error, then the resulting conclusions will be based on error.
What you are seeing with 5 shot groups is a more accurate picture of the actual group size of a shooter with that rifle. Sample size of the group will generally be more accurate with a larger number of shots than smaller. Three good shots is fun, five is, unfortunately, more realistic, and ten about sums it up.
I think what you are observing is quite factual - it's the natural result of a larger sample size. If this is really a discussion about the tools used measure it, my bad.