His argument was that in order for it to be properly considered a 'sample' the numbers had to be randomly selected across the entire population; since they were taken sequentially one after another he felt that disqualified the use as a 'sample' for inferential statistics. WTF he didn't just come out and say that... I dunno.
It doesn’t disqualify them as a sample for inferential statistics. Sequential sampling is literally a sampling method. Also, the ANOVA method he uses all the time, guess what? It treats the data as samples regardless if he calls them a populations. If you have population data, you don’t need ANOVA to compare means.
Also, all of the components that go into building a round are random in nature when you use them. The powder is dispensed randomly, the bullet is seated randomly, the primer compound and material is random, etc. The population is the components you have or intend to use. You only care about the components you have because you’ll be using the components you have. Brass for example, 200 pieces of brass for me are going to outlast my barrel. If for whatever reason you have to buy new brass while a barrel still has life, then the population might change and you’ll need to do more testing to see if the population changes. But, I’m not really concerned about the other million possible pieces of brass I will never used. If the population changes because you got a new batch or lot, then retest to see if the previous sample’s population is different from the new sample’s population.
If you want to call three shots group a population, then those three rounds used have to be exactly the same every time you use one of those three rounds for any future shooting. The moment you use a similar but different complement like a primer, case, bullet, etc., the population has changed.
Furthermore, since reloading and firing a round is more of a process, the samples that are more closely related is call a rational subgroup of the population. You are comparing a rational subgroup to other rational subgroups. If they are statistically the same, then nothing in the process changed. If they are not statistically the same, then something in the process changed (different batch, lot, etc.). Using inferential statistics is fine.