stinkypete said:
As a rule-of-thumb statistics thing, a sample that is the square root of the population is sufficient. In other words, 10 shots is most likely a good representation of what 100 shots will look like. The more shots you take, the more likely your claim.
Unfortunately, that doesn't work out very well because, on average, groups always get bigger with sample size because the more shots you fire, the more chances you give less probable results to appear, so the more likely it is you will get one. For example, you wouldn't expect a 2-shot group to be representative of your typical 4-shot groups. You'd expect the latter to be bigger. The stats say it will be 1.8 times bigger, on average. So the square root rule has problems in small sample sizes. My old company's manufacturing statistician said the sample should be the square root of the total number of items in a run (the population) or they should be thirty, whichever is larger. This is for the purpose of estimating population standard deviations and mean value, though, and not for estimating the extreme spread, which always has a random element.
The first plot below shows how much extreme spread grows with sample size for the same SD. For example, for a 9-shot group, the ES is expected to be about 3 times the SD on average. For a 27-shot group, ES is expected to be about 4 times the SD on average. And for a 95-shot group, ES is expected to be about 5 times SD on average.
Below that plot is another that shows the 95% confidence limits for sample size. You can see in that lower plot that a sample of 2 has very high upper and lower limits that subsequent samples of 2 might turn out to have as the difference in extreme spread between the two samples. The closer those lines are to the average, the smaller the difference your next sample that same size is likely to have. You can also see that by the time you get to 30 samples, the spread is no longer converging very fast.
The bottom plot also shows, though, that a sample of ten is fine as long as you are satisfied with 95% confidence limits in expected variation from one sample to the next that fall within those plotted limits. For ten, it's within about ±20%. That's part of the fun with this stuff. You get to decide how certain you need to be. But if someone tells me they will build me a 3/8 moa rifle, I will want to know for what group size and confidence level and at what range I can expect it to shoot 3/8 moa. Otherwise, even for a machine rest, the number is meaningless. For example, we can all stay within 3/8 moa group diameter with any gun for a 1-shot "group".