Home Forums Reloading Big Game Rifles Group statistics

Everybody be careful about which SD is being considered at a given time. There's velocity SD and group size SD.

And that’s exactly what Litz said you shouldn’t do, but common.

So how many groups to get an accurate group SD? I may be wrong, but for me to get a fairly accurate velocity SD is 30-50 shots. So for group SD I would think to be fairly accurate minimum of 10 groups, preferably twice that. Again most won’t go to those lengths.

Regarding the "humidity issue" you may want to check out Keith Glasscock's "Winning in the Wind" videos on YouTube. He did some testing a while back involving storage of loaded ammo in different humidity environments and had some interesting results. He is an F Class Shooter as well and I believe a Process Engineer by profession.

Statistical validity is pretty much why I discount the Ladder Method.

30+ groups.

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.

denton,

Could you elaborate on your reasoning here?

It's just a mathmatical truth.

If you are taking inteval/ratio data such as FPS, peak pressure, millimeters, etc., then Central Limit kicks in and the Distribution of Means will have a strong tendency toward normality. That is very convenient for users of the T Test and ANOVA because you don't usually have to worry much about the normality of the data, and the Standard Error of the Mean converges pretty quickly.

Switch to any measure of dispersion, and it's a different world. There is no tendency toward normality. The Distribution of Means looks just as awful as the raw data, and separating normal random variation from real change takes a lot bigger sample. If you're terminally curious, I could scan a page or two out of a text and post it for you.

So for interval/ratio data, we use T and ANOVA. For SD we use F, Bartlett, or Levene's Test.

Right..I shoot one group for conservation of resources. I've been shooting since I can remember. Anymore and I can tell pretty quick when the rifle handles the load well. 30+ groups is about the funniest thing I've seen all day.

Outstanding. I will take a look.

Your intuition is about right. Starting from a baseline of 3 5-shot groups giving you your long term precision within +/- 25%, going to 12 groups gets you to +/- 12.5%, and 48 groups gets you to +/- 6.25%. Quadruple the number of samples to halve the error. It gets out of hand in a hurry.

As you say, most people aren't going to go to those lengths.

I get it fully but these two guys are pushing the cutting edge forward and data collection is typical of most methods seeking a factually supported process.

Not saying that a group of 1 can’t be nirvana but I will say that it is unlikely.

Lightning does strike…but even Lightning has rules.

I’m with you btw - based on my skills I’m not going to burn 30 groups worth of components seeking a conclusion that I likely would not draw a worthwhile, conclusion from…These two fellows are different than me tho and it’s really cool to learn from them.

It's just a demonstration of the difference between the seat of the pants variations most of us use and more rigorous analysis.

I know what they're saying. Applying statistics to this analysis can be fun. I guess. I have a degree in M.E. plus certification in 6 Sigma, so yes Jordan is correct in requesting a sample group of 30 specimens for analysis. Problem is this works for 30 data points, but not with 30 groups of 5 data points.

I have a 21 pound test platform that measures 1 3/16" dia at the end of the straight 26" barrel. This eliminates most of the variation I'm likely to induce into the system. If I place one hole on top of another at 100yds it's game on. If I see a shot fly off where I know I wasn't holding it's game over.

It's not 30 groups of 5 data points. Each group of 5 generates one data point.

I was also curious about the underlying distribution. Can you elaborate on that?

In terms of the CLT, I don't follow the reasoning. It seems to me that group size can be considered an independent random variable, in itself, with some underlying distribution. Random sampling of group size, regardless of its underlying distribution, should follow a Gaussian distribution as the number of samples tends to infinity. As least that's how it seems to me, but I'd be interested to understand this better if I'm wrong.

Exactly. We're talking about different independent random variables; bullet POI versus group size.

Ever weigh all the bullets in a box of components? Boy I sure hope that press operator down at Sierra bullets was having a good day. How about those benchrest primers? Equal amounts of compound? Neck tension all the same? Making consistent ammo is one thing. Then you have to shoot it, and shooting heats things up. It's a mission of controlling variation