Statistics for differentiating between groups?
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Wind Gypsy
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Something something, lies, damn lies, and statistics.
Hey, it is what it is. mtmuley
BrentD
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Statistics is what your heart surgery will be based on. Such snide remarks ignore the fact that nearly everything that benefits your life was developed and applied through statistics.
You can go through life without understanding much about math, physics, biology, etc. And yes, statistics, but you would be a fool to denigrate any of them. They are all part of what allows you to live as you do.
Thanks Brent. mtmuley
BrentD
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Exactly. And that is at least additive variance, so the worse you are at shooting, the more you need precision equipment. Again, understanding something about statistics could be helpful to you.
Also, knowing something about additives of variances will also give you an idea of how much better you could perform with better equipment.
One of the more stupid statements I often hear from shooters ( besides the Twain quote) is that better precision in equipment is pointless "if my rifle shoots better than I do".
And we haven't even gotten to interaction terms.
yakimanoob
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This is a bit ironic to say only a few posts after telling me to spend more time practicing my technique and less time worrying about ammo.
MTLabrador
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He got tired of the Facebook like drama
BrentD
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No, probably not. Think about it. Under field conditions, what is the variance in your shooting overall, and which contributes the most to that variance? You or the gun? A more precise gun will help you but I would wager that you could cut 1/2 MOA out of your field shooting with practice more easily than you can cut 1/2 MOA out of your rifle's precision. Yes, both have the same effect on the target, but one will be easier and chances are you can cut a whole bunch more MOA with serious practice than you can ever hope to get with your rifle/ammo.
That said, even a tiny increase in equipment precision will have a positive effect. But most hunters have huge chunks of precision to gain by practicing, learning to shoot from weird positions (including offhand!), judging the wind, the elevation angles, etc. The low hanging fruit is generally the shooter, not the gear.
yakimanoob
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OK.
yakimanoob
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Returning to this: it doesn't matter how many groups you shoot. Groups with fewer shots will always average smaller sizes than groups with more shots. If you shoot more groups and take the average, you'll get a better average, but you'll still only be measuring the average size of your n-shot groups, which will be quite a bit smaller than your probable strike zone as long as n is small.
Please note I'm not saying that you have to shoot 100-shot groups. If you have the funds and you like shooting, then go for it (and send me your data so I can play with the stats!), but the last thing I mean to do is join the chorus of stats-minded folks (especially stats-minded folks who have a vested interest in having people buy more components, as in the case of the Hornady videos) telling others that their small groups aren't good enough. 2 shot groups are great for some applications, you just have to be careful. Same goes for 3 or 5 shot groups.
The entire point of this thread is that I'm trying to figure out the statistically rigorous way to balance costs and precision. I am an economist after all. Constrained optimization problems are what we do.
BrentD
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I think I'm not explaining this very well, but part of your increase in group size is because environmental changes happen and part is because of simply sample sizes.
If all you are doing is measuring group size, then two-shot groups minimize the former issue and, for moderately reasonable numbers of shots fired, will also cover most of the former (the second issue being one of diminishing effect as sample size increases.
If you are going to plot every shot in x-y space, calculate a geometric mean vertical and horizontal, compute distance from that geometric center to each shot and average that as a measure of precision (as stated in the essay I sent you), that will be best. But doing that is a whole bunch of work. The two-shot groups accomplishes that same thing with less effort (albeit more ammo).
And, of course, what are you going to do with whatever information you choose to collect? A simple and reasonably powerful method is spelled out in that essay. Your experimental design matters, of course, but then maybe we should start at the beginning and be sure we know what we want to test first.
yakimanoob
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A big part of what I'm trying to say is that these two methods (calculating average radius and calculating the average distance between two-shot groups) absolutely do not accomplish the same thing, unless by "same thing" you mean that both are measures of precision. Sure, they're both that, but they're two very different measures of precision and need to be carefully interpreted for what they are.
BrentD
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We will have to disagree on that.
yakimanoob
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Are you saying that, given a big enough n, the average size of n 2-shot groups gives you the same number as the mean radius of a single group of size 2n??
BrentD
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Among other things, yes, as n increases the two samples will converge, all else being equal. But all else won't be equal, and therein lies the second or third advantage of 2-shot groups. Conditions will change and the 2-shot groups will track what with minimal effect. The one big group will not.
yakimanoob
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How do you figure this?
BrentD
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Why wouldn't they? More to the point, why does it even matter? What you want to know is which of two loads is more precise.
It gets bad at times. Not enough to chase me off from enjoying the good parts. The most civil site I visit is the Hammer site. But, it's dedicated to one bullet type and therefore is not for everybody. mtmuley
yakimanoob
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It matters because the mean radius has a well-established interpretation in the shooting world, as it defines the Circular Error Probable and the military and many other research bodies have established ways of inferring your likelihood of hitting your target based on previous measurements of the mean radius.
Conversely, the 2-shot group method you describe gives an entirely different metric. A quick simulation pulling samples from a standard bivariate normal distribution gives a mean radius of 1.25" from 1M shots and an average size of 1.77" from 0.5M 2-shot groups. They do not converge. (python file attached just to make sure Hem isn't still hanging with us).
Among other things, the distribution of 2-shot group sizes is not normally distributed, which means the t and other common parametric tests between samples are not valid. Even with half a million groups, the distribution is still notably right-skewed (I presume it's a Nakagami distribution of some kind, but I'm not sure). Image attached.
All this to say, the mean radius, given a large enough sample, empowers you to calculate the circle within which 95% of your shots are expected to land (2.08 times the mean radius). It's not clear to me how one would translate the average size of the 2-shot groups to a hit probability, but in any case, they're certainly not the same metric.
Conversely, the 2-shot group method you describe gives an entirely different metric. A quick simulation pulling samples from a standard bivariate normal distribution gives a mean radius of 1.25" from 1M shots and an average size of 1.77" from 0.5M 2-shot groups. They do not converge. (python file attached just to make sure Hem isn't still hanging with us).
Among other things, the distribution of 2-shot group sizes is not normally distributed, which means the t and other common parametric tests between samples are not valid. Even with half a million groups, the distribution is still notably right-skewed (I presume it's a Nakagami distribution of some kind, but I'm not sure). Image attached.
All this to say, the mean radius, given a large enough sample, empowers you to calculate the circle within which 95% of your shots are expected to land (2.08 times the mean radius). It's not clear to me how one would translate the average size of the 2-shot groups to a hit probability, but in any case, they're certainly not the same metric.
