Questions about statistics of groups

[Pareto]

Just nerding out a bit. Don't read if that's not your thing.

I've been looking through Volume 2 of the Bryan Litz book on shooting and find a table where he lists how much your group size will vary depending on how many shots fired. But then he goes on to discuss statistical analysis. Here's where I disagree a bit with his presentation.

Strictly speaking, I would prefer to say that if your gun can shoot a group, or more accurately, shoots POI within x inches of the POA, there is a 95% chance it would land within A, then that is how accurately your rifle/ammo shoots under ideal conditions. If we use this standard there is really no difference due to group size. That is, if you have shot (to take an extreme case) 1000 shots with all within 1 inch of POA, then 2 follow-up shots 2 inches off are not significant enough to change that assessment.

Conversely, the fewer the shots/groups you've fired, the less likely it is that a flyer is not part of your 95% confidence interval.

Of course, this also means that too many shots may also exaggerate your true 95% MOA. Why? Because a large group assumes ALL variables confounding variables are unchanged. That includes weather, pressure, temperature of the barrel, consistency of ammo, and in the case of a non-fixed rest shooting arrangement, shooter error. But when you're testing for the quality of your gun/ammo, you don't want to include shooter error into the calculation of group size. So the larger your group is, the larger the chance that your aim wandered, the weather changed, your barrel heated up, or that you got a randomly off piece of ammo.

 

[CharlieNC]

My analysis of the topic.

Target Statistics For Shooters

How many shots are required to statistically show loads are different? It's actually straight forward, and is a bit of a different than you have been led to believe. I discuss this and include an excel program for your use. Caution.... it's nerdy.

forum.accurateshooter.com

 

[K22]

In my professional life I was a quality assurance engineer. I was well versed in statistical analysis, and it has a significant place in process control and evaluation.

Dr. Deming, renowned for transforming the Japanese industry after WWII, wrote several books of the subject. In my day, he was considered the leading authority on process improvement using statistical techniques. I read his books, attended his seminars, and applied his methodology.

The problem I see applying statistics to the shooting sports is that there are too many uncontrollable variables, the most significant is the person behind the rifle. Then there are the environmental effects which are constantly changing. If you could eliminate the first two, then you might be able to draw some valid conclusions on component and reloading process variability, but you can't eliminate these variables in the measuring process.

 

[jelenko]

shoots POI within x inches of the POA

Group size has nothing to do with POA.

 

[Pareto]

Group size has nothing to do with POA.

You can measure the size of group from center of gravity or from a fixed point. That fixed pount us what I'm calling POA. You want a fixed point to deal with changing CofG

ERROR: I should have said Center of Group.

 

[jelenko]

You can measure the size of group from center of gravity or from a fixed point. That fixed pount us what I'm calling POA. You want a fixed point to deal with changing CofG

You mean the center of the group?

 

[ORjeff]

Also a former process engineer. I agree with all the above including the OP. This is why some ammo companies use something like a rail gun in a tunnel and swap barrels a lot.

Ultimately how you analyze the data depends on your purpose. A hunter cares about one cold bore shot, in Fclass every shot matters (sighters need to represent the shots for record), and in both cases fliers matter and they can ruin your day. So, they need a 100% con,fidence interval.

POI v POA only matters after you're sighted in and if you did that correctly it should correlate with group size. Except that systematic shifts in POI can be meaningful.

So, group size matters and that includes the fliers...at least for me.

 

[Pareto]

In my professional life I was a quality assurance engineer. I was well versed in statistical analysis, and it has a significant place in process control and evaluation.

Dr. Deming, renowned for transforming the Japanese industry after WWII, wrote several books of the subject. In my day, he was considered the leading authority on process improvement using statistical techniques. I read his books, attended his seminars, and applied his methodology.

The problem I see applying statistics to the shooting sports is that there are too many uncontrollable variables, the most significant is the person behind the rifle. Then there are the environmental effects which are constantly changing. If you could eliminate the first two, then you might be able to draw some valid conclusions on component and reloading process variability, but you can't eliminate these variables in the measuring process.

I am an academic and have experience with publishing work based on imperfect data. I think there's a lot of potential for rigorous hypothesis testing in shooting, but it may require some sophisticated work that neither academics nor shooters may care about. Nor may producers be willing to share data. But I am starting some preliminary reading to see if I can make a contribution somewhere based on existing work.

Certainly, one has to sort out different hypotheses before even making a claim to test anything. At the minimum, I want to learn the extent of semi formal work on this based on current books and specialist journals.

 

[Pareto]

You mean the center of the group?

Yes. But you don't want to let the Co group change. Sorry, not gravity.

 

[dellet]

Having 2 shots out 1002 outside of the statistical average is no big deal. On paper. But there are other ways to interpret the data. The easiest is that those two shots could have happened anywhere between shots 1-1002. Next would be that you need to shoot another 998 shots and compare the two groups.

A simple explanation is imagine playing Russian roulette. The first contestant made 1000 safe attempts. The next two contestants made zero. Did someone rig the game? Or was it complete chance.

 

[Pareto]

My original post was just random musing, because I was surprised there was not more high powered stat work in this field given how much data are relevant to things like the military. But presumably, those guys don't want to share their homework and private companies want to keep proprietary matters proprietary. I looked up some engineering and military pubs and those seem stronger on the physics of things, but not on hypothesis testing.

Nonetheless, reading Bryan Litz's book is giving me ideas about how to really raise the stakes on serious stat testing if there were a way to get the relevant people interested. I have worked with a number of top analytical scholars including fellows of both the American Statistical Association and the Econometric Society and know what to read or whom to run to when questions arise.

 

[jelenko]

By any chance do you know Happy Hellfire?

 

[Pareto]

No I don't. Although with a name like that, he sounds worth knowing.

 

[jackieschmidt]

I guess I am behind the times.

I always thought that group size was determined by the center distance of the two furtherest shots

That being said, you should, (sooner or later), shoot groups that is required in what ever Discipline you choose to participate in. If you are shooting Short Range Group, your set up has to be able to agg at a competitive level shooting 5-Shot Groups. In Unlimited, it’s 10-Shot Groups. You can have nine shots in a .150, and one hanging out to make it .350, that’s just the way it is.

I am aware that when it comes to shooting at longer ranges at different types of targets from different positions that there are different parameters in determining the accuracy potential of a given set up.

 

[Pareto]

I guess I am behind the times.

I always thought that group size was determined by the center distance of the two furtherest shots

That being said, you should, (sooner or later), shoot groups that is required in what ever Discipline you choose to participate in. If you are shooting Short Range Group, your set up has to be able to agg at a competitive level shooting 5-Shot Groups. In Unlimited, it’s 10-Shot Groups. You can have nine shots in a .150, and one hanging out to make it .350, that’s just the way it is.

I am aware that when it comes to shooting at longer ranges at different types of targets from different positions that there are different parameters in determining the accuracy potential of a given set up.

Group size is determined by the center distance between two shots. But if you're looking at more than one group you also need to consider if the group wanders. So that (assuming perfect point of aim) imagine 2 5x groups that are each 1 inch in width (center to center) but the first is a bit to the left of the bullseye and the second to the right. Well, as far as a shooter is concerned this is a much larger group. You can treat this as one large group, but under certain circumstances, you might also want to treat each group as separate but then include a variable for distance of center of group from the POA

 

[Pareto]

The main thing I'd bring to the table, is a shift from just looking at stats as a means of the optimal description of what we find to using it as a means of testing various hypotheses, such as, does temperature change affect the precision, or can tuners work and under what conditions? For different questions, you may not need the same large samples required in a straight classical perspective. All you need to do is statistically distinguish between two cases that are otherwise similar. The naive thought that you can figure this all out with just bigger samples is what I want to get away from because that method is often inefficient in the statistical sense.

 

[Pareto]

To take a simple example. Let's say you make a change in the rifle and want to say if that change/treatment made a difference, (This could be due to a tuner, different bullet, different seating etc.). Then you might be able to shoot say 8 3x groups under the pre and post treatment. Now, for the sake of knowing exactly "HOW" precise the gun is (whether it's a 0.5 or 0.75moa shooter) those groups may not be conclusive. However, depending on the difference between the two sets of groups you might still be able to conclude that the change made a difference. For example, an F test between the two groups would tell you if there were a statistically significant difference between the shots you took pre and post treatment. This would be statistically valid even if you felt the total sample size were not big enough to tell you what your "true" rifle grouping is under ideal conditions.

 

[JEFFPPC]

Maybe video games are your thing.

 

[memilanuk]

@Pareto FWIW, I've asked one of the guys @ Hornady something similar - why not use statistical methods (like ANOVA) more sophisticated than brute force of raw sample size. The response was that their observations - over many, many, MANY rounds from a test rig in an instrumented indoor range - didn't bear out the usefulness/accuracy of those methods, compared to their actual, on-target results.

I know there's a fair bit of controversy on various forums about their approach to things, but they might have some large sample size data that they would be willing to share, for you to work with.

 

[Jeff Porter]

Listen to the Hornady podcasts “Your groups are too small! “

2 part series where they compare group size and mean radius of a rifle system over different numbers of shots included in the groups. Consensus comes that you need 20-30 shots to get the true zero( poi ) and capability of grouping to be able to assess performance and to be more accurate with adjustments made for wind and distance etc.