Questions about statistics of groups

[Coyotefurharvester]

For me there is not a better example of actual poi error(center of group) than when I "zero" a thermal scope during the day. For me zeroing a thermal optic is a very slow process 1. During the day a very degraded image in the digital display. 2. Barrel/suppressor mirage 3. Still experimenting with targets to optimize aiming points. This is especially true when using a "proven" load. It's very easy to "believe" the target after just a couple shots. Of course the results are bullet impacts not quite where I'm expecting(aiming) at night on coyote/fox. When image quality of the target is much improved and FIRST SHOT PRECISION is required.

 

[Wild Bill IV]

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.

It is called a universal receiver where they swap out barrels on that reciever!!!

 

[Wild Bill IV]

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.

I had a course in Statistics and Probability over 45 years ago with an Industrial Physics degree! The problem you are having is there is two different formulas used in your analyses!! It is based on population size (number of samples). Generally, populations of 5 to 50 (20-25 is sufficient) for Scientific Standard Deviations with a (n-1) in the denominator (n = population or sample size). Populations greater than or equal to 25, (n) is in the denominator. Therefore the Standard deviation will decrease slightly on high population statistics. But, PROBABILITY will kinda be the inverse of the standard deviation mathematically. That being said, the fewer the shots, the less chances of a flyer!!! Increase the population, the higher probability of a flyer or 2! And it will grow as the population grows!!!

 

[CharlieNC]

Group size is not data, it is a statistic. The location of individual shots is data which can be analyzed in many ways. 50 2-shot groups, 20 5-shot groups, 2 50-shot groups, etc , which is better in terms of statistical validity? All are 100 shots and every shot should be utilized as data to quantify shot dispersion.

 

[6ShotsOr5?]

In case you haven’t seen it there is an interesting analysis on group size here:

Group Size Analysis

I didn’t compare their results with Litz table.

Finally, I think that you have the perfect screen name for a stat guy.

 

[6ShotsOr5?]

For me there is not a better example of actual poi error(center of group) than when I "zero" a thermal scope during the day. For me zeroing a thermal optic is a very slow process 1. During the day a very degraded image in the digital display. 2. Barrel/suppressor mirage 3. Still experimenting with targets to optimize aiming points. This is especially true when using a "proven" load. It's very easy to "believe" the target after just a couple shots. Of course the results are bullet impacts not quite where I'm expecting(aiming) at night on coyote/fox. When image quality of the target is much improved and FIRST SHOT PRECISION is required.

There is no such thing as “FIRST SHOT PRECISION”. It takes at least two shots before precision can be measured.

 

[Wild Bill IV]

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.

That is kinda the breaking point in using scientific STD formula (n-1 in the denominator) vs population STD forula (n in the denominator) in Statistics and Probability!!! "n" is the population or number of samples! Generally the scientific STD best population is 20!! Generally, population greater than or equal to 25, the population STD formula is used!! Population STDs will be lower than scientific STDs. PROBABILITY is kinda the inverse of STD formulas!! The less you shoot, the less chance of changing impacts! The more you shoot, the great the chances of changing impacts!!!

 

[Wild Bill IV]

There is no such thing as “FIRST SHOT PRECISION”. It takes at least two shots before precision can be measured.

Accuracy is group size!! Precision is how close you get to POI. Statically, 20 shots minimum for precision or increasing the probability of finding true POI!!!! The 20 shot sample is the ideal population needed for a good scientific STD formula (n-1 denominator). 25 and greater population uses population STD formula (n denominator)! 20 to 25 shots when looking at best probability!!!!

 

[6ShotsOr5?]

Accuracy is group size!! Precision is how close you get to POI. Statically, 20 shots minimum for precision or increasing the probability of finding true POI!!!!

You’re confused.

 

[Wild Bill IV]

You’re confused.

My Bed!! My inverse sign (+ to -) in the study of physics has come back to haunt me!!! Accuracy is how close the group size is to POI, and precision is the group size!!! Forgot my parameter from STATISTICS AND PROBABILITY course!!! Statistically, both needed at least 20-25 shots to move on to probability analysis!!! It could be 7 3 shot groups, 4-5 5 shot groups, for precision!!! But, 20-25 shots for best POI or accuracy!!!

 

[jelenko]

There is no such thing as “FIRST SHOT PRECISION”. It takes at least two shots before precision can be measured.

But my first shot just looks so precise.

 

[6ShotsOr5?]

But my first shot just looks so precise.

Yep. I had a snubby with a bad crown once and even my one shot groups did not look good.

 

[jelenko]

Yep. I had a snubby with a bad crown once and even my one shot groups did not look good.

Yeah. That's when you know you're in trouble.

 

[jackieschmidt]

Obviously the way Long Range Shooters look at group size is different than the way Short Range Shooters, (100/200/300 yards) look at it.
We look at it brutally simple. You sit down, clear the rifle, maybe put a few sighters to see point of impact, then go to the record and shoot a five, or ten shot group. You might even return to the sighter to see if the conditions are pushing the bullet to a different location on the target. You might have to hold accordingly in order to keep the group small in the allotted time.
In Short Range Score, you do the same thing, only instead of shooting a group on one target, you are shooting five individual bulls eyes at one sitting in the allotted time.

There is always the possibility that the actual point of impact might change a little. It is up to the shooter to recognize this and compensate accordingly before the Aggregate is ruined.

As for tuning, my definition of a well tuned combination, which includes everything, even the shooter, is”the only thing that keeps the next bullet from taking the exact same path to the target as the last is the conditions into which you are shooting”.

I suppose that is why Short Range Shooters put so much emphasis on Flags and learning to analyze what they are telling you.

 

[K22]

I find these theoretical kinds of debates entertaining but not practical.

There is a practical technique, perhaps too technically simplistic to gain much favor with "experts", but I found it to be revealing and useful. It's explained in Chapter 11 of the 47th Edition of the Lyman Reloading Handbook, the section entitled, "Testing for True Accuracy Potential".

I have used this technique for many years and found it to be revealing, practical and humbling. It presumes, though load development, you have selected a "go to load." While the technique is primarily designed for hunters, I believe it has value for any shooting discipline.

Summarized, it involves shooting at least a 5 shot group in the exact manner in which you intent to use the rifle using 2 targets. That session's target which is replaced after each range session and another target placed behind that one which is not replaced each session.

The latter target over time will give you a composite of all shots fired thus reflect the true capability the system (shooter / equipment / load) over a range of changing environmental conditions and shooter's bio-rhythm cycles. The idea is to shoot at least 5 groups over 5 different range trips thus giving you a 25-shot composite. (Note A).

At the completion, you will have 2 sets of data:

1.) A series of individual targets that show the environmental conditions (temperature / wind / mirage) conditions and the shooter's notes, e.g., called shots, mental state, physical state, etc.).

2.) A composite of all shots showing the true dispersion of the system over a wide range of conditions.

Note A: As a standard practice, I use a second target at all practice range sessions. I often have composites of 50 to 100 shots which give me a fairly reliable understanding my system's true capability.

 

[memilanuk]

Summarized, it involves shooting at least a 5 shot group in the exact manner in which you intent to use the rifle using 2 targets. That session's target which is replaced after each range session and another target placed behind that one which is not replaced each session.

The latter target over time will give you a composite of all shots fired thus reflect the true capability the system (shooter / equipment / load) over a range of changing environmental conditions and shooter's bio-rhythm cycles. The idea is to shoot at least 5 groups over 5 different range trips thus giving you a 25-shot composite. (Note A).

I've done something similar on occasion in the past, and plan to do it more frequently in the future. I do think that for many (most) people interested more in 'practical' accuracy ie what is the true grouping or zero of my hunting rifle it's a much more useful approach. Maybe not as good for the ego, but it'll definitely give one a more realistic evaluation of their true combined system (rifle, ammo, shooter) performance.

The one thing that I find - for me at least, and I suspect I'm not alone - is that when you go down and change out the top target, it's pretty much impossible to not look at the 'backer' target - and to some degree, that gets in your head. It's easy to say 'put it out of your mind'; harder to do in actuality.

 

[K22]

I've done something similar on occasion in the past, and plan to do it more frequently in the future. I do think that for many (most) people interested more in 'practical' accuracy ie what is the true grouping or zero of my hunting rifle it's a much more useful approach. Maybe not as good for the ego, but it'll definitely give one a more realistic evaluation of their true combined system (rifle, ammo, shooter) performance.

The one thing that I find - for me at least, and I suspect I'm not alone - is that when you go down and change out the top target, it's pretty much impossible to not look at the 'backer' target - and to some degree, that gets in your head. It's easy to say 'put it out of your mind'; harder to do in actuality.

No question, part of high-performance shooting is mental.

If the backer target causes a negative mental reaction, I would suggest avoiding using it. However, you can still accomplish the same collection results by manually plotting that range session shots on a separate target to be designated at the composite shot collection target. Thus by doing this after each range session you will have composite data.

Yes, it can be hard on one's ego. But having a realistic understanding of your systems capability is more important. Another positive aspect of this technique is that it can be used as a baseline to measure improvement. I have use it this purpose and its works.

 

[jackieschmidt]

No question, part of high-performance shooting is mental.

If the backer target causes a negative mental reaction, I would suggest avoiding using it. However, you can still accomplish the same collection results by manually plotting that range session shots on a separate target to be designated at the composite shot collection target. Thus by doing this after each range session you will have composite data.

Yes, it can be hard on one's ego. But having a realistic understanding of your systems capability is more important. Another positive aspect of this technique is that it can be used as a baseline to measure improvement. I have use it this purpose and its works.

What will be hard on someone’s ego will be going to a Registered Short Range Score Match.

There are no alibis. You sit down and shoot your Score Target in the allotted time. You will do this 5 times. 25 record shots.

That Score or Aggregate, is your rifles true accuracy capability. Notice I said accuracy, not precision.

I have found, through personal observation, that this can be a very humbling experience to a lot of theoreticians.

 

[Coyotefurharvester]

One(first) shot precision is the end result when hunting and what matters. Regardless of statistics.

 

[jelenko]

'backer' target - and to some degree, that gets in your head.

For me this actually a good point.
Because getting my mind in the right mental state is a key element in competition, seeing something I don't like would give me an opportunity to practice.