A Statistical Approach to Measuring Accuracy

[DBinNY]

Lately there have been a lot of debates on the board about the statistical validity of shooting various sized groups or even single shots to determine accuracy. The fact is that all methods have their place and can be statistically valid. Having a little background in statistics, I will attempt to shed some light on the subject and provide some simple methods that any of you can use with your own data.

I’ve put together a description of how to calculate and interpret means and standard deviations from your own shooting data for group sizes and first shots. I’ve also included examples that you can apply to your own shooting data. The goal here is to give you a better understanding of the variability in your results. Click on the link below to access it.

Calculating and interpreting means and standard deviations for shooting data

[Harley]

Thanks, DB, for presenting this. I passed my post-graduate statistical certification in 1973; that's a long time ago, and I remember less than I would like to admit. What you've done is bring it back in a way that a determined person can follow. I especially like your single shot analysis of variance. I think we're talking "confidence intervals" that, after a good number of 1-3 shot groups, would yield close to the same probability as the actual results of, say, a five shot group.

Harley

[Dave W]

Thanks for taking the time to put that together DB.

[younghunter86]

Great writup DB! Very easy to understand. I'm working on my thesis/data analysis this semester and swore I WOULD NOT look at statistics over the weekend. I guess I was wrong!

[dougedwards]

Good info there. I shoot groups to develop a load at any particular distance. The first shot tells me something. Flyers tell me something. Sometimes I am aware that I am getting tired or somewhat recoil sensitive. That tells me something. But after I am satisfied with groups of three shots with the load and 2" is acceptable to me at 100 yards for hunting accuracy, I become most concerned with only the first shot out of a cold barrel. I want that shot to be within one inch of my intended target at 100 yards. Of course wind plays a part and also the measuring of the powder plays a part and also the eventual pressure exerted to the bullet with the ramrod is also crutial. There are several aspects of shooting that must be right before I even shoulder the rifle.

Consistency if the key to shooting confidence. I could shoot a five shot-one hole group and post it for all to see, but if in my heart of hearts I know that shooting session was definitely the exception.......it gives me no peace. I am only confident in my load when the first shot from a cold barrel falls right where I want it and at 300 yards that might be within a 4" circle.

Now if I were a bench rest shooter I would have a different approach but as a hunter I want to have confidence in my rifle and my load as I make adjustments for drop and windage. It seems rather fruitless to begin doping the wind when I am not even sure where my shot will place with no wind influence at all. I usually don't get to shoot a three shot group at a whitetail. I must develop confidence in that first shot......if not I have no confidence at all.

Doug

[Deleted]

.........It comes easy to some and then to some like me it doesn't ;D.....It was interesting; at least the part I understood
Zen

[DBinNY]

Harley, think of it this way. Every 5 shot group is a three shot group after three shots. They are not independent events. The group can get larger if shots 4 or 5 do so (and sometimes they will!) or it will stay the same size. It cannot get smaller. That 68% within 1 standard deviation, 95% within 2 standard deviations.. is the empirical rule. Fortunately somebody else already proved it so we don't have to. You can apply this stuff without understanding every (or any) detail.

DaveW, you are welcome. I like to try to give something back to board members once in a while. Lord knows they have given so much to all of us. A classic example of the benefits of open sharing of knowledge.

Younghunter86, statistics can be interesting when applied to things you care about. Good luck with your thesis. I can't begin to tell you how many times I have wished that the ML II was around when I was your age. When I started out the only option during gun season was a smoothbore slug gun. You had plenty of variability to deal with in those days.

dougedwards, your thinking is sound on all counts IMO.

Zen, the beauty of this is you don't have to understand it to use it. All you need to do is put your numbers into that website calculator and it does the work for you. Then take the mean plus or minus 1 standard deviation and that will describe the bounds for 68% of your shots etc. Based on the results that you've posted, I don't think you have to worry about this stuff anyway! The main reason I did this was to demonstrate that you can get valid results from a variety of approaches.

[edge]

Nice job, but the "Goat" looked miffed

edge.

[DBinNY]

Feb 28, 2009 21:03:44 GMT -5 edge said:

Nice job, but the "Goat" looked miffed

edge.

I intentionally avoided discussing terminal effects and the pros and cons of machined recoil lugs ;D.

[Hossdaniels]

MAN, that's complicated! Just take 3 shots(*makes you a expert markman*), or take five if you think you really wanna know.

[glow=red,2,300]You can not brag about a 2" group on the internet!!! ;D[/glow]

[wilmsmeyer]

I'm with Dougedwards thinking on this one. The statistics...averages are great for a big picture analysis. However, If my average group size was 1.5 inches over 30 shots with a load...BUT 2 of those shots strayed 3-4 inches from the group....I freak a little.

If a great paper load with miles on it and deer to its' credit, gives me a cold barrel shot 3-4 inches off intended POI one day...I will freak.

I'm the personality type that thinks if something can go wrong it will. Those 1 or 2 shots....instead of being discounted, carry more weight to me...and play with my head more then the other 28-29. To me, that flier will happen when I one day get the 200 yd shoot I prepare for...but haven't taken yet. At that range, the erroneous shot will be off twice as much or more.

So, I guess I shy away from absolute statistical analysis of groups. I just shoot and shoot until I am satisfied that a load is doing the right thing. Cold days, warm days, gun left loaded a while, clean or fouled barrel, clean or slightly fouled plug...over a lot of time. An entire weekend shooting a great load that statistically makes every grade may come unglued that first time the temps dip into the teens and my gun has been loaded for a week.

The one variable of a load that I do sometimes discount is the POI changes that do occur over great temperature changes. (As long as grouping is still tight I don't care) Since I see this enough in all my guns and many years of shooting in Western NYS, I just know to constantly check POI during the season and its' temp swings. Mind you, the POI changes we are talking about is more of a minor "wandering" within a few inches...nothing severe...yet enough to adjust for now and then.

It's the hunter....not shooter...part of me I guess. I hate to miss...ever. I hate wounding even more. Most of us are great shots here. The likelyhood of wounding...IMO....is generally greater then missing clean.

Chasing the elusive MOA is fun as a target shooter. For a deer hunter =<2 MOA all day, all ranges, may not be front page news but awfully deadly while hunting. Any flier be damned.

[Harley]

Wilms, nothing to be argued about in your post; makes good reading and good sense.

Harley