Brent,

I am very intrested.  I think it depends on what match you shoot. Mimimum Group size is very important to the bench rest shooter particularly if shooting re-entry matches.

But I try to only shoot the Hudson 100 shot offhand match.  I think Standard deviation is the best measurement to determine potential scores and more important see what is required to improve.

Although many years ago I had one Statistics class Most of what I know about SD as it relates to shooting is from " The Russian Book"  Competitive Shooting by A.A. Yur Yev.  He does not call it SD but Bullet Dispersion.  Yur Yev makes the case for a analysis of targets on departure from the center.

Couple of years ago I took my 10 10 shot Hudson postal targets and overlaid them one by one on a fresh target. I put a pencil mark in the center of each hole. Then I took a hole puncher about bullet size and punched out all 100 shots.

It it intresting to look at and could be measured and analizyed. So far all I have done is figured the center of impact and size of the group in total and for the majority of shots as Yur Yev recomends.

I droped my P/S subscription a few years ago but will try to look that one up. And anything you post on the subject I am sure will be interesting

Boats

This post is not a disputation of anything, rather just a statement of thought on this subject. I am certainly a believer in science and in statistical analysis but there is a nagging memory when it comes to applying them to cartridges and rifle performance, etc. For probably twenty-five years the world of modern BR shooting was ruled by the .222 Remington (only to be displaced by the PPCs). The .222 was not (according to much I have read) a low SD cartridge and yet delivered extreme accuracy. The PPCs ARE better in terms  of SD, yet beat the older round by only a tenth or two of minute of angle (and I know that is more than enough in BR competition). I guess that where I am going with is that the proof still remains in the shooting.

PS: If anyone knows from actual shooting experience that what I have read re: the .222 Rem is incorrect, I would llike to know.

DonH,
Your comments are entirely correct in so far as small SD's in some measures are no guarentee of high scores.  This is especially true when measuring velocity.  For a good example, you may find that you can achieve a near zero SD with regards to velocity when shooting an 800 gr bullet out of a .38-55. But obviously, there is little chance that it will be accurate because a bullet that long will probably not be stable once it leaves the muzzle.   

But suppose we are to measure SD's for the radial dispersion of a group shot at a target.  The article I indicated describes this rather well - but it's sorta like doing a string measure, only rather than measuring from the center of the target, it's measured from the center of the group.  A small SD in this case is a good  indication of precision.  In fact, it is proof of a level of precision.  Nonetheless, if the group was shot ignoring the wind, or with the sights consistently misaligned or any of a host of other things, it may well be that this very precise group (small SD) is off in the 17 ring on a 25 ring target - in other words a great group in the wrong place.   

How many times have you said, "if I just centered that up on the target, it would be a great score"?  Happens to me all the time because I screw up with regards to one or more steps along the way.   

So, SDs are just a tool that helps, but not a magic cure all that will instantly make you into a world-class shooter.  Accuracy on the target is the summation of a huge number of variables and steps, each one having some degree of influence on the final outcome.  And while one or two of those steps may be executed close to perfection, if the rest of them are done poorly, the result is bad scores.   

So, never confuse a smaller SD with a guarentee of higher scores, but rather with having improved the steps involved in that one process that is being measured.   

Brent

I started analyzing my groups (or maybe patterns) years ago, when a fellow schuetzen addict and I took a couple of university courses in statistics.  Here is our method.  If you have an Excel (or other) spreadsheet it saves time.   

Lay or construct a grid over your target. A T-square & triangle will be helpful.  If you are shooting at a bull, it may better not to use the bull or x-ring as the center of the grid.  Just number the bullet holes and assign them horizontal (X) values and vertical (Y) values from an arbitrary point (the center of the grid).  I use inches & 1/100s for my measurements, but anything should work as long as the measurements are consistent from hole to hole.  The mean of the Xs and the mean of the Ys will give the X & Y coordinates for the center of the group.  Then compute the difference between each individual X and the mean X and the difference between each individual Y and the mean Y.  Then square each difference (individual X and corresponding individual Y), add each pair of differences together, and take the square root of each pair.  (The Pythagorean Theorem revisited).  That gives you a measurement of radial dispersion from the center of the group.  Now calculate means & SDs on the radial dispersion figures.  I use this to evaluate the effects of changing lubes or powder charges, or just about anything else.

I think one of the first things to understand about Standard Deviations is that they are a measure of the variability of whatever it is you are measuring.  Whether it's distance from the center of a group for each shot, or the velocity of each shot, the SD is the measure of the amount of variability.  The square of the SD is called the VARIANCE and it is similarly a measure of the variability of the measure.  If you know SD then you know Variance, so let's just stick with SD as they tell you exactly the same thing.   

Below is a sample of something that you might find when using your chronograph.  These two strings produce the same average velocity.  They both produce exactly the same ES too.  But you can see that the SDs are considerably different.

        Load #1      Load #2
     1282      1282
     1307      1301
     1298      1302
     1295      1303
     1307      1300
     1306      1301
     1293      1302
     1305      1302
     1307      1307
Average      1300      1300
St. Dev      8.233      6.633
E. Spred      25      25

Now, of course, there is no way of knowing which of these loads will shoot best, but first indications are that the second load is more predictable from shot to shot that the first load.   

The bottom line is that ES does not contain much information, it is also highly sensitive to sample size (number of shots per load or group), and does not well characterize the precision (repeatability) of whatever is being measure.

Of course, you can often get by using ES because they tend to run the same direction more or less as SD, but because they are less informative, when you are trying to make small improvements, ES can be very misleading and even SD can sometimes not be as perfect as you would hope. 

I'll try to post something about how to statistically determine if two loads are shooting differently in another post.

Brent

Waterman, 
I really don't follow much of what you posted.  There is a historic connetion between Guinness beer and a well renowned statistician, but frankly, in the big picture of stats, it doesn't go very far.  And it had even less to do with counting beer drinkers.   

That aside, I'm willing to wager that anything you feel will make a 0.005" difference in group size is really just a figment of your imagination and not actually happening in the real world.   

And that is the problem with folks that do not understand nor use statistics.  Many are happy as clams and many will out shoot me, but they would shoot even better and be even happier if they used statistics constructively.

There are two basic errors to be dealt with when using statistics.  Not surprisingly, they are called Type 1 and Type 2 errors.   

As we all know, any of us will shoot two targets with ammunition as perfectly indentical as we can make it, under conditions as unchanging as we can hope for, and with technique that is as unwavering as possible, and yet get two very different results.  Why is this?  pure chance is of course the simplest answer and easy to understand.  A rifle/ammo/shooter/conditions combination that averages 1 MOA will not shoot exactly 1 MOA every time.  That is the nature of the beast and the reason why we need statistics.

So, what are these types of errors that we need to avoid?  Type 1 (T1) is the most commonly considered.  It is the probability that the difference in two observations (think of them as two different targets shot with two different loads) are in fact, the result of a true difference.  That is they really do perform differently and the difference is not just pure chance.  Statistics, in it's most precise definition can tell us that the likelyhood that the two observations (targets) have the same properties (come from a system with the same accuracy), is of a given probability.  If that probability is small enough, we might conclude that they are, indeed different, and proceed from there.  If the probability is not especially small, then we might be wary of concluding anything.  We could decide to test some more or to decide that they are the same.   

Type 2 (T2) is the probability that the two observations are indeed different, but we can't see detect the difference.  This is less commonly considered explicitly, but here is an example.  Suppose that you have two loads that differ only in primers.  But the loads, or the rifle, or you or the wind when testing, are not particularly good so that both loads shoot in the neighborhood of 4-5 MOA.  If one of those primers is actually contributing a 0.25 MOA inprovement in accuracy, you are not likely to detect the difference under these conditions unless you shoot extremely large numbers of targets.   

On the other hand, suppose your normal load and shooting system is running right around 1 MOA and now you make that same change of primers and get that 0.25 MOA improvement.  Now, in relatively few targets, you will be able to detect that difference with a high degree of confidence.  This "confidence" is called statistical Power and it is directly related to T2.   

So, having bored most of you, and for sure, turned off a few folks, how do you apply all of this to shooting directly?  I think there are two ways.

One is the direct methods that I can describe in gory detail if anyone cares.  I could even make up an Excel spreadsheet I think that would do most of it for anyone willing to trouble with it.  But I suspect that most ASSRA folks are pretty unlikely to do that so I won't waste my time or anyone else's if no one is going to use it anyway.

The other use is to at least understand the general principles, some of which I've tried to lay out here and use them in an informal and implicit method.  Many of you already do, including the most anti-statistics shooter of them all (and he knows who he is, because I've beat him over the head with this dead horse a million times to no effect).   

Some of those general principles would include using SD's instead of SE's to make decisions.  The best thing you can do with the SE is to throw it out!  The one exception to that is if you cannot calculate the SD.  It's a crutch that is better than nothing but that's all it is.   

The second thing you can do is to think about how you decide what constitutes an improved load.  If you are in the early stages with a recalcitrant rifle (as I am with my .38), then all you can hope to find shooting a few groups with each load, are differences that are relatively large improvements.  Those things that seem to have no effect or perhaps even a backwards effect need to be revisited after you have refined the load a bit more.

I could write more, but this darn thing won't let me.  This website has a few strange properties to be sure.

Brent

" Many of you already do, including the most anti-statistics shooter of them all (and he knows who he is, because I've beat him over the head with this dead horse a million times to no effect). "

Brent,
  Gee! I didn't know you cared!! 

  Actually tho I hope you keep discussing this SD thing even tho the Forums program seems to be giving you fits. Keep hacking away at it.

  I'll go along with the SD thinking as being valuable, and I'm beginning to see that it is more important than ES in figuring out if one load is better than another.

  I think our disagreement is in the statiscal analysis part where you've told me you need a 100 shots to be meaningful, statistically, when I figure three or four five shot groups will tell me all I need to know about that load.

  The way I'm seeing it now is that SD will tell me more postively that what I see with those three or four groups is true. Thus if on succesive days under varying conditions I'm not able to shoot up to the norm the SD's will tell me that, in fact, it's me, or the conditions, and not the load.

  The work I just got done doing with the .38/55 tho shows how you can have nice SD's that should indicate that you should be shooting around that MOA mark or under, but in reality are getting 5 + MOA. You just can't use SD's, or statistical analysis to figure out where the problem is. You can only use it to verify when you have the problem under control.

PETE