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
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