GWarden;

How about a "practical", non-scientific answer to your question? A good number of years ago (when the .222 ruled modern benchrest) I decided that, as a rifleman, I needed at least one REAL rifle to work with. A REAL rifle's definition was created for ME . It turned out to be a heavy varmint class .222 with metalwork by Ferris Pindell and a benchrest fiberglass stock "glue-in" stocked by me.

The rifle was a success. It turned out to be a genuine one-quarter minute rifle (thank you, Ferris). I had no intention of limiting my shooting to benchrest. However, I had determined that to further my shooting education I needed a rifle that did not lie to me.

After some use, in working up loads I determined that three shot groups were useless. A single five shot group was useless. It took three consecutive five shot groups before I decided to either discard the load or it needed further testing. I learned that a single ten shot group was about three times as useful as a five shot group (as far as determining the quality of the load - what we would now call determining the "probabilities"). I also learned that it is derned difficult to maintain absolute concentration for ten straight shots. I suspect that is why modern benchrest shooting is done five shots at a time.

So, I have concluded that 3-5 five shot groups for load development. Then when I have my load, I have learned that I need to practice, during ALL conditions with ten shots on score targets if that is what I shoot at the matches (the ASSRA Schoyen match, for instance). Since it is so hard to shoot ten perfect shots, it is a MUST to practice with ten shots. 

I'll say it again, you must practice in BAD conditions if you want to win matches in the real world. Excellent conditons seldom happen at Etna Green, for instance, and shooting only when the conditions are good is NOT good enough to learn how to win...

FWIW
Dale53

Dale, If you want to compare groups like that, you might think about using binomial testing - commonly called a sign test.

In such cases, you wish to compute the probably that you could get one load to be better than the other for every group, just by chance alone (i.e., assuming there is not a true difference in accuracy between the loads).   

To do this you want to shoot enough groups that you can be sure that when all of them favor one load in particular, that the chances of that happening by chance alone is small.   

This is EXACTLY the same as judging the fairness of a coin in coin toss.  If you tossed a penny three times and it came up heads each time, would you be confident that this coin was NOT fair (ie, that it was biased towards heads)?  The possibility of this happening is 1/2*1/2*1/2 = 1/8 or about 12.5% of the time when you fire three groups of each about 12.5 times out of one hundred such trials, you will get this result.   

Generally, I advocate at least 5 such comparisons.  This gives a probability of 1/32.  But you may have to choose what level of confidence you want.   

Now, if you shoot 5 such pairs of groups and one load wins out 4 out of 5 times what are the odds of that happening even if there is no difference in the accuracy of the loads?  It's a bit more difficult to compute, but some calculators can do it for you (like my ancient HP 15C) or I can give you the figures to compute this quickly in a spread sheet.   

This sort of calculation is exactly what I was thinking about when I suggested that nonparametrics may have a wide range of application to shooting.

Brent

I won't address this to GWarden or Brent, or even Dale53 since they probably know what I think about GWardens question anyway. So this is for the rest of you.

  What I do is to shoot a 5 shot group first. After all, if it shoots an 1 1/2" with 5 shots it's not gonna get any smaller with 10 shots. If a group looks promising then I will repeat it the next day, or, if the chronograph shows it might be promising I'll repeat it. After I have tested a 5 shot group load at least 5 times I'll then try for 10 shots to see if it holds up. But this only comes after I have several promising loads.

  As Dale hints at, the more shots you put into a group the bigger the chance for error to creep in. 5 shots will at least tell you if a load has promise, and if not will allow you to move on to other bullets, loads, and powders. I hate casting, so the fewer I send down range the better I like it!

  After you have selected what you feel is the best load then it's time to practice. Practice does not mean picking the best weather conditions. It means going out on any given day whether the weather is good or not. I do draw the line at getting rained on, but have shot many times when it was raining straight down and I'm under a roof. I've shot in fog, and rain, so heavy you could barely make out the target at 100 yds., and in wind so strong it was blowing things off the bench. I don't know how many times my chronograph has blown over, even with a facing brick attached to the tripod!

  Dale mentions keeping your attention span over a period of ten shots can be difficult. So true if all you're doing is practice! What I do is to always have an experiment of some kind to work with. For me, this forces me to pay attention or else the experiment is wasted. If you don't have something that keeps you interested practice very quickly gets to be boring and you'll soon give it up.

PETE

I've had trouble with variation in group size-sometimes I get small groups and sometimes I get big groups, with the same loads and under the same conditions. 
I did statistics to the problem, and got the solution. The topic, and title of the article, is: Detecting Accuracy Differences."
The answer is a table showing how many five or ten shot groups must be shot to be either 90% sure or 95% sure that there's a difference in two different loads-all varied by the percent of difference.
As I suspected, for small differences in group size a hell of a lot of groups must be shot to be reasonably sure that one load is REALLY more accurate than another.
I've got the article done and am working with The Fouling Shot folks to get it printed there. I will also offer it to the Journal Editor. 
I'm writing this to bring what I previously wrote on this topic to a close, and to offer to e-mail the article to any interested parties.
You won't like the answers, but that ain't my fault.
joe b.
joeb33050@yahoo.com

Joe
I sure would like to get a copy of your paper.
Bob
rthsrdr@iowatelecom.net

Brent,

  Well, you ask a good question. I won't argue that with enuf of the "proper design" in the test it might yield results that can be counted on....... maybe! I don't doubt that SA can be very useful when the conditions of the test can be controlled enuf to get reliable data. I just don't believe this can be done under normal shooting conditions by the average shooter.

  In my last post I mentioned some things that we have no control over that would skew any data results. The other side of the coin is shooter error, unless of course you do all your shooting from a machine rest. That combined with shooting in a vacuum would probably give you meaningful data. Since few of us have access to those two conditions any results you get would be very suspect. It would be like tossing a coin.... Every toss is a 50/50 chance that it will come up heads or tails. No amount of tossing will change those odds in favor of one or the other. The same goes for any group you shoot. No matter how many thousand you would shoot, the odds will be 50/50 that you will have a "good" group for analysis, or not. The question is...... How do you separate out those "good" groups from the "bad" ones?

  So...... I would imagine that everyone "replaces" statistical analysis the way they have for hundreds of years when it comes to shooting. They go out on several decent days and shoot some groups to establish which combo works the best in their guns.

PETE

Joe,

  Perhaps you don't understand my comments because I don't really know what I'm talking about. I am trying to understand, and the comments I make are probably thoughts that many have also, but which you don't connect with since you seem to believe that Statistical Analysis is the only true way to find out a most accurate load.

  To me shooting a dozen, or whatever number you, or anyone else, seems to think needs to be fired in order to get a valid set of data in order to be certain load A is better than load B, just seems to be a waste of time in most cases.

  Now I realise that Statistical Analysis is a very useful tool under the right conditions. I just don't believe that it can be usefully applied to shooting just due to the myriad of factors you have to deal with that can skew the results. Possibly you're right that if I fire enuf groups I will be able to statistically determine that one load is better than another.

  But most anybody on here that has been shooting for a few years can tell within one group whether a load has possibilities. If they have several groups that look good, they can tell within three or four groups on several different days, which is the best and most consistent one. And..... If more than one load is equal to another most would pick the one that's easiest and cheapest to assemble.

  To me there's just no sense blowing off a hundred dollars worth of components to prove statistically what you knew with the expenditure of a coupla dollars worth.

  Bench rest shooters pretty well determine the best load for their guns with as few groups fired as possible since the maximum accuracy life of their barrels is measured in the hundreds of rounds. If they shot as many groups as a Statistical Engineer felt was needed to determine with 95% certainty they had the best load, they would never be able to really find out because their barrel would be shot out long before that 95% certainty factor was reached.

PETE

  Now Joe.... You're confusing what I'm saying. I didn't say Statistical Analysis wasn't useful. Far from it. I'm only saying that I'm not positive it's "reasonably" useful for shooting.

  I've read your purposed article and find it very interesting and hope both the CBA and ASSRA see fit to publish it. It does point up a few of the arguments I've tried to present here. In your articles first example where the average group size difference is 1/4" or 20% difference, you say that a total of 9 groups must be shot in order to attain 95% surety that one load is better than another. This seems reasonable, but experience would tell me in a far shorter time than that which was best for that big a difference. Next you say that if the difference is 10% then 38 groups would have to be shot to achieve 95% certainty. Again. Probably not to  bad. Then you go down to 1% difference in groups where you mention 4050 five shot groups are needed in order to be 95% certain one load is best. Now as you mention this is bordering on the ridiculous and no one would try to achieve it.

  The premise for my whole argument is where do you draw the line between what can reasonably be achieved and what becomes impossible to test for?

  I feel that God gave me a brain to differentiate between what is reasonable, as far as accuracy is concerned, and what is ridiculous in trying to seperate out. If several groups sizes for two different loads are within 1% of each other then a myriad other factors are present that will cloud any difference and would probably cause a greater disparity than 1% anyway.

  What I would like to hear is what is a REASONABLE number of groups that I need to shoot in order to be REASONABLY certain I have the best load.

  Your mention of one guy at a match dancing around because his scores/groups are great, and another is down in the dumps because his are terrible, is exactly what I'm trying to see if Pressure (PA) & Density (DA) Altitude has a bearing on. These good and bad scores/groups are not due to a bad load, because the very next day the emotions of these two shooters might be exactly opposite...... and I've seen that happen. I'll even go so far as to say I've seen it happen before and after lunch, and between early in the morning and late in the afternoon!!

  If you have ever kept an eye on PA & DA you will have seen that it changes from minute to minute, and the changes can be rather astonishing at times. How much of a change is needed in order to affect score/group size at Schuetzen ranges I don't know, but is one of the things I want to find out in the near future. I know it affects sight elevations, but I also want to see if these conditions have a bearing on group size. I think they do, because some experimentation done by Ed Stutz many years ago show that a change in temp. and humidity can mean you need to change your load to compensate in order to maintain the same accuracy. PA & DA are just a refined version of the testing Ed did.

PETE