I would prefer to shoot more 3 shot groups vs. fewer 5 shot groups but would also like some idea of how my results compare to the standard five shot groups. Is there a prescription for calculating the expected average size of 5 shot groups given the complete data set for the 3 shot groups?

Working from memory late at night, maybe not so good. But I think the group size was expected generally to increase by 40%. Of course the truth is 3 or even 5 shot groups are rather thin to base much upon. Unless you do the average of several of them.

Elsdude,

Sorry that I didn't phrase my question better. I was assuming that the number of groups shot was "big enough", i.e., perhaps a dozen or so(?) for statistical significance. Also that for the dozen or so 3 shot groups, the complete data were available so that one could determine the distribuion around the mean. (I am not knowledgeable about this so maybe I am not using the right vocabulary.), Then, given that information, what would the expected average of a dozen 5 shot groups be?

If the rule of thumb is an increase by 40%, that answers my question. Thanks. I'm not really looking for a fancy result and a rule of thumb is fine.

I can feel a bell curve coming on....

Okay, yeah, so with enough groups to mean something as an average I think it is a 40% difference in 5 and 3 shot groups again working from memory.

Did a quick search and ran across this.

http://www.bobwheeler.com/guns/GroupStat.pdf

This is way worse than a bell curve. Most people likely won't care to delve into it. However, if I understand this correctly, he too shows something at or just below a general group size difference of 40% when going from 3 to 5 shot groups.

http://www.shootingsoftware.com/ftp/Perverse%20Nature%20of%20SD.pdf

This is a little more straighforward. If anyone cares to read about the normal variation among 5 shot group results.

Esldude,

Thanks for the references. I did attempt to wade thru both of them. The first one looks like just what I am after for anwering the question of the expected size of 5 shot groups given a statistically significant number of 3 shot groups but I could not figure out which table or paragraph led to the 40% conclusion. But I am unfamiliar with the vocabulary so help steering me to the portion of the paper that has that information would be much appreciated. It seems like a general enough question so that others are hopefully interested in the answer.

Thanks for your help in this.

Okay, not an expert in this stuff myself. But do know a little bit. Hopefully not a case of a little knowledge being dangerous.

We are interested in the first link mainly in table #12. ES here is extreme spread. Which is how most people measure groups, by using the two furthest apart shots.

Now the funny looking U symbol is Greek letter MU which denotes the average group size. The O with the thing on top is SIGMA which denotes standard deviation.

One standard deviation plus or minus an average will cover 68% of all groups sizes assuming a normal bell shaped distribution. Two standard deviation above and below average will cover 95% of the group sizes.

You wanted the increase in group size, so standard deviations aren't the key to your question. But you see in his example in the first column of table #12, that 3 shot groups averaged 2.42 while 5 shot groups were 3.07 for average. That is actually a 27% increase. I just looked at it and having 40% in mind it looked about right. So I was a in error. His numbers support something close to 30% in general here for the average size difference between 3 and 5 shot groups.

I don't know that I can competently explain the purpose of the several columns which are standard deviation ratios without confusing someone more than I help. If you looked while the numbers increase the difference in extreme spread average stays right around 30% in all those cases going from 3 to 5 shots.

The point of the second link is mainly to make clear that shooting one group doesn't tell you much. When shooting three shots or five shots the group sizes would be expected to vary quite a bit. Only by shooting lots of groups and averaging the size can you be sure of your results.

It may not be clear, but the implication is shooting lots more of smaller groups is a bit more precise than shooting fewer larger groups. By this lets say you are prepared to shoot 45 rounds to figure out your general accuracy. You could shoot 15 groups of 3 shots. You could shoot 9 groups of 5 shots. You could shoot one group of 45 shots. The most repeatable with least error would be 15 groups of 3 shots. If you change ammo and shot 15 groups of 3 shots the comparison of average group size would be the most meaningful this way.

This may seem backwards. In table 12 you might notice that large shot groups have lower relative standard deviations. That means two different 45 shot groups are likely to be more similar in size than two 3 shot groups. But for 45 shots, 15 groups of 3 shots when done twice will average out even closer together than two 45 shot groups if the conditions don't change.

The other thing to notice is you really need to fire a fair number of shots to get repeatable results which don't vary so much as to be meaningless. 30 is good, 50 is better. The benefit beyond 50 shots becomes pretty small. Best is probably a series of 2 shot groups. 25 groups of 2 shots averaged will be pretty good as an indicator of accuracy in a rifle. But you see little of that. Another poster reported using 2 shot groups for ammo evaluation I think in the thread at the top of on rimfire ammo testing.

Here is that method. Works too I have tried it.
http://www.public.iastate.edu/~jessie/PPB/Stats/Testing%20loads.htm

I think if you are willing to do 25 2-shot groups and average the size you will get almost as much benefit without doing the extra calculations. Though they are simple to do with Excel.

If you care to read Saeed's rimfire ammo test you will see a lively discussion. It is my opinion Saeed's efforts are not helping much because it is not properly conceived. Others have differing opinions. I don't intend any denigration of Saeed's effort personally, just that done differently his efforts could have born better fruit.

Esldude,

Thanks! You gave a very nice clear explanation and I appreciate it. I think that lots of us will benefit from the kind of discussion that you and (I believe ) Brent provided. It will certainly change the way that I do things.

Daryl

esldude,

Very good explanation! (I'm a math and statistics teacher) I'm actually going to use this post and make it into a problem/lesson for my AP statistics class.

Thanks for the compliments guys.

If this helps explain things use it freely. I feel flattered as I don't make my living as a mathematician. Glad it was clear to other people.

quote:

Originally posted by Esldude:
If you care to read Saeed's rimfire ammo test you will see a lively discussion. .

Not to knock statistics as such, or even higher learning, but my problem is I can't see the practical relivance.
EG, If your trying to show in some way the fall of the next shot or the next 3 whatever, I don't give a damn what Excel says. Excel doesn't know that I am going to pull that/those shots,or the wind may differ, or the ammo/barrel/bedding etc is going to throw a wobbley. I think most people shooting groups have to put up with the odd "flyer", and stats. may well show a group getting bigger gradually, but some of mine get NO bigger for 5 shots after the first three. Figger that out Excel!

Been there done that JAL. Even explained it to you in the other thread a couple times at least. Only you refuse to see it.

Check the second link above about variance between groups. That should explain it well enough. Again, unless you refuse to see it.

Statistics, Excel, whatever can figure that out. Why can't you?

Sometimes, your first two shots will be the furtherest apart. You might fire 20 or 50 shots and have the same group size. Doesn't happen often, do it enough, it will happen. And the stats show nothing different. You just have to understand what probabilities tell you.

If one is contemplating an ammo test it would behoove the tester to obtain a Winchester Model 52a,52b or 52c.

[QUOTE]Originally posted by Esldude:


Statistics, Excel, whatever can figure that out. Why can't you?
QUOTE]


Stuff Excel, when I want a group size I'll go and shoot my own.

Wow, that much fussing and math can knock all the fun out of shooting real quick.

I took statistics all the way up through grad school and that's the last thing I want to do while shooting.

Given, rimfires can be very individual on the ammo they prefer but I just grab a few boxes, shoot some groups and see what each gun likes. In fact I have a whole "range kit" of different ammo brands I keep handy to try in new guns I'm playing with.

If I had to start calculating the standard deviation, confidence interval, etc. etc. it doesn't seem like much fun at the range.

Kyler

I am not telling anyone you have to do all these statistical calculations. However, they can be done and are relevent to tell you what is worth doing.

You can grab a few boxes and shoot a few groups. But if that is say 3 groups of 5, using the results to pick a good ammo is a crap shoot. You might well get a different asnwer on which ammo is best each time you do it.

You might get slightly more meaningful results shooting 8 groups of 2. You really need to shoot a total of 30 shots or more if you only wish to average groups sizes. The method Brent came up with lets you use a couple of stat routines in Excel so you can get good results with fewer shots. But you either need enough shots or more sophistacated use of data for useful results that don't fool you half the time.

The other thing of relevance is if you don't shoot enough groups and average them, you won't get reliable results. Two, three, four groups won't get it done. You can wish to do it some other way, but it won't work very well.

I guess it just depends on what you're trying to accomplish.

If you're trying to place in every bench rest match and you've invested in the best equipment you must have the absolute tightest shooting ammo possible.

If you're shooting a few varmints, the occational casual match and ammo price is a consideration (color me guilty) then the one that groups "pretty well" for several groups on a few different range days is plenty good enough.

Kyler

JAL,

I just can't follow what you're saying.

Kyler,

I think that I understand your point but my goal is probably different from yours. I want to find out which ammo works well with my 22's and I also want to do some practice shooting with low recoil and expense both for fun and more importantly to make clean kills. I am not a benchrest shooter, but being able to kill small "varmits" or small game cleanly requires more than casual sighting in and selection of ammo. I arrived at this view long ago, since at one point, woodchuck was an important part of our diet. Factory ammunition was then very expensive and significantly less accurate than handloads. My father was a precise sort of guy (a template maker and errors there cannot be easily concealed). He handloaded and tested the results carefully. Consequently he was able to make headshots a long ways out. Without doing that, there isn't much meat left and misses are frequent.

Esldude answered the question that I asked and gave a clear explanation.

quote:

Originally posted by daryldouthat:
JAL,

I just can't follow what you're saying.

Esldude answered the question that I asked and gave a clear explanation.

Well your all set then you can't go wrong.
Heck, do I know what your on about?
We are in the rimfire section arn't we?

Anyway your original title says it all.
"Expected group size".
Well you can "expect" all you like, but Excel will NEVER tell you where your next shot will go when shooting in the field esp. or anywhere else for that matter.
IF you eventually arrive at a theoretical group size slightly less than one you have proven by shooting, you then have to shoot in the real world. Winds, differing ranges, etc. and don't forget yourself. Can you shoot well enough in the field to take advantage of a possible slight improvement of groupings compared to all the other problems of field shooting?
So what I am on about is, Get real.

JAL,

I feel like you have no intention of understanding this. In the past you argue about something and then admit you didn't bother to read or think about it. Don't know what world that makes any sense, but it isn't REAL.

There are many possible errors when taking a shot. One is accuracy potential of the ammo. You can only reduce your chances to miss any given shot by reducing the size of potential errors. One of those is ammo. If you select the most accurate for your purposes and your rifle you are one step closer to making the shot.

No one said this was all that mattered. But it is one part of all that matters. The reason to shoot from a benchrest is too eliminate or minimize other errors. This allows you to uncover the best ammo for your rifle, or too make a tougher shot than could be made off-hand. Then you can work on other things, like your own ability to shoot well. For all I know the poster has done that, and wants the slight edge better ammo gives him.

Your apparent opinion he can have no idea is incorrect. Your apparent opinion that to shoot three 5 shot groups gives him all the information possible is also incorrect.

quote:

Originally posted by Esldude:
JAL,

I feel like you have no intention of understanding this. In the past you argue about something and then admit you didn't bother to read or think about it. Don't know what world that makes any sense, but it isn't REAL. [Quote]

------------------------------------

Well, I quess I'd better explain. I'm not well.
Feels like Cronic Fatigue Syn. Thinking for me is harder than digging post holes when I was young. Then there is the motivation factor.

If you can't explain very simply to me up front just what your on about, I switch off.
You seem to expect people to believe in your system just because you do.

Well I've been shooting and reloading for over 40 years, so you could say I'm kinda set in my ways. You may remember Saeed wouldn't have anything to do with your system, I've never heard of such a thing before, except from you and Brent. EG in the "reloading" site at the moment at the end of page 2, there is a long discussion about "COST of TESTING LOADS for ACCURACY". Now, not one word of STATS.
Why don't you go and save these old reloaders some money? Kindly give up on me.

Now if we're talking .22 Rf. My rifles have either shot quite well enough for ME with the first ammo tried (Anchutz), or quickly shown a marked preference in a particular brand. Then it is my hobby to continue to "prove" this round, AND also to try anything else that comes along.
I am not like a lot of people (esp in the states), that have to find out the best/ own the best/ use the best/ use what some hot-shot uses/ disect everything to the nth degree etc.

I am happy with my mediocrity.

-----------------------------------

[Quote]
Your apparent opinion that to shoot three 5 shot groups gives him all the information possible is also incorrect.

Did I say that? Strange, I never do that myself. RF or CF I am always shooting groups of as little as one shot (if it's continually in the right place), or up to 5/6 shots at once to confirm. Again this is MY hobby. After over 1000 shots thru one of my feral rifles I am still trying different combos. (now primers.)
(and different temps., comming into our summer.

Any theoritical/mental work would NOT be part of my hobby.

I often read that there are three things affecting accuracy:
1) Rifle
2) Ammo
3) Shooter

I would like to add that in the Seattle area there are wicked:
4) Wind gusts

I check the weather on line for the range zip code on the hour that I would be there. 3 miles per hour or less is ok for 100 yards shooting, 6 mph or less is ok for 50 yards.

I have also noticed that the 3 shot group is more a measure of the gun and the 5 shot more a measure of the shooter. The exceptions to this are heat and fouling effects.

I have mostly been shooting 5 shot groups, because that is what I read about on the internet for the last 13 years.

I shoot 3 shot groups in rifles that kick hard, or if I have lots of 30 caliber big game rifles to test in one day.


With 5 shot groups, I have noticed that when with the same gun and load taken to the range many times for many groups there is a spread for :
1) Best group ever = 1/2" nominally
2) Average or median group =1" nominally
3) Worst group ever = 2" nominally

That example would be more typical of a varmint rifle or very good big game rifle. Most of my big game rifles average at least 1.5".


Bart Bobbit keeps telling me to shoot 10 or 20 shot groups, and focus on the worst group as the tell all. He is training for Camp Perry long range shooting, where the shooter is big part.

I have getting varmint or big game rifles ready to go hunting.
For hunting, I care about measuring the average group size with no wind. I want to:
1) Tune up the rifle
2) Tune up the load
3) Sight in the scope
4) Be able to compare this rifle to my other rifles

When I am shooting at varmints, there is usually a wind and some strange distance. I look for the puff of dust and try to correct with Kentucky windage.

But after I have read this thread, I am beginning to think that shooting several 2 shot groups and taking the median, I would have weeded out the flyers and lucky shots.

One problem with that is I have a decade of 5 shot data on my guns. A new system would be apples and oranges.

I could shoot a number of 5 shot groups with rimfire or .223 and take the median group, but I recently got a 270 feather weight barrel that shot a .9" 5 shot group followed by a 2.7" 5 shot group as it heated up and/or fouled.

So maybe my behavior will stay the same, but my interpretation of the data will change.

I have an old Remington 512 with a barrel cut to 18 " and an old Weaver 2.5 that I mounted. If I shoot sub sonics I will get a hole at 25 yards. If I shoot 3, or 5, or 10 rounds I have one hole. Stats are fine, but shooting is better.

I have a Remington 510 with Weaver mounts and an old B&L 2.5x8 scope at 50 yards with Win Power Point ammo, 5 shot groups:
1) 1.85"
2) 0.15"
3) 1.18"
4) 1.10"
5) 1.02"
6) did not shoot


This is an extreme example of throw out the best and worst group to characterize the rifle.

tnekkcc,

There is some truth in your saying 3 shots is the rifle, 5 shots the shooter (or similar to that).

I am sure we have had the feeling after 4 shots are almost one hole. That 5th shot is a little more difficult for fear it will 'ruin' the group.

Two shot groups are very easy. Shoot one careful shot. Shoot one more. Okay, relax and do it again. Another point is variable wind. Easier to shoot one and then another before wind changes. Or if using flags, shoot one, and wait for the same conditions to shoot the second. Reduces a little bit the variable of wind, a little bit the error from lost shooter focus. Becomes more about the rifle/ammo.

At least with rimfire, a nationally known competitor has said he evaluates ammo at 25 yards. Said he has never seen one shoot better at 50 than 25 yards. 25 yards greatly reduces wind effects for evaluation of ammo. Now two shot groups at 25 yards will be very small. Still one ammo will be better than the other. Do 25 two shot groups and you should have a good result for comparison purposes.

Not sure why there is so much resistance to it. Much more than 3 shot groups for some reason. Too easy to claim two shots tells you little. While true, I am talking two shots done many times which is quite different.