HOW MANY SHOTS PER GROUP?
We test to estimate the long term accuracy of a load. A load, here, is defined as a recipe, a sum of elements; gun, shooter, sight, powder, charge,…   
Here, group size, the center-distance between the two furthest-apart holes in the group, is the accuracy measure.
The “correct” number of shots per group has been discussed and argued about for years.
We test by shooting a number of groups, each with some number of shots per group. We then measure the groups and calculate the average. 
Testing for accuracy results in a set of measurements, and enables us to make statements such as: “Based on this test, we are 95% sure that long term group size = the test average group size +/- some %.”
Although the 95% can be varied easily, here we will use 95%.
We’re left with “+/- some %”, which varies with the number of shots per group.

Example: 120 total shots to be fired. These can be divided such:
SHOTS PER GROUP      NUMBER OF GROUPS      +/- SOME %      
2                  60                  12
3                  40                  11
4                  30                  11
5                  24                  11
6                  20                  11
7
8                  15                  12
9
10                  12                  12
No matter how many shots per group are selected, “+/- some %” remains pretty constant.
Only by varying total shots fired does “+/- some %” vary.
Example: 60 total shots to be fired. These can be divided such:
SHOTS PER GROUP      NUMBER OF GROUPS      +/- SOME %      
2                  30                  17
3                  20                  15
4                  15                  15
5                  12                  15
6                  10                  16
7
8                                    
9
10                  6                  17

The number of shots per group does not vary the precision of the estimate very much, the “+/- some %”. 
Varying the 95% doesn’t vary the outcomes much.
I am happy to send the explanatory EXCEL workbooks to anyone. I’m at joeb33050@yahoo.com.

   Shooting groups and measuring "extreme spread" is statistically naive.  One is then only considering 2 shots out of each group.   It is much more informative to measure mean radius for each impact, which considers each shot. The information obtained is, moreover, more interesting to target shooters, who are concerned with how far each shot is from the center of the target.

CHRIS
RGChristensen

rgchristensen wrote on Sep 4^th, 2018 at 3:34pm:


This is often said and always wrong.

MR and group size are easily interchangeable. 
MEAN RADIUS

     . The Mean Radius, (MR), of a group of shots is the mean or average distance of each shot from the center of the group.
Some contend that MR, is a "better" measure of accuracy than "Group Size", (GS), the distance between centers of the furthest-apart two shots in a group.
MR measurement is very difficult to make and understand; and has no detectable advantage over GS, except to lend an air of expertise to the advocate. 
MR and GS both measure the same thing, accuracy, and thus are the same thing except for a little arithmetic. When you know GS, you know MR; and vice versa. 
This table show the little bit of arithmetic required to change GS to MR, and vice versa,.

Shots per      MR times this      GS times this
group      = GS      = MR
2      1.93      0.52
3      2.40      0.42
4      2.67      0.37
5      2.87      0.35
6      3.02      0.33
7      3.14      0.32
8      3.24      0.31
9      3.32      0.30
10      3.40      0.29

Example: With 5 shot groups, multiply MR by 2.87 to get GS; multiply GS by .35 to get MR.

Get it?

joeb33050 wrote on Sep 4^th, 2018 at 4:40pm:


Must have been sometime in the '50s when gun mag reports of accuracy testing began shifting from the traditional 10-shot groups, which had previously been the "standard," to 5-shot groups; the purpose being, I presume, to save shooting time.   

If not done in a controlled environment it is really all meaning less. Error factors for shooter ability, wind, mirage etc. when taken into consideration = totally false findings.

joeb33050 wrote on Sep 4^th, 2018 at 4:31pm:

For me, the interesting part would be the shooter's comments about what it's like to collect the data from multiple 120 shot strings from say a 45-70. I'd think the only way to convert down range targets into pure stats would be with test barrels on machine rest setups in a tunnel, with all sorts of controls and reconfirming. I'm probably not thinking this through right.

Cat_Whisperer wrote on Sep 4^th, 2018 at 9:24pm:


I shot a few, what do you want to know? 

BTW, I shoot 10 shot groups because that is what it take to make 250 

Looks like Brent Danielson has been teaching statistics again.