TESTING CARTRIDGE VARIATION AND ACCURACY
There are 2 furthest-apart holes that determine group size.
We wish to know if some variation in one cartridge, of five, increases group size with 5-shot groups.
Group size is the distance between the two furthest-apart holes in the target; call the holes A and B.
Call the hole made by the cartridge with variation, V.
The probability that A = V is .2; 20% of the groups will have A = V.
80% of the groups will not have A = V. This 80% has one of the holes = A; 1 of 4 = 25%; 25% of 80% of the groups has V = B.
The summed probability = 20% + (25% X 80%) = 40% of the groups shot will have either V = A or V = B.
If % A or B = V > 40, then the variation probably increases group size.
If % A or B = V ~ 40, then the variation probably does NOT increase group size.
If % A or B = V < 40, then the variation probably reduces group size.