Interesting take on accuracy evaluation of ammunition and gun dispersion.

While this was written from a rifle perspective I see no reason to believe that the concept is restricted to rifles.  The concept is that the accuracy of a firearm is also subject to statistical evaluation.  In essence if your pistol shoots into, say, a 1.5 inch group at 50 yards. Do you really have a 1.5 inch pistol?  The only way to tell is to shoot a series of groups  and determine the average and standard deviation of the gun and ammo combo.  Statistical significance requires about 7 groups and 10 are better…. That becomes a largish sample in a hurry.  
What This  distribution of accuracy means is that your gun and ammo that shoots an average group of 1.5 inch with a standard deviation of .25 inch then the gun is performing within expected performance if it shoots a group at any size from 1.0 inch to 2.0 inch as I can expect 95% of all group sizes within 2 standard deviations from the average.  

If you keep records of your target group testing you can get an idea of your accuracy distribution without shooting 100 rounds per session.  And up I wouldn’t get too wrapped around the axle if my pistol had a bigger average dispersion than within the “X-ring”.  Just be aware that one group doesn’t say much and 10 groups gets notice.  


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This book goes into depth about that. The first edition was published in 1949. Great book.

https://www.abebooks.com/servlet/BookDetailsPL?bi=31639512425&searchurl=an%3Droper%26ds%3D30%26rollup%3Don%26sortby%3D17%26tn%3Dexperiments%2Bof%2Ba%2Bhandgunner

You can quickly prove something is not acceptably accurate (or rather disprove that it is accurate) with a small number of shots.  Most of the time I only have one or two things to test anyway, and if one falls out of the running in 5 shots then I have my answer of what not to do. However "my gun won't hold the 9 ring with XYZ" doesn't sound very impressive in conversation. I didn't prove ABC is a 10 ring group combination, but it's my best choice and I don't have the primers to dig any deeper. 

Some day when I have the resources I'm going to sit down and make a taguchi test and see what that gets me.

Another approach, as discussed in the article below, is to shoot all your test shots into one group. Then you see the dispersion of shots your gun/ammo produced. That, then, is your measure of accuracy.

https://www.ssusa.org/articles/2019/9/25/accuracy-testing-shortcomings-of-the-five-shot-group/

I have seen the ssusa article before, and so only skimmed it this time.  So if I am repeating something from the article I apologize.

The 5x5 matrix, that is, 5, five- shot groups is commonly presented when firearms are tested.  What seems to be lost is what to do with those data.  That specific test is a non-parametric statistical test, which allows for a simplified analysis of the data.  One can take the mean of the groups and add +/- 1/2  of the range (largest - smallest) to yield a 95% confidence interval.  Example:  group ave. is 2" where the smallest is 1.25" and the largest, 3.25", then 1/2 the range is 1", and the 95% confidence interval is 1" to 3".  So, as they say on Rimfire Central "my gun will shoot less than 3" groups all day (if I do my part, of course)" and be fairly confident that is true. I think 5x5 is useful, since we usually load five and shoot five.  Now, some have argued that the first shot may be different, and thrown out of the group (and data set) but as I have argued before, you don't get mulligans on the line.  The command is "...with 5 rounds, load".
Shoot more or less groups of different numbers and the math is different, but concept the same.

Now I present the above from memory, so it might not be entirely accurate, but I don't have my references at hand.  If you really want them, I can get them, but it will be awhile.

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