• Last Post 09 October 2018
joeb33050 posted this 05 October 2018

I emailed this to 

[email protected]



Statistics and NRA accuracy testing.


The NRA most frequently tests accuracy with a set of five, 5-shot groups.


Group size, the accuracy measure, is the center distance between the two furthest-apart holes in the target, in each group.


With the assumption that shot location is distributed NORMAL, the ratio of largest group / smallest group has been calculated for both shots per group and number of groups per set.


For example, sets of five, 5-shot groups have the largest / smallest ratio  = 1.91, the average over many sets.


This ratio is due to random NORMAL variation alone, unusual effects such as wind and shooter ability would increase the ratio.


My center fire 5-shot average ratio for 121 sets of five, 5-shot groups is 1.97. The expected ratio is 1.91. Actual / expected = 1.97 / 1.91 = 1.03.


My rimfire 10-shot average ratio for 45 sets of ten, 5-shot groups is 2.69. The expected ratio is 2.42. Actual / expected = 2.69 / 2.42 = 1.11.


The Cast Bullet Association National Match results, 2015, 2016, 2017; sets of four, 5-shot groups, (rifle):


100 yards, 118 sets of four groups, actual ratio = 2.05, expected ratio = 1.77, actual / expected = 1.16.


200 yards, 115 sets of four groups, actual ratio = 1.98, expected ratio = 1.77, actual / expected = 1.11.


The NRA, American Rifleman, 198 sets of five group 5-shot tests ending in October 2018:


Pistol, 93 sets of five groups, actual ratio 1.61, expected ratio = 1.91, actual / expected = .84.


Pistol, 105 sets of five groups, actual ratio 1.58, expected ratio = 1.91, actual / expected = .84.


I can think of no reason that NRA actual / expected ratios would have a large-sample, (198), value LESS than 1; and can think of many reasons why it might be GREATER than 1.


I consider the NRA results to be suspect-perhaps / probably false.


(EXCEL workbooks including the data and explanations of the statistics are available, just ask.)


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HuskerP7M8 posted this 09 October 2018

I've never thought much of the NRA's testing protocol and the validity of their results until Joe brought the subject up, but it certainly appears there may be a problem. 

Because I learned long ago when Al Gore invented the internet that it was impossible to believe anything on internet forums, I decided to mine through some of my data in an effort to discover if Joe's hypothesis on the NRA data had any merit.


Rather than use Joe's "Ratio", I decided to use "CV" or "COV" (Coefficient Of Variation). For all practical purposes, it doesn't make a lick of a difference since the two are directly linked due to the math involved in calculating both. 

As regards the Statistical Correlation for Joe's ratio vs the COV, it's 0.9320. A correlation of 0.9320 means the probability is far less than 1 out of 100 that the results are due to random chance.  

Fact is, the correlation is so strong that I can't even find a statistical table that calculates the "True" probability.


For those with any interest, the COV is simply the Standard Deviation divided by the Mean and expressed as a percentage. This percentage is how much "on average" each individual grp differs from another in a "Universal Population".


In a "Universal Population", the COV for 5-shot grps is predicted to be 27%. That percentage has been derived in various ways over several decades and I've always been surprised at how rarely it ever gets mentioned on forums considering how useful and how many potential questions it can answer.  

If you look at the screenshots for the charts I've presented, you'll see that my data set has that same exact COV of 27%  that's predicted for the sample specific tests I've presented.


How about that....this voodoo we call statistics matches actual or empirical data every time! But, and it's a big but, only if you gather enough data!


If say we'd have been using 2-shot grps rather than 5-shot grps, the COV would be approximately 50% and the ratio would increase accordingly to somewhere in the range of 3.00 instead of the 1.91 to 1.98 for Joe and I using the 5-shot grps.


Joe's ratio (1.91) differs from my ratio (1.98), but that's not statistically significant and the quality of my data in a ballistic tunnel may possibly make me lean more towards my ratio than Joe's. I'm not going to add thousands of rds of more data to make that determination, because it's inconsequential.


Regardless of the difference, it's obvious that if Joe's data is correct, the NRA is doing something (?) in its test methodology that I have no explanation for.  


The data I used was randomly selected from over 80,000 rds of  testing I've conducted over many years in the Ballistic Tunnel I constructed a long time ago for the purpose of proving that empirical data always matches Statistical Theory.


The rifle used is from lot testing a Stiller Copperhead action with a Shilen Octagon rifled barrel during May to September of the current year. It consists of 71 (5 x 5-shot grps) or a total of 1,775 rds of various lots of RF ammo.

I could have mined through considerable more data, but it's seem obvious to me after my analysis that the calculations wouldn't have changed the results any, if at all.


“In God we trust; all others must bring data.” “Without data, you're just another person with an opinion.” “If you can't describe what you are doing as a process, you don't know what you're doing.” “It is not enough to do your best, you must know what to do, and then do your best.” W. Edwards Deming (October 14, 1900 - December 20, 1993)

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Ken Campbell Iowa posted this 06 October 2018

... good for you , joe ....  it is too easy in this life to be discouraged from thinking that every little nudge can actually help to make this anthill a better place ....

... hopefully there is still  ::  someone at the NRA  who actually gives a ... darn .... 


Heck it wouldn't hurt them to publish your recent thoughts on expectations of long term accuracy based on short term results ....  they could even have a sidebar on how they themselves consistently beat the odds ....  


geepers when i wuz a kid i wrote a couple questions to the tech crew ... got good answers right back ....

....  still waiting for my reply from modern-era tanyametaskaclan tho ... my suggestions on how to quadruple the NRA membership might have got lost in the mail i spose .....

thanks for your efforts





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