AMERICAN RIFLEMAN GUN TESTS
It appears that the National Rifle Association, NRA, is reporting gun test information that is not true.
The NRA magazine, “American Rifleman”, (AR), publishes the results of gun tests. These tests include tests for group size, of sets of five, 5-shot groups. (Group Size is the distance between centers of the two furthest-apart target holes in a group.)
The published group size measures, for each set, include: smallest group size, largest group size, and average group size.
The Coefficient of Variation, CV, is the standard deviation / the average.
CV varies with the number of shots per group.
The EXPECTED CV average of group size of sets of five, 5-shot groups is .27. (“A Group Size Model&rdquo
The standard deviation = Range / d sub 2, and d sub 2 for n = 5, 5-shot groups, is 2.326.
(On the Extreme Individuals and the Range of Samples Taken from a Normal Population
L. H. C. Tippett
Vol. 17, No. 3/4 (Dec., 1925), pp. 364-387
d sub 2 = the number of standard deviations that the Range of a sample, from a normal distribution, encompasses; and varies with sample size.)
The AR largest group size / AR smallest group size = the AR Range.
The (AR Range / 2.326) / the AR average group size, = the AR CV = .18.
For 237 AR tests ending with the 12/2018 AR, the average AR CV is .18.
Sample CV values greater than the expected value are explainable; but sample average values less than the expected value are not explainable, by me or anyone to whom the question has been posed.
Similar analyses have been performed on data from the Cast Bullet Association 2015, 2016, 2017 Nationals, from the International Benchrest Shooters 2017 Nationals, from Larry Landerdasper and from my records. In all cases the sample average CV is greater than the expected CV.
My conclusion is that the NRA AR test results are not true, that at least one of the three reported results is false in a large fraction of the tests.
All supporting data is available on request to firstname.lastname@example.org.