AMERICAN RIFLEMAN GUN TESTS

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joeb33050 posted this 17 October 2018

 

 

I emailed this to 

 

[email protected]

today, 10/17/18

 

AMERICAN RIFLEMAN GUN TESTS

 We are interested, here, in the American Rifleman, AR, reported accuracy of sets of five, 5-shot groups.

 The NRA magazine, “American Rifleman”, publishes the results of gun tests. These tests include accuracy tests, generally for group size of sets of five 5-shot groups. Group Sizer is the distance between centers of the two furthest-apart target holes in a group. The group size measures for each set are: smallest group, largest group and average group size.

If we assume that shot location is distributed NORMAL, then we know the relationships between the three AR measures, can calculate the EXPECTED values of some measures, and compare them with RECORD measures.

With the AR RECORD measures and some calculation, we find that:

 The EXPECTED long-term average ratio of largest group / smallest group in sets of five, 5-shot groups is 1.91.

 For 207 AR tests ending with the 10/2018 AR, the average RECORD ratio is 1.595.

 The EXPECTED long-term average of group size of sets of five, 5-shot groups is 1.141.

 For 207 AR tests ending with the 10/2018 AR, the average RECORD average is 1.771.

 Because the differences are so large, the sample sizes are large, and calculations of other reported results support the assumption; I conclude that the AR results are probably false.

(The AR data is similar to describing a room as 12 feet long, 20 feet wide, and 180 square feet.)

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joeb33050 posted this 17 October 2018

 

EXPECTED RATIO, LARGEST / SMALLEST GROUP SIZES

 The EXPECTED ratio of largest group size / smallest group size, in a set of five, 5-shot groups, is 1.91. 

 With average group size = 1;

 CV = stdev / average = stdev / 1 = stdev. CV = stdev

 stdev = R / d sub 2 = R / 2.326

 CV = stdev = R /2.326;

 R = CV * 2.326

 CV for 5-shot group size = .269

 R = .269 * 2.326 = .626 * average group size

 With average group size = 1

 1 + R/2 = EXPECTED largest group size; 1 – R / 2 = EXPECTED smallest group size;

 (1 + R/2) / (1 – R / 2) = EXPECTED ratio, largest group size / smallest group size;

 (1 + (.626 / 2)) – (1 - .626 / 2) = 1.313/ .687 = 1.91

 EXPECTED AVERAGE GROUP SIZE

 Knowing the largest and smallest group size, we can estimate the EXPECTED average group size, and compare EXPECTED and RECORD group sizes.

 the Coefficient of Variation, CV, Standard Deviation / Average, of group sizes, for 5-shot groups, is .27.

  The Range, R, is the (largest group – smallest group).

 Assuming that shot location is distributed NORMAL;

 The standard deviation, stdev, of a set of group size records, = R / d sub 2.

 (d sub 2 varies with the number of group sizes in the set.)

 For sets of five, 5-shot groups; CV = .27, and d sub 2 = 2.326.

 stdev = R / 2.326;

 stdev / average = CV, = .269;

  average = stdev / .269;

 average = (R / 2.326) / .269;

 average = (R / 2.326) * 1 / .269;

 Expected average = R / (2.326 * .269) = R / .626

 A set of five, five-shot group sizes will have EXPECTED average group size = R / .626. The EXPECTED average group size for any ONE set of five, 5-shot groups will vary from R / .626; the average of a LARGE NUMBER of five, 5-shot group size averages will approach R / .626.

 

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joeb33050 posted this 17 October 2018

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Ken Campbell Iowa posted this 18 October 2018

joe, great stuff, making that migraine you are giving me worth it ...

*************

i think you have a slight error in the following line .... digit switching ...

_____   R = .269 * 3.236 = .626 * average group size _______    should be 2.326 ??  = 0.601

the sense is the same though ... good work ...

ken

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joeb33050 posted this 19 October 2018

Ken;

It took a while for me to figure it out. The 3.236 should have been 2.326. The .626 is correct. I can multiply, just can't write. I need all the editing I can get.

Thanks;

joe b.

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Ken Campbell Iowa posted this 19 October 2018

joeb ... uh, 0.269  x 2.236 is 0.601 ...  but you still scored a fuzzy bullseye with your point ... no need to change anything.

ken

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joeb33050 posted this 19 October 2018

kEN, it's .269 X 2.326, which on my slide rule = 0.625694 

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beagle6 posted this 19 October 2018

Think I'll stick with the NRA.Thanks anyway.

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lotech posted this 20 October 2018

I think few of us are mathematical or statistical perfectionists, perhaps to our disadvantage. However, any such disadvantage may indeed be insignificant for most purposes. The simple average of five, five-shot groups does provide some useful information.   

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John Alexander posted this 20 October 2018

lotech,

Absolutely.  Even one five shot group of each when comparing loads may give you fairly reliable information if the difference is big enough. If one group is twice as big it is a pretty good guess (reasonable degree of confidence) that the smaller group indicated the best load. It's when the difference in group sizes is small that we may kid ourselves that we have found the better of the two even if we have shot four of five groups of each load. I tried to show this in my recent post about unlubed bullets when four groups each showed the groups with lubed bullets being 16% larger. Also see “Lube Test” in Fouling Shot #233 where I was led astray even with 5-5 shot groups with each.

As I see it the practical role of statistics to shooters isn’t to inspire them to buy a statistics book or to claim that they need dozens of groups (which is entirely impractical) when trying to find out if upping the powder charge one grain will improve accuracy. 

Instead I think the value of statistics is that it allows statisticians to produce tables like the ones Joe has given us that can help us develop a better “feel” about the PROBABILITY, or likelihood that a test is telling us the truth. That is, giving us some idea of how likely (what level of confidence) the results are right.

To make the best decisions as we struggle to improve our loads or our equipment we need to have a feel for what those probabilities are the same as a good poker or blackjack player needs to understand the appropriate probabilities. If he doesn’t he will make unnecessarily bad decisions and soon be separated from his money.

Without a feel for the probabilities associated with shooting, a shooter may make similar unforced errors. For example, if a shooter has digested the fact that in a string of 5 five shot groups that on average the largest will be 1.9 times the smallest (and sometimes more) he now has a “feel” for how uncertain the measurement of any one group really is.  Although he may have measured it to .01” as .87 in., He understands that .87 may be far from the real accuracy of that rifle/load/shooter combination. This understanding should prevent him from claiming he has a 1-MOE rifle or shooting a series of five shot groups each with a slightly different powder charge and deceiving himself that he has found the best charge.  He understands that he has nothing but the very weakest and most unreliable indicator of what might be a good load.

 

 

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lotech posted this 20 October 2018

John-

Well stated.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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Scearcy posted this 20 October 2018

I don't need no math to tell me what I just seed with mine own eyes.  Now I'll throw away the bad group and put the good group in my billfold. I wonder if I can still get more powder from that lot?

Even most of the math geeks among us wishes it were that simple to identify the best load and repeat our very best groups. Now if I could just figure out why I am the only person who owns rifles that won't shoot under 1/2 moa when other shooters are watching.

This summer the top 3 finishers in our annual 2 day regional match were separated by .003" in the aggregate of all 12 groups. We were all using the same rifles and loads we had used for the past two years.  Records were set. Yet there is a very good chance that none of us were using the best available load for our rifle. This accuracy game is a very strange game.

Sometimes we just need to shoot a groundhog with a 30-30.

Jim

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RicinYakima posted this 21 October 2018

Jim, Were the shooters having fun? Was the shooting condition at least good? Were the shooters comfortable with their rifles and loads? Remember, this is art not science. Best wishes, Ric

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Ken Campbell Iowa posted this 21 October 2018

kinda interesting that:

the first 5 shot group you shoot has only 1 in 10 chance of being your largest or smallest ...  or 10 to 1 that your group IS somewhere in the middle ...

you have to shoot 5 of 5 shot groups before your group has an even chance of being your largest or smallest .

.... and then reduce those above chances by yet about a third ....

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..... Einstein asked " did god have a choice ?  " about how things work ....  and of course BillClinton observed that " it is what it is " ...

these statistics go on with or without us ....  but i think we cast bullet shooters have a better natural feel for what our groups mean .... than, say, ...._guns and ammo_ or _the american rifleman_ ( since 1987 ) ...  i think cast shooters are more interested in how things work ...  than just * bullets as a tool * ....  probably because we HAVE to be ( g ) ...

.... good for us ...

ken
     

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joeb33050 posted this 22 October 2018

kinda interesting that:

the first 5 shot group you shoot has only 1 in 10 chance of being your largest or smallest ...  or 10 to 1 that your group IS somewhere in the middle ...

you have to shoot 5 of 5 shot groups before your group has an even chance of being your largest or smallest .

.... and then reduce those above chances by yet about a third ....

 

I don't get it. With sets of 5 groups, the probability of any group, including the first, being largest, is 1/5.

You're not going Bayesian here Ken, are you?

 

 

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..... Einstein asked " did god have a choice ?  " about how things work ....  and of course BillClinton observed that " it is what it is " ...

these statistics go on with or without us ....  but i think we cast bullet shooters have a better natural feel for what our groups mean .... than, say, ...._guns and ammo_ or _the american rifleman_ ( since 1987 ) ...  i think cast shooters are more interested in how things work ...  than just * bullets as a tool * ....  probably because we HAVE to be ( g ) ...

.... good for us ...

ken
     

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Ken Campbell Iowa posted this 23 October 2018

..... while we are writing queries to the nra techies, i see in my last issue ...that while testing some new SIG ammo, they found that powder that burns completely in short barrels kicks less than powder that leaves some unburned grains to have to blow out of the barrel ....

just thought i would mention this, we certainly could use a LAUGH in these times of unending grief and peril ...

heh

ken

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Ken Campbell Iowa posted this 23 October 2018

joeb .... good one about Bayesians .... bill clinton might not have been totally correct ... maybe "" it "" ... is not always what "" it "" is ... heh ...

kinda like cast bullets ...scary, Eh ??  think i will go hide under my Newtonian bed ...

thanks, i enjoyed that.

ken

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