What Does 0.5 MOA Mean?

[seymour fish]

Charlie, I don't think there is any point in statistical analysis of groups/scores without establishing a Baseline re: the mechanics of firing shots (bags , rest, bipod, hood of truck, national champ shooter vs nitwit, etc), and secondly, firing in a standardized condition (tunnel, happy mirage and flags ie steady, direction of wind, atmospherics the system is tuned for, etc, etc). Until you become aware of, and manage to isolate all the variables, you are 'shooting in the dark' IMHO. Thus garbage in/garbage out. Meaningless. Seymour

 

[DWalt]

No question that shot groups follow a normal Gaussian distribution, and that is what my dispersion simulation is based upon. The advantage of a Monte Carlo simulation as I have performed is that is based upon a pre-established CMD, and the average ES for each group of N shots is referenced to that CMD. What it does through a brute force method is to determine how many groups are required of group size of N shots are required to obtain an average ES with high precision. As discussed, firing five 10-shot groups and averaging the respective ES values establishes with less than a 5% SD what the "true" mean ES of a 10-shot group is for a given CMD. The CMD/ES ratio is the CMD multiplier, true for any CMS. The same can be done for any group size (shots/group). What it clearly shows is working with group sizes much less than 10 shots is a wasteful exercise as far more shots than necessary are required to establish a statistically reliable mean ES. It also shows that as few as 40 to 50 shots is adequate to establish a reliable mean group ES if N is between 10 and 20 shots, but many more are required if smaller values of N are used.

 

[dcali]

Here's what I'm not following. It sounds like you're suggesting that the best answer is always to shoot one huge group. Which method is going to give you a better confidence of the population standard deviation - the ES of one 100-shot group or the ES's of ten 10-shot groups?

 

[DWalt]

Not at all. I never once suggested shooting one big group (i.e., large numbers of shots per group), as you say, although firing a single 100-shot group would give you an almost certain result in which ES = CMD. As I noted, a 100 shot group has a CMD multiplier calculated as 1.05, close enough to 1.0. However, you can get equivalent results from my suggested use of five (or more if you wish) 10-shot groups and averaging all ESs which uses half the ammunition. I believe shooting five 10-shot groups and averaging the ESs is more practical than firing fewer and larger groups or more and smaller groups. I'd even stretch it to say that three (or more) 15-shot groups would also be OK. But I can never advocate using three-shot of five-shot groups for purposes other than for sighting in. There is just too much group-to-group variability to base grouping determinations upon.

None of this concerns competitive target shooting, wind direction or velocity, sand bags, scope power, or anything else of an environmental nature - only that all shots be fired in a consistent manner under the same conditions from the same gun by the same shooter using the same cartridge loading. The purpose is to recommend a viable methodology to more precisely evaluate the grouping performance differences among different cartridge loads in the same rifle, or possibly differences between/among different rifles firing the same cartridge loads. And I also believe the concept of being able to estimate the CMD and CEP from the average ES for different group sizes has practical applications for many.

 

[dcali]

OK. that makes sense. I don't mean to put words in your mouth - just trying to understand. What would be a really cool analysis would be the best way to shoot X bullets to get the highest confidence in the standard deviation, and what that uncertainty is. So if I a only willing to shoot 40 rounds, for example, how should I shoot them (x groups of y rounds) and what have I lost (confidence-wise) relative to shooting 50 rounds optimally (or 60 or 70 or 20).

Does that make sense? My stats knowledge is rusty.

 

[DWalt]

2 X 20 would be good for 40 shots. I just like more groups. CMD multiplier is 1.15, and SD is about 4.2% for 2 X 20
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I would be remiss to not mention the proper statistical method to compare grouping performance between different loads or rifles. The use of five groups of 10 shots each is adequate to use this method, which is called the "Student's T-Test" (which is another reason to use five 10-shot groups as a standard procedure).. I will not go into the theory behind the T-Test, as most will not have a statistical background adequate to understand its principles. You can Google T-Test and find out more about it should you desire. However, you really don't need to understand it to use it. It is a built-in part of Microsoft Excel, and is very simple to use in performing a T-Test analysis. Excel "help" will tell you everything you will need to do. The T-Test performs a mathematical comparison of two (or more) sets of data to determine the degree of similarity between the two data sets. Let's say you have fired a set of 50 shots composed of five groups of 10 shots for each of two different loads, under identical conditions, and have determined the ES of each 10-shot group. You will go into Excel, and enter all of the ES data for the first load in five cells one column. The ES data for the second load is similarly entered into the adjacent column. You will need to read the Excel help as to what is to be done next (look for help under "T-Test"), but you will then get a number between zero and one as a result. This number is called the T-Statistic. The smaller the number, the more different the data in the two columns are. I cannot give an exact interpretation of the numbers, but if T-Statistic is 0.1 or less, there is certainly a significant statistical difference in the two loads. The closer the T-Statistic gets to 1, the more similar the loads are. In general, I'd say (my opinion) that if the T-Statistic is 0.2 or more, there is very little significant difference between the two loads, and if it is 0.1 or less, there is a statistically significant difference between the loads. The mathematics of statistics deals in probabilities and confidence levels, not exactness.

I earlier mentioned my analysis of U. S. Navy lot acceptance testing data for the MK262 5.56 round. This involved firing of five 10-round groups for each of 10 production lots, in each of two test barrels to determine the ES for each group and the average ES for each lot. I went through the exercise of comparing a large sample of groups to each other using the T-Test (not all, as that would require 380 comparisons). I chose 50 comparisons randomly as being more manageable. As it turned out, in 47 comparisons, there was no significant statistical difference in grouping performance noted between different lots and different test barrels. Only three comparisons had a T-Test statistic indicating a statistically significant difference. That is nearly phenomenal, and speaks very highly of the manufacturing quality control exercised by Black Hills. Even so, none of the lots failed the Navy's grouping requirements. The Navy is completely sold on this grouping acceptance test method vs use of all the other possible comparisons, such as horizontal plus vertical standard deviation, diagonal, figure of merit, mean radius, or anything else of a similar nature, as they just do not add any practical value or advantage to the comparison beyond the much simpler ES measurement, and are much more difficult and time-consuming to apply. I agree with that opinion wholeheartedly.

 

[Joe Salt]

Man you guys have to try real world shooting! Last year I shot 11.6758 Ave. for 100 rounds in L.G. at 1000 yards in what ever condition I had. And 11.0921 with my H.G. Score I finished 5th with an 89.5 ave. And I feel my guns will shoot with the best of them, given the right conditions. Just because your gun shot 4.5" one day doesn't mean you are going to do it day after day, I don't care how good you are.

joe Salt

 

[CharlieNC]

You got it Joe. Just returned from the range to prep for the Bang Steel long range praciical match coming up next Sat. My damn range is closed this week for ''enhancements'.

 

[Joe Salt]

You are lucky are's is still snowed in! This has been a long winter, I've got all kinds of thing going through my head I want to try. Maybe April! There I go wishing my life away.

Joe Salt