Shot Group Mean Radius .....

NoSecondBest said:
The three degrees of lies from best to worst:
Lies
Dam*ed lies
Statistics

As posted by a retired statistical/quality engineer. As soon as you start averaging averages, you've covered up a lot of sins.
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Like firearms, statistics is a tool for good and evil. Average of averages is fine if it is explained and understood. It is no difference from aggregated average if the averages have same sample sizes.

Was that said statistician a liar, a damn liar, or worse?

-TL

Sent from my SM-G930T using Tapatalk
 
Opening questions of a statistics class instructor:

If you have one pair each of green, red, white and blue dice, roll each color pair once, which color pair will roll the biggest number? The smallest?
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One has to remember statistics of the sort we are using here are meant to estimate how identical rounds will behave in the future. You want to know something about group size because you want to know how reliably you can hit a certain size of target in the future with that same load. They don't lie. Lying with them is done on purpose by people cherry-picking from among statistics to cite one that, in isolation, appears to confirm a bias they want to claim support for. Misunderstanding significance is a way people can fool themselves about what statistics mean, and in shooting it is usually this latter situation that arises.


TL,

I think a group's radial SD is a Rayleigh distribution. We should check with member Statshooter, who teaches this stuff for a living. You can also look at a group as a bivariate Gaussian distribution, with one distribution on each of two perpendicular axes, assuming you want to keep negative numbers intact to indicate left or right or up or down relative to the mean.

Statshooter always uses 30 round samples and has a good rationale for using this number. I was editing it at one point to put into a sticky. I'm way behind and should finish that and put it up.

If you have an infinitely large sample with either distribution, the median absolute distance from the mean (the distance that contains half the population) is at 0.674 standard deviations, so the 7.5" radius shown by Mehavey for M2 should be at 6.74" by my figuring, but they are in the ballpark and you don't expect to resolve all those decimal places without firing closer to a 1000 round sample. In any event, the mean radius has a constant relationship to the SD in an infinitely large sample, so either is a valid basis for comparing groups.
 
Working in automotive design and reliability, a sample size of thirty was the absolute minimum size used to indicate any level of confidence. The larger the better. That's one of the reasons I simply can't understand why anyone talks about the size of their three shot groups.....it's pretty meaningless. Ten shots is a much better indicator, and even more if you want significant information.
 
NoSecondBest said:
That's one of the reasons I simply can't understand why anyone talks about the size of their three shot groups.....it's pretty meaningless.
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They think 3 is good enough.

Most commercial rifle makers use 3 as the limit for their accuracy claims.

Most rifles start walking shots away from aim point after 3 due to barrels heating (expanding) up.
 
The American Rifleman fires 5 groups of 5 shots per load for 25 shots total with 5 data points. Three shots is not a test.

A single 10 shot group is ONE data point. N=1 not 10.
 
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I think one 25 shot group would be better, proper barrel fit and stress relief assumed. That is 25 data points in my thinking, all relative to one group center.

The centers of each of five 5-shot groups are probably not at the same place relative to the point of aim. That can skew the results to smaller numbers.
 
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fourbore said:
A single 10 shot group is ONE data point. N=1 not 10.
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Any single group, be it a 2 or a 2000 shot group, is a single data point if the data you are collecting is group diameters or group mean locations of the particular shot count fired. But if the data you are collecting is about individual shot locations, each shot is a datum and n then equals the number of shots. So you need to decide what the data is for. The advantage of staying with individual shot locations is you can always combine them to get larger values of n, and with them, higher certainty about the location of the average for an infinite population of shots. That spot has the highest probability of a shot landing on it, so it is where you want your sights set.


Bart B. said:
The centers of each of five 5-shot groups are probably not at the same place relative to the point of aim. That can skew the results to smaller numbers.
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This is key to understanding the nature of the beast. We already know that no two five-shot groups will be the same size. That's true of any shot count smaller than infinity. It's just that how much they differ increases as the shot count gets smaller, and so does how close the average position of those shots (the mean location) is likely to differ from the infinite shot count mean location. The average location of any shot count that is wandering around will also wander around; just less so than the individual shots because it is an average.

So, how much will they wander? The statistic that estimates this is called the standard error. It is found by dividing the standard deviation by the square root of the sample size, n. It is the standard deviation of the value of the mean. So if my groups of five have a radial standard deviation of 0.75 moa at my test range, the radial standard deviation of the center of those groups will be 0.75/√5 = 0.34 moa.
 
Descriptive statistics, including means, modes, medians, standard deviation and standard error are not answers. They are descriptors. Most especially, they are not predictive.

And the Rayleigh, mentioned twice here, relies on the normal, and is not inherently better for calculating these statistics.

I'm not saying you shouldn't take measurements, or pay attention to them, but they don't say all that much about your rifle. They offer a snapshot of you and your rifle, with particular loads on that day.
 
Mean Radius
Mean Radius is a method that the US Ordnance Department uses to measure the accuracy of ammunition. It is defined as:
Mean Radius: is the average distance of all the shots from the center of the group. It is usually about one third of the group size.
To obtain mean radius of a shot group, measure the heights of all shots above an arbitrarily chosen horizontal line. Average these measurements. The result is the height of the center of the group. Then in the same way get the horizontal distance of the center from some vertical line, such as for instance the left edge of the target. These two measurements will locate the group center.
Now measure the distance of each shot from this center. The average of these shots is the Mean Radius
 
If you've already located the shots in the first two measurements, you don't need the last measurement. Just make the horizontal and vertical measurements for each shot in the same shot order so you have the horizontal and vertical locations of each individual hole as a pair. Subtract the mean horizontal value from each hole's horizontal location and the mean vertical value from each hole's vertical location. When you have those pairs of mean differences for each hole, square them, sum them and find the sum's square root. The result is the distance of that hole from the mean. Take the average of those distances for all your holes to have mean radius. Excel makes all that pretty easy to do.

The basic difference between finding a mean distance and finding the standard deviation of that distance is that standard deviation has you average the squares of the mean differences before taking the square root of them all at once. Also, if you use the sample standard deviation method (mean square divided by n-1 before taking the square root) you get a number that makes different sample sizes comparable. With mean radius and population standard deviation (mean square divided by n) the larger shot-count groups average a larger result over the long run, and not the same result.

To get radial standard deviation, use the Excel STDEV.S function to get the SD's for the horizontal and vertical mean differences separately. Square and sum the two SD's and take their square root.
 
The question was what is the definition of "mean radius" not its validity. At one time the US Army used Figure of Merit in lieu of mean radius.
 
That picture in post #33 of 270 shots...

Lake City Army ammo plant regularly used 3 or 4 different lots of bullets in one production run of ammo. One or more lots came from bullet making set of dies producing better quality bullets. The other machines, not so good. Sometimes, different jacket metal was better quality in some machines than others. Bullets made in the best set of dies with best quality jacket metal would shoot most accurate.

Military teams often pulled the 173 gr. FMJBT match bullets from arsenal 7.62 M118 match ammo then seated commercial match bullets in the cases. Sub MOA accuracy at 600 yards was the norm, sometimes almost half MOA.
 
Cosine26 said:
Mean Radius
Mean Radius is a method that the US Ordnance Department uses to measure the accuracy of ammunition. It is defined as:
Mean Radius: is the average distance of all the shots from the center of the group. It is usually about one third of the group size.
To obtain mean radius of a shot group, measure the heights of all shots above an arbitrarily chosen horizontal line. Average these measurements. The result is the height of the center of the group. Then in the same way get the horizontal distance of the center from some vertical line, such as for instance the left edge of the target. These two measurements will locate the group center.
Now measure the distance of each shot from this center. The average of these shots is the Mean Radius
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That is an average not the mean. Close enough for govt work and probably about the same value. The exact definition of mean would be the value where 1/2 the shots were inside and other half are outside.
The reason mean is used: image one shot hit the dirt. You measure and now 20 foot has to get averaged into the the calculation where other shots vary from 0 to 8 inches!
 
I recognize that this not the mean. I was defining the term "Mean Radius" as used by army ordnance. The question was about 7.62 Match ammo as specified by Lake City.

After reviewing my statics reference:
Mean = Average.
Defined as the sum of the values of an event divided by then number of events.

Median is defined as: the value where the number of values above the median value is equal to the number of values below the median without regard to individual values.
In the series below,

19,14,10,-7-6,4,3
The median is Seven

If you had the individual values you could compute te standard deviation
IMHO
FWIW
 
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Definition of MEAN

Sorry for the repeated post

After reviewing my statics reference:
Mean = Average.
Defined as the sum of the values of an event divided by then number of events.

Median is defined as: the value where the number of values above the median value is equal to the number of values below the median without regard to individual values.
In the series below,

19,14,10,-7-6,4,3
The median is Seven

If you had the individual values you could compute te standard deviation
IMHO
FWIW
 
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