STATISTICS AND GROUPS

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joeb33050 posted this 01 March 2020

 

STATISTICS AND GROUPS

 This is about groups shot with a rifle or pistol, the measurement of those groups, Statistics applied, and the conclusions that can be made. It’s as simple and non-mathematical as I can make it.

 1 A GROUP SIZE MODEL

 Much of the Statistics here is based on a model of group size, that assumes that groups are round, and that X and Y deviations are distributed random Normal. This model is available on request, should anyone be interested.

  2 GROUP SIZE ESTIMATES

 Sample groups are shot and measured to estimate the population group size. Think of the population group size as the long-term average, average group size of a zillion groups shot. The more groups that are shot, the closer the sample group average is to the population group average.

 Example, 5-shot groups:

 

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joeb33050 posted this 01 March 2020

 

3 ACCURACY DIFFERECES

Is there a difference in accuracy between two loads?

 Select the number of shots per group.

 Shoot both loads, the same number of groups per load.

 Measure group sizes and calculate the average for each load.

 Calculate (Larger Average) / (Smaller Average) = Test Ratio.

  If the test ratio is greater than the table ratio, there probably IS an accuracy difference.

  If the 5 shot 10 group average test ratio is 1.12, we are 85% sure that there IS an accuracy difference.

 

4 EXPECTED AND UNEXPECTED FLYERS

We define, here, EXPECTED flyers as wide shots that are part of the distribution of the other shots; and UNEXPECTED flyers as so wide that they are unlikely to be part of the distribution of the other shots.

Measure the groups with and without the flyer, divide the larger number by the smaller.

If (5 shot group size) / (4 shot group size) is greater than 1.6, then we are 95% sure that the fifth shot is an unexpected flyer.

If (5 shot group size) / (4 shot group size) is greater than 1.8, then we are 99% sure that the fifth shot is an unexpected flyer.

If (10 shot group size) / (9 shot group size) is greater than 1.4, then we are 95% sure that the tenth shot is an unexpected flyer.

If (10 shot group size) / (9 shot group size) is greater than 1.5, then we are 99% sure that the tenth shot is an unexpected flyer.

 

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joeb33050 posted this 01 March 2020

 

5 GROUP SIZE RATIOS

 What is the expected or average ratio, (largest group size) / (smallest group size), in a set of various numbers of groups with various numbers of shots per group?

 

6 GROUP SIZE vs. SHOTS PER GROUP

 What are the expected or average sizes of groups as the number of shots, n, varies?

 

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joeb33050 posted this 01 March 2020

 

7 MEAN RADIUS

 GROUP SIZE is the distance between centers of the two furthest-apart holes in a group.

 MEAN RADIUS is the average distance between the centers of group holes and the group center.

 Some contend that mean radius is a better measure of accuracy than group size; others disagree. The two measures measure the same thing, dispersion; so, they are related through a simple set of values. Like CENTIGRADE and FAHRENHEIT; neither is a “better” measure.

 The measures are related thus:

(GS = group size; MR = mean radius)

 

 

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joeb33050 posted this 01 March 2020

 

8 SHOTS PER GROUP

 

Group size increases as the number of shots per group increases. Ten shot group averages are larger than five shot group averages, all other things being equal. The relationships are:

 

Each bullet hole in a target contains a certain amount of information. We can extract only that amount of information, and no more, no matter what arithmetic gyrations we go through.

The accuracy of a measurement of group size DOES vary as the total number of shots fired.

The accuracy of a measurement of group size DOES NOT vary with the number of shots per group.

As an example, 30 shots can be fired from 15 groups of 2, to 1 group of 30. The average or expected plus or minus error-the difference between the actual group size and the test group size, 95% of the time varies as shown. This variation varies little enough to be considered none.

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Bohica793 posted this 01 March 2020

My head hurts after reading all of that.  A lot of great information but not that easy to digest for my mathematically challenged brain.  Thanks Joe.

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John Alexander posted this 01 March 2020

Thanks Joe the tables allow a shooter to have a much better feel for how likely the data in his notebook are giving him the right answer as to which of two bullets, alloys, powder, over all lengths are what the seem to be.

I particularly appreciate the confidence levels down to 75% in number 3.  Statistics usually only mention 90, 95, 99% confidence levels.  But when making a decision if you have 75% confidence of it being right that is much better assurance than a lot of decisions we make in life.

I know that looking at all the tables posted at one time is a bit like drinking from a fire hose. But I think most all our members can understand how to use them if taken one at a time.

I will tape these tables up inside the cabinet doors in my shop for ready reference.

John

 

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