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| − | This site explains and demonstrates | + | This site explains and demonstrates statistics for analyzing the precision of projectile weapons firing a single projectile on a vertical target within the line of sight. <ref name="nuance">Typical examples would be target shooting with a rifle or pistol. Such weapons as shotguns, mortars, and ballistic missiles would have some similar characteristics, but also have factors that are neglected in the discussions and measurements.</ref> |
High level topics, which are good places to start exploring the site, include: | High level topics, which are good places to start exploring the site, include: | ||
| − | * [[What is Precision?]] | + | * [[What is Precision?]] |
* [[Describing Precision]]: Units, terms, and relationships | * [[Describing Precision]]: Units, terms, and relationships | ||
* [[Precision Models]]: Statistical approaches for efficient estimation and inference of precision | * [[Precision Models]]: Statistical approaches for efficient estimation and inference of precision | ||
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= Synopsis = | = Synopsis = | ||
| − | When testing a gun, shooter, and/or ammunition the most popular measure is [[Range Statistics#Extreme Spread|Extreme Spread]] or "group size" of a sample of target shots. However Extreme Spread must be used with care since it is frequently and easily abused. As with all measures, the single best | + | When testing a gun, shooter, and/or ammunition the most popular measure is [[Range Statistics#Extreme Spread|Extreme Spread]] or "group size" of a sample of target shots. However Extreme Spread must be used with care since it is frequently and easily abused. As with all measures, the single best sample is meaningless in isolation. The proper statistical estimator is an "average" or expected value of some sort. |
| − | Another consideration is that some measures, such as Extreme Spread, change value when there are more shots in a group. Measures that have such a dependency | + | Another consideration is that some measures, such as Extreme Spread, change value when there are more shots in a group. Measures that have such a dependency are variant measures. There are [[Describing_Precision#Invariant_Measures|invariant measures]], like [[Circular Error Probable]] or Mean Radius, for which the expected values do not change with the number of shots in a group. Instead [[Precision_Models#How_large_a_sample_do_we_need.3F|having more shots only increases the confidence in the measure's value]]. Of course the error of either type of measurement can also be decreased by increasing the sample size (i.e., shooting more groups). |
| − | Furthermore, by first making assumptions about the inherent shot dispersion, then it is possible to use theoretical | + | Furthermore, by first making assumptions about the inherent shot dispersion, then it is possible to use theoretical distributions to estimate measurements and their precision. The distributions are of two basic types. If the expected values and the expected precision factor for the measurements depend on distributions which have a [[Closed Form Precision|closed-form expression]] then the values can be calculated formulaicly. If the values don't have a distribution with a closed form expression then they can be estimated via Monte Carlo approaches. |
[[:Category:Examples|Examples]] of the application of these [[Precision Models|methods]] and [[Measuring Tools|tools]] include: | [[:Category:Examples|Examples]] of the application of these [[Precision Models|methods]] and [[Measuring Tools|tools]] include: | ||
Revision as of 12:55, 24 June 2015
This site explains and demonstrates statistics for analyzing the precision of projectile weapons firing a single projectile on a vertical target within the line of sight. [1]
High level topics, which are good places to start exploring the site, include:
- What is Precision?
- Describing Precision: Units, terms, and relationships
- Precision Models: Statistical approaches for efficient estimation and inference of precision
- Prior Art: Reviews of past efforts to address this question
- FAQ
Synopsis
When testing a gun, shooter, and/or ammunition the most popular measure is Extreme Spread or "group size" of a sample of target shots. However Extreme Spread must be used with care since it is frequently and easily abused. As with all measures, the single best sample is meaningless in isolation. The proper statistical estimator is an "average" or expected value of some sort.
Another consideration is that some measures, such as Extreme Spread, change value when there are more shots in a group. Measures that have such a dependency are variant measures. There are invariant measures, like Circular Error Probable or Mean Radius, for which the expected values do not change with the number of shots in a group. Instead having more shots only increases the confidence in the measure's value. Of course the error of either type of measurement can also be decreased by increasing the sample size (i.e., shooting more groups).
Furthermore, by first making assumptions about the inherent shot dispersion, then it is possible to use theoretical distributions to estimate measurements and their precision. The distributions are of two basic types. If the expected values and the expected precision factor for the measurements depend on distributions which have a closed-form expression then the values can be calculated formulaicly. If the values don't have a distribution with a closed form expression then they can be estimated via Monte Carlo approaches.
Examples of the application of these methods and tools include:
- Determining how many sighter shots you should take.
- Determining the likelihood of a hit on a particular target by a zeroed shooting system.
- Comparing the inherent precision of different shooting systems.
- Determining which ammunition shoots better in a particular gun.
- ↑ Typical examples would be target shooting with a rifle or pistol. Such weapons as shotguns, mortars, and ballistic missiles would have some similar characteristics, but also have factors that are neglected in the discussions and measurements.
