# Difference between revisions of "FAQ"

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[[File:Bivariate.png|400px|thumb|right|Distribution of samples from a symmetric bivariate normal distribution. Axis units are multiples of σ.]] | [[File:Bivariate.png|400px|thumb|right|Distribution of samples from a symmetric bivariate normal distribution. Axis units are multiples of σ.]] | ||

− | The [[Closed_Form_Precision#Symmetric_Bivariate_Normal_.3D_Rayleigh_Distribution|most convenient statistical model]] for shooting precision uses a bivariate | + | The [[Closed_Form_Precision#Symmetric_Bivariate_Normal_.3D_Rayleigh_Distribution|most convenient statistical model]] for shooting precision uses a bivariate normal distribution to characterize the point of impact of shots on a target. In this model the same ''σ'' that characterizes the dispersion along each axis is also the parameter for the [http://en.wikipedia.org/wiki/Rayleigh_distribution Rayleigh distribution], which describes how far we expect shots to fall from the center of impact on a target. |

Shooting precision is described using [[Describing_Precision#Units|angular units]], so [[Closed_Form_Precision#Typical_values_of_.CF.83|typical values of ''σ'']] are things like 0.1mil or 0.5MOA. | Shooting precision is described using [[Describing_Precision#Units|angular units]], so [[Closed_Form_Precision#Typical_values_of_.CF.83|typical values of ''σ'']] are things like 0.1mil or 0.5MOA. | ||

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''σ'' also tells us what to expect from other precision measures. For example, [[Range_Statistics#Example_1|on average a five-shot group has an extreme spread of 3''σ'']]. So if ''σ''=0.5SMOA and we are shooting at a 100-yard target we would expect the extreme spread of an average 5-shot group to be 1.5". | ''σ'' also tells us what to expect from other precision measures. For example, [[Range_Statistics#Example_1|on average a five-shot group has an extreme spread of 3''σ'']]. So if ''σ''=0.5SMOA and we are shooting at a 100-yard target we would expect the extreme spread of an average 5-shot group to be 1.5". | ||

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+ | == What is the best number of shots per group? == | ||

+ | [[File:Extreme Spread Relative Efficiency.png|400px|thumb|right|Relative Efficiency of Extreme Spread estimation by group size.]] | ||

+ | [[Range_Statistics#Efficient_Estimators|Five or six]]. | ||

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+ | If you intend to use "group size" (e.g., Extreme Spread) to estimate precision then you'll spend 13% more bullets shooting 3-shot groups to get the same statistical confidence. | ||

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+ | Four-shot groups are only 3% less efficient than five-shot groups, so practically just as good. | ||

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+ | <br clear=all> | ||

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== How many shots do I need to sight in? == | == How many shots do I need to sight in? == | ||

== How do I tell whether ''A'' is more accurate than ''B''? == | == How do I tell whether ''A'' is more accurate than ''B''? == |

## Revision as of 11:58, 25 May 2014

## Contents

## What is sigma (*σ*) and what does it mean?

*σ* ("sigma") is a single number that characterizes precision. In statistics *σ* represents standard deviation, which is a measure of dispersion, and which is a parameter for the normal distribution.

The most convenient statistical model for shooting precision uses a bivariate normal distribution to characterize the point of impact of shots on a target. In this model the same *σ* that characterizes the dispersion along each axis is also the parameter for the Rayleigh distribution, which describes how far we expect shots to fall from the center of impact on a target.

Shooting precision is described using angular units, so typical values of *σ* are things like 0.1mil or 0.5MOA.

With respect to shooting precision the meaning of *σ* has an analog to the "68-95-99.7 rule" for standard deviation: The 39-86-99 rule. I.e., we expect 39% of shots to fall within 1*σ* of center, 86% within 2*σ*, and 99% within 3*σ*. Other common values are listed in the following table:

Name | Multiple of σ |
Shots Covered |
---|---|---|

1 | 39% | |

CEP | 1.18 | 50% |

MR | 1.25 | 54% |

2 | 86% | |

3 | 99% |

So, for example, if *σ*=0.5MOA then 99% of shots should stay within a circle of radius 3*σ*=1.5MOA.

*σ* also tells us what to expect from other precision measures. For example, on average a five-shot group has an extreme spread of 3*σ*. So if *σ*=0.5SMOA and we are shooting at a 100-yard target we would expect the extreme spread of an average 5-shot group to be 1.5".

## What is the best number of shots per group?

If you intend to use "group size" (e.g., Extreme Spread) to estimate precision then you'll spend 13% more bullets shooting 3-shot groups to get the same statistical confidence.

Four-shot groups are only 3% less efficient than five-shot groups, so practically just as good.