Difference between revisions of "Glossary"

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(changed definitions of dispersion and precision. Changed H and V to lower case.)
(added definitions for mu and s; fiddled with a couple of others)
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: The horizontal dimension of a target.  Typically synonymous with the ''X'' axis.
 
: The horizontal dimension of a target.  Typically synonymous with the ''X'' axis.
  
; Mean
+
; Mean (Sample Mean)
: The mean of a set of values <math>\lbrace x \rbrace</math> is also called "x-bar" and defined as <math>\bar{x} \equiv \sum_{}^n x_i / n</math>.
+
: The mean of a sample of ''n'' values from the population of values (i.e. the set of all values), <math>\lbrace x_1, x_2, x_3, ..., x_n\rbrace</math>, is also called "x-bar" and defined as <math>\bar{x} \equiv \frac{1}{N} \sum_{i=1}^n x_i </math>.
  
 
; Mean Diameter (MD)
 
; Mean Diameter (MD)
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; [[Angular Size|Milliradian]], a.k.a. mrad or milrad
 
; [[Angular Size|Milliradian]], a.k.a. mrad or milrad
 +
 +
; <math>\mu</math> (Greek letter mu)
 +
: The mean value for the population, as opposed to <math>\bar{x}</math> which is the mean of a sample. In the limit as ''n'' approaches infinity, then <math>\bar{x}</math> approaches <math>\mu</math>.
  
 
; [http://en.wikipedia.org/wiki/Normal_distribution Normal distribution]
 
; [http://en.wikipedia.org/wiki/Normal_distribution Normal distribution]
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; [[Describing_Precision#Radial_Standard_Deviation_.28RSD.29|Radial Standard Deviation (RSD)]]
 
; [[Describing_Precision#Radial_Standard_Deviation_.28RSD.29|Radial Standard Deviation (RSD)]]
 +
 +
; s
 +
: The [http://en.wikipedia.org/wiki/Unbiased_estimation_of_standard_deviation standard deviation] of a set of ''n'' values <math>\lbrace x_1, x_2, x_3, ..., x_n\rbrace</math> which is calculated as:<br />
 +
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<math>s \equiv \frac{1}{N-1} \sum_{i=1}^n (x_i - \bar{x})^2 </math>, where <math>\bar{x}</math> is the sample mean.
 +
:In the limit as ''n'' approaches infinity, then ''s'' approaches ''σ''.
  
 
; <math>s^2</math>
 
; <math>s^2</math>
 
: [http://en.wikipedia.org/wiki/Bessel's_correction#Terminology Unbiased sample variance]
 
: [http://en.wikipedia.org/wiki/Bessel's_correction#Terminology Unbiased sample variance]
  
; Sigma (σ)
+
; σ (Greek letter sigma)
 
: [http://en.wikipedia.org/wiki/Standard_deviation Standard Deviation] (true value of the population, as opposed to a sample)
 
: [http://en.wikipedia.org/wiki/Standard_deviation Standard Deviation] (true value of the population, as opposed to a sample)
 
: Also the parameter for the '''Rayleigh Distribution''', and hence for [[Closed Form Precision]]
 
: Also the parameter for the '''Rayleigh Distribution''', and hence for [[Closed Form Precision]]
  
; Sigma-hat (<math>\hat{\sigma}</math>)
+
; <math>\hat{\sigma</math> (Sigma-hat)
 
: An estimate of '''Sigma (σ)'''
 
: An estimate of '''Sigma (σ)'''
  

Revision as of 18:16, 23 May 2015

Accuracy
Of a gun: The distance between the point of aim and point of bullet impact. Smaller differences reflect greater accuracy. See What is Precision?#Precision vs Accuracy
Colloquially interchanged with Precision.
Bivariate Distribution
\(c_B(n)\) – Bessel Correction Factor
\(c_G(n)\) – Gaussian Correction Factor
\(c_R(n)\) – Rayleigh Correction Factor
Circular Error Probable (CEP)
CEP(p), for p ∈ [0, 1), is the radius of the smallest circle that covers proportion p of the shot group. When p is not indicated it is assumed to be 50%, so by default CEP is the median shot radius.
Chi-squared (\(\chi^{2}\)) distribution
Closed form
Confidence Interval
A range about an Estimate associated with a Confidence Level K. The correct way to read these values is to say, "If we repeatedly computed this Estimate using this same sampling method, we would expect the Estimate to fall within the Confidence Interval K% of the time." Therefore, the smaller the Confidence Interval the closer our Estimate is likely to be to the true value.
Confidence Level K
The probability associated with a Confidence Interval. K ∈ (0, 1), and we expect that in n' estimates n / K' will fall within the Confidence Interval.
Covering Circle Radius (CCR)
Degrees of freedom
Dispersion
A term to denote that shots are spread around the Center of Impact (CoI) without regard to any particular statistical model or measure. Shot groups that have a small spread around the CoI have low dispersion, and shots groups that have a large spread around the CoI have a high dispersion. Thus high precision implies low dispersion. In this mathematical sense precision and dispersion are inversely related.
Estimator
A formula or algorithm for estimating the true value of population parameter from samples of the population
Extreme Spread
When discussing precision, and throughout this site, this refers to Group Size, a Range Statistic defined as the maximum distance between any two shots on a target.
In shooting sports it can also refer to the difference between the highest and lowest value recorded for muzzle velocity.
Figure of Merit (FOM)
Gaussian Distribution
Synonym for Normal Distribution
Group size
Center-to-center distances between the two widest shots on a sample target. Because it is measured from center points it is independent of the caliber of the projectile. In practice this measurement is typically produced from the outside edge of projectile holes in a target and then the projectile caliber is subtracted.
h
The horizontal dimension of a target. Typically synonymous with the X axis.
Mean (Sample Mean)
The mean of a sample of n values from the population of values (i.e. the set of all values), \(\lbrace x_1, x_2, x_3, ..., x_n\rbrace\), is also called "x-bar" and defined as \(\bar{x} \equiv \frac{1}{N} \sum_{i=1}^n x_i \).
Mean Diameter (MD)
Twice the Mean Radius
Mean Radius (MR)
Mean value of the Radius of shots on target.
Minute of Angle (MOA)
Synonym for Minute of Arc, i.e., one arc minute
Mil
One thousandth.
Milliradian, a.k.a. mrad or milrad
\(\mu\) (Greek letter mu)
The mean value for the population, as opposed to \(\bar{x}\) which is the mean of a sample. In the limit as n approaches infinity, then \(\bar{x}\) approaches \(\mu\).
Normal distribution
Radius (r)
Here this almost always refers to the distance of a shot on target from the center, or sample center, of a target group.
If the target is analyzed with polar coordinates this is just the polar radius.
If the shots are recorded with Cartesian coordinates {x, y}, then \(r_i = \sqrt{(x_i - \bar{x})^2 + (y_i - \bar{y})^2}\)
Probability density function (pdf)
Precision
A term to denote how shots are spread around the Center of Impact (CoI), generally in reference to a particular statistical model or measure. Shot groups that have a small spread around the CoI have high precision, and shots groups that have a large spread around the CoI have a low precision. Thus low precision implies high dispersion. In this mathematical sense precision and dispersion are inversely related.
Rayleigh Distribution
Radial Standard Deviation (RSD)
s
The standard deviation of a set of n values \(\lbrace x_1, x_2, x_3, ..., x_n\rbrace\) which is calculated as:

     \(s \equiv \frac{1}{N-1} \sum_{i=1}^n (x_i - \bar{x})^2 \), where \(\bar{x}\) is the sample mean.

In the limit as n approaches infinity, then s approaches σ.
\(s^2\)
Unbiased sample variance
σ (Greek letter sigma)
Standard Deviation (true value of the population, as opposed to a sample)
Also the parameter for the Rayleigh Distribution, and hence for Closed Form Precision
\(\hat{\sigma\) (Sigma-hat)
An estimate of Sigma (σ)
Shooter's MOA (SMOA)
Angular measure defined as one inch at a hundred yards.
v
The vertical dimension of a target. Typically synonymous with the Y axis.