Difference between revisions of "Ragged holes"

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The more efficient measures use the location of each and every shot on a target within the calculations for the measurement.  It is possible — and with larger shot groups and/or more precise rifles increasingly likely — that the target will exhibit a "ragged hole" into which one or more shots has disappeared.
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It is possible — and with larger shot groups and/or more precise rifles increasingly likely — that the target will exhibit a "ragged hole" into which one or more shots has disappeared. In statistics this is known as a "center-censored" sample.  [http://stats.stackexchange.com/questions/76533/estimating-variance-of-center-censored-normal-samples A detailed explanation and discussion of the problem is here].  This frustrates the direct calculation of [[Describing_Precision#Invariant_Measures|Invariant Measures]] like Mean Radius and Variance, which require the location of each and every shot on a target.  Alternatives:
  
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In statistics this is known as a "center-censored" sample. [http://stats.stackexchange.com/questions/76533/estimating-variance-of-center-censored-normal-samples A detailed explanation and discussion of the problem is here], but presently no good mathematical solutions have come up. This is especially exasperated by the small sample statistics used by shooters. 
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* [[Describing_Precision#Range_Statistics|Range Statistics]] can still be measured directly from a center-censored target.
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* [[Order Statistics]] can also provide good estimates of precision in most cases.
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In practice there are three options.
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* Another alternative is to [[Closed_Form_Precision#Summary_Probabilities|use CEP]] to back into an estimate of ''σ'':
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*# Find the radius ''r'' of the smallest circle that covers the ragged hole.
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(1) The best solution is to avoid this problem in the first place. Shoot few shots per target (i.e. target meaning one POA since some paper targets have more than one POA), and then aggregate them into a data set.  Software to automate this process exists, e.g.,
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*# From ''n'', the number of shots fired, and ''c'' the number outside the circle, calculate the proportion of shots inside that covering circle ''p=(n-c)/n''. This turns the target into a sample with CEP(''r'').
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* [http://ontargetshooting.com/tds/ OnTarget Target Data System] - uses coded target sheets that can be scanned to automatically aggregate one shot per aiming point.
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*Avoid ragged holes by shooting fewer shots per target (meaning per "point of aim" since some paper targets have more than one POA), and then aggregate them into a data set.  Software to automate this process exists, e.g. [http://ontargetshooting.com/tds/ OnTarget Target Data System] offers coded target sheets that can be scanned to automatically aggregate shots across multiple aiming points.
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(2) Use a measure that can be done on a target with ragged holes. In general such measures are not as efficient statistical estimators as those which use all the shot positions. Pragmatically ease of use on the range may outweigh the benefit of being able to use less shots to get the same precision.
 
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(3) It may be possible to "salvage" a target with a ragged hole and get at least some notion of the precision.
 
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:(a) If there are a small number of "censored" shots, place them "evenly" inside the hole.
 
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:(b) If the number of censored shots is large, and there is still a reasonable number outside the ragged hole, then a better solution is to:
 
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:: - Find the smallest hole such that covers the ragged hole.
 
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:: - From n, the number of shots fired, and c the number outside the circle, determine p=(n-c)/n that the radius of CEP(p) for the number of holes censored by the circle.  
 
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:: - Use the experimental CEP(p) measurement to estimate CEP(50) so that the measurement is repeatable.
 
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= Measures On Ragged Holes =
 
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The following measures can be made on targets with ragged holes.
 
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* [[Covering Circle Radius]] - Smallest circle that covers all the shots
 
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* [[Diagonal]] - Conceptualizing the horizontal and vertical range as forming a rectangle on the target, then the measure is the diagonal of the rectangle.
 
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* [[Extreme Spread]] - distant between two widest shots
 
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* [[Figure Of Merit]] - average of the horizontal and vertical range
 

Latest revision as of 13:24, 9 August 2023

It is possible — and with larger shot groups and/or more precise rifles increasingly likely — that the target will exhibit a "ragged hole" into which one or more shots has disappeared. In statistics this is known as a "center-censored" sample. A detailed explanation and discussion of the problem is here. This frustrates the direct calculation of Invariant Measures like Mean Radius and Variance, which require the location of each and every shot on a target. Alternatives:

  • Range Statistics can still be measured directly from a center-censored target.
  • Order Statistics can also provide good estimates of precision in most cases.
  • Another alternative is to use CEP to back into an estimate of σ:
    1. Find the radius r of the smallest circle that covers the ragged hole.
    2. From n, the number of shots fired, and c the number outside the circle, calculate the proportion of shots inside that covering circle p=(n-c)/n. This turns the target into a sample with CEP(r).
  • Avoid ragged holes by shooting fewer shots per target (meaning per "point of aim" since some paper targets have more than one POA), and then aggregate them into a data set. Software to automate this process exists, e.g. OnTarget Target Data System offers coded target sheets that can be scanned to automatically aggregate shots across multiple aiming points.
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