Difference between revisions of "Ragged holes"

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Throughout the rest of this site we assume that we can measure the location of each and every shot on a target.  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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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.
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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, given a target with a ragged hole and a small number of "censored" shots, it is probably adequate to place them evenly inside the hole. If the number of censored shots is large a better solution is to:
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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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# Set ''p'' = proportion of shots that were censored.
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*# Find the radius ''r'' of the smallest circle that covers the ragged hole.
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# Find the smallest sigma such that CEP(p) covers the ragged hole.
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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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*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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The best solution is to avoid this problem in the first place: Shoot no more than three rounds per target, and then aggregate them into a data set.  Software to automate this process exists, e.g.,
 
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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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Another easy and powerful approach is to use [[Prior_Art#Danielson.2C_2005.2C_Testing_loads|Brent Danielson's clever 2-shot method]] of generating and analyzing data.
 

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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