Difference between revisions of "Prior Art"

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= [http://www.public.iastate.edu/~jessie/PPB/Stats/Testing%20loads.htm Danielson, 2005, ''Testing loads''] =
 
= [http://www.public.iastate.edu/~jessie/PPB/Stats/Testing%20loads.htm Danielson, 2005, ''Testing loads''] =
[http://www.public.iastate.edu/~jessie/PPB/Stats/Testing%20loads.htm Brent J. Danielson] suggests that a practical and statistically efficient way to assess and compare precision is to shoot many 2-shot groups and measure the extreme spread of each. (A one-tailed T-test for two samples with unequal variance can be used to test hypotheses.)
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[http://www.public.iastate.edu/~jessie/PPB/Stats/Testing%20loads.htm Brent J. Danielson] suggests that a practical and statistically efficient way to assess and compare precision is to shoot many 2-shot groups and measure the extreme spread of each.
 
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* When one simply wants to assess whether one sample is more precise than another that probability is given by the one-tailed T-test for two samples with unequal variance -- i.e., the spreadsheet function <code>=1-TTEST({Sample1},{Sample2},1,3)</code>.
[[ToDo|This merits inclusion in the current framework: It's only half as efficient (two shots produce 1 sample radius, not two) but it's significantly easier to measure.]]
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* Using the same data it is possible to determine the precision parameter.  It is also noteworthy that the square of the 2-tailed T-Test gives the exact confidence range for which the precision parameters of two samples do not overlap -- i.e., the probability that two samples have different precision parameters is <code>=POWER(1-TTEST({Sample1},{Sample2},2,3), 2)</code>.  This is all illustrated using Danielson's own data set in [[Media:DanielsonExample.xlsx]].
  
 
= Grubbs, 1964, ''Statistical Measures of Accuracy for Riflemen and Missile Engineers'' =
 
= Grubbs, 1964, ''Statistical Measures of Accuracy for Riflemen and Missile Engineers'' =

Revision as of 01:41, 2 December 2013

Danielson, 2005, Testing loads

Brent J. Danielson suggests that a practical and statistically efficient way to assess and compare precision is to shoot many 2-shot groups and measure the extreme spread of each.

  • When one simply wants to assess whether one sample is more precise than another that probability is given by the one-tailed T-test for two samples with unequal variance -- i.e., the spreadsheet function =1-TTEST({Sample1},{Sample2},1,3).
  • Using the same data it is possible to determine the precision parameter. It is also noteworthy that the square of the 2-tailed T-Test gives the exact confidence range for which the precision parameters of two samples do not overlap -- i.e., the probability that two samples have different precision parameters is =POWER(1-TTEST({Sample1},{Sample2},2,3), 2). This is all illustrated using Danielson's own data set in Media:DanielsonExample.xlsx.

Grubbs, 1964, Statistical Measures of Accuracy for Riflemen and Missile Engineers

Statistical Measures of Accuracy for Riflemen and Missile Engineers, Frank Grubbs, 1964: Often referenced, but we haven't been able to find a manuscript.

If anyone can share one please contact David!

Hogema, 2005, Shot group statistics

Jeroen Hogema provides an accessible proof of the equivalence between the symmetric bivariate normal and Rayleigh distributions. He provides extensive examples, simulations, and applications to scoring and load selection, and begins to address the problem of estimating the Rayleigh parameter.

Hogema, 2006, Measuring Precision

Picking the most precise ammo, probably. Jeroen Hogema:

  • Reproduces Leslie’s 1993 results.
  • Confirms that for radius measures it is preferable to incorporate all data at once, not to break them into separate groups.
  • For FOM and ES it is best to generate many groups so as to preserve more data points.
  • Looks at T-tests for significance and shows very large groups are needed to detect statistically meaningful differences.

Leslie, 1993, Is "Group Size" the Best Measure of Accuracy?

Is "Group Size" the Best Measure of Accuracy?, John "Jack" E. Leslie III, 1993. Notes:

  • Extreme Spread: Maximum distance between any two shots in group. Note that this effectively only uses two data points.
  • Figure of Merit (FOM): Average of the maximum horizontal group spread and the maximum vertical group spread. This uses only 2-4 data points depending on the group.
  • Mean Radius: Average distance to center of group for all shots.
  • Radial Standard Deviation: Sqrt (Horizontal Variance + Vertical Variance).
  • Found military using RSD and Mean Radius as early a 1918.

His Monte Carlo analysis shows sample RSD to be most accurate predictor of accuracy, followed closely by Mean Radius. I.e., they can distinguish between loads of different inherent accuracy more accurately and using fewer shots than the other measures.

Siddiqui, 1961, Some Problems Connected With Rayleigh Distributions

Some Problems Connected With Rayleigh Distributions, M. M. Siddiqui, 1961.

Siddiqui, 1964, Statistical Inference for Rayleigh Distributions

Statistical Inference for Rayleigh Distributions, M. M. Siddiqui, 1964. Summarizes and extends Siddiqui, 1961.