http://ballistipedia.com/index.php?title=Leslie_1993&feed=atom&action=historyLeslie 1993 - Revision history2024-03-28T14:18:05ZRevision history for this page on the wikiMediaWiki 1.31.6http://ballistipedia.com/index.php?title=Leslie_1993&diff=1254&oldid=prevHerb at 21:18, 14 June 20152015-06-14T21:18:01Z<p></p>
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<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>= Leslie, 1993, ''Is "Group Size" the Best Measure of Accuracy?'' =</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>= Leslie, 1993, ''Is "Group Size" the Best Measure of Accuracy?'' =</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>[[Media:Is_Group_Size_the_Best_Measure_of_Accuracy_by_J.E._Leslie_III.pdf|''Is "Group Size" the Best Measure of Accuracy?'', John "Jack" E. Leslie III, 1993]].   </div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>[[Media:Is_Group_Size_the_Best_Measure_of_Accuracy_by_J.E._Leslie_III.pdf|''Is "Group Size" the Best Measure of Accuracy?'', John "Jack" E. Leslie III, 1993]].   </div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;"></ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">'''ABSTRACT:'''</ins></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Compares the following measures as a function of the number of shots per group.</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Compares the following measures as a function of the number of shots per group.</div></td></tr>
</table>Herbhttp://ballistipedia.com/index.php?title=Leslie_1993&diff=1253&oldid=prevHerb: /* Leslie, 1993, Is "Group Size" the Best Measure of Accuracy? */2015-06-14T21:17:11Z<p><span dir="auto"><span class="autocomment">Leslie, 1993, Is "Group Size" the Best Measure of Accuracy?</span></span></p>
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<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>His Monte Carlo analysis shows sample RSD to be most efficient predictor of precision, followed closely by Mean Radius.  I.e., they can distinguish between loads of different inherent precision more accurately and using fewer sample shots than the other measures.</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>His Monte Carlo analysis shows sample RSD to be most efficient predictor of precision, followed closely by Mean Radius.  I.e., they can distinguish between loads of different inherent precision more accurately and using fewer sample shots than the other measures.</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>'''Notes:'''  </div></td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>'''<ins class="diffchange diffchange-inline">Ballistipedia </ins>Notes:'''  </div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div><ol></div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div><ol></div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><li> In discussing Extreme spread measurement Leslie makes the following statement:</div></td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><li> In discussing Extreme spread measurement Leslie makes the following statement: ''Also, by only using data from two shots within the group, it ignores the data represented by the other, more likely to be repeated, shots.''</div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del class="diffchange diffchange-inline"><blockquote></del>''Also, by only using data from two shots within the group, it ignores the data represented by the other, more likely to be repeated, shots.''<<del class="diffchange diffchange-inline">/blockquote</del>></div></td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div> </div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del class="diffchange diffchange-inline">:: </del>This is the right notion, but not quite correct from the point of view of statistics. From a statistical point of view there is the sample size, the number of shots in a group, and an "effective" sample size also known as the degrees of freedom. On average the ES will increase as the number of shots in a group increases. But with each increase in average ES, the next shot is less likely to increase the size <del class="diffchange diffchange-inline">for a random particular group</del>. Thus subsequent shots don't increase the degrees of freedom by 1, but only by a fraction, and <del class="diffchange diffchange-inline">the </del>fraction gets smaller and smaller as the number of shots increases. <del class="diffchange diffchange-inline"> </del></div></td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><<ins class="diffchange diffchange-inline">p</ins>>This is the right notion, but not quite correct from the point of view of statistics. From a statistical point of view there is the sample size, the number of shots in a group, and an "effective" sample size also known as the degrees of freedom. On average the ES will increase as the number of shots in a group increases. But with each increase in average ES, the next shot is less likely to increase the size <ins class="diffchange diffchange-inline">of the ES</ins>. Thus subsequent shots don't increase the degrees of freedom by 1, but only by a fraction, and <ins class="diffchange diffchange-inline">that </ins>fraction gets smaller and smaller as the number of shots increases. <ins class="diffchange diffchange-inline"></p> </ins></div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del class="diffchange diffchange-inline">:: </del>The point  would apply to the Diagonal and the FOM measurements as well.  </div></td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div> </div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><li> Leslie, like Grubbs, estimates MR by sampling the mean of radii.  This is less efficient than using <del class="diffchange diffchange-inline">the Rayleigh estimator on the radii, and than </del>[[Closed_Form_Precision#Mean_Radius_.28MR.29|<del class="diffchange diffchange-inline">computing </del>MR <del class="diffchange diffchange-inline">based on </del>the <del class="diffchange diffchange-inline">sample </del>Rayleigh parameter]].  The latter process is equally and maximally efficient for all invariant measures that are products of the Rayleigh distribution parameter <math>\Re</math> .</div></td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins class="diffchange diffchange-inline"><p></ins>The point  would apply to the Diagonal and the FOM measurements as well.<ins class="diffchange diffchange-inline"></p></ins></div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><li> Leslie compares "load differences" to get a notion of the relative performance of the statistics. Take the analysis with a grain of salt. There are additional considerations to such an analysis. First, different "loads" would probably have different COI's as well as different dispersions. Second, since 5-shot groups are about optimal for ES, then 20 total shots should be shot as four 5-shot groups<del class="diffchange diffchange-inline">. The </del>average of 4 groups would have a much better precision than the ES of one 20-shot group. Third, this analysis ignores fliers.  </div></td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><li> Leslie, like Grubbs, estimates MR by sampling the mean of radii.  This is less efficient than using [[Closed_Form_Precision#Mean_Radius_.28MR.29|<ins class="diffchange diffchange-inline">the </ins>MR <ins class="diffchange diffchange-inline">computed from </ins>the Rayleigh parameter <ins class="diffchange diffchange-inline">fitted to the sample</ins>]].  The latter process is equally and maximally efficient for all invariant measures that are products of the Rayleigh distribution parameter <math>\Re</math><ins class="diffchange diffchange-inline">.</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins class="diffchange diffchange-inline"><li> Leslie notes "The RSD was the most accurate measure I examined for determining the tightest grouping load."</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins class="diffchange diffchange-inline">: But of course, since the simulation is based on the Rayleigh model for which the RSD measurement is essentially the fitted parameter</ins>.  </div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><li> Leslie compares "load differences" to get a notion of the relative performance of the statistics. Take the analysis with a grain of salt. There are additional considerations to such an analysis. First, different "loads" would probably have different COI's as well as different dispersions. Second, since 5-shot groups are about optimal for ES, then 20 total shots should be shot as four 5-shot groups <ins class="diffchange diffchange-inline">since the </ins>average of 4 groups would have a much better precision than the ES of one 20-shot group. Third, this analysis ignores fliers.  </div></td></tr>
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</table>Herbhttp://ballistipedia.com/index.php?title=Leslie_1993&diff=1252&oldid=prevHerb at 20:55, 14 June 20152015-06-14T20:55:49Z<p></p>
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<td colspan="2" style="background-color: #fff; color: #222; text-align: center;">Revision as of 20:55, 14 June 2015</td>
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<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>[[Media:Is_Group_Size_the_Best_Measure_of_Accuracy_by_J.E._Leslie_III.pdf|''Is "Group Size" the Best Measure of Accuracy?'', John "Jack" E. Leslie III, 1993]].   </div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>[[Media:Is_Group_Size_the_Best_Measure_of_Accuracy_by_J.E._Leslie_III.pdf|''Is "Group Size" the Best Measure of Accuracy?'', John "Jack" E. Leslie III, 1993]].   </div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del class="diffchange diffchange-inline">Abstract:</del></div></td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins class="diffchange diffchange-inline">Compares the following measures as a function of the number of shots per group.</ins></div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>* Extreme Spread: Maximum distance between any two shots in group.  <del class="diffchange diffchange-inline">Notes that this effectively only uses two data points.</del></div></td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>* Extreme Spread: Maximum distance between any two shots in group.   </div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>* 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.  Like Diagonal, FoM becomes more efficient than Extreme Spread for larger group sizes.</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>* 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.  Like Diagonal, FoM becomes more efficient than Extreme Spread for larger group sizes.</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>* Mean Radius: Average distance to center of group for all shots.</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>* Mean Radius: Average distance to center of group for all shots.</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>* Radial Standard Deviation: Sqrt (Horizontal Variance + Vertical Variance).</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>* Radial Standard Deviation: Sqrt (Horizontal Variance + Vertical Variance).</div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del class="diffchange diffchange-inline">* </del>Found military using RSD and Mean Radius as early a 1918.</div></td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div> </div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>Found military using RSD and Mean Radius as early a 1918.</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>His Monte Carlo analysis shows sample RSD to be most efficient predictor of precision, followed closely by Mean Radius.  I.e., they can distinguish between loads of different inherent precision more accurately and using fewer sample shots than the other measures.</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>His Monte Carlo analysis shows sample RSD to be most efficient predictor of precision, followed closely by Mean Radius.  I.e., they can distinguish between loads of different inherent precision more accurately and using fewer sample shots than the other measures.</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del class="diffchange diffchange-inline">Note that</del>, like Grubbs, <del class="diffchange diffchange-inline">Leslie </del>estimates MR by sampling the mean of radii.  This is less efficient than using the Rayleigh estimator on the radii, and than [[Closed_Form_Precision#Mean_Radius_.28MR.29|computing MR based on the sample Rayleigh parameter]].  The latter process is equally and maximally efficient for all invariant measures that are products of the Rayleigh parameter <del class="diffchange diffchange-inline">σ</del>.</div></td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins class="diffchange diffchange-inline">'''Notes:''' </ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins class="diffchange diffchange-inline"><ol></ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins class="diffchange diffchange-inline"><li> In discussing Extreme spread measurement Leslie makes the following statement:</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins class="diffchange diffchange-inline"><blockquote>''Also, by only using data from two shots within the group, it ignores the data represented by the other, more likely to be repeated, shots.''</blockquote></ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins class="diffchange diffchange-inline">:: This is the right notion, but not quite correct from the point of view of statistics. From a statistical point of view there is the sample size, the number of shots in a group, and an "effective" sample size also known as the degrees of freedom. On average the ES will increase as the number of shots in a group increases. But with each increase in average ES, the next shot is less likely to increase the size for a random particular group. Thus subsequent shots don't increase the degrees of freedom by 1, but only by a fraction, and the fraction gets smaller and smaller as the number of shots increases.  </ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins class="diffchange diffchange-inline">:: The point  would apply to the Diagonal and the FOM measurements as well. </ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins class="diffchange diffchange-inline"><li> Leslie</ins>, like Grubbs, estimates MR by sampling the mean of radii.  This is less efficient than using the Rayleigh estimator on the radii, and than [[Closed_Form_Precision#Mean_Radius_.28MR.29|computing MR based on the sample Rayleigh parameter]].  The latter process is equally and maximally efficient for all invariant measures that are products of the Rayleigh <ins class="diffchange diffchange-inline">distribution </ins>parameter <ins class="diffchange diffchange-inline"><math>\Re</math> .</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins class="diffchange diffchange-inline"><li> Leslie compares "load differences" to get a notion of the relative performance of the statistics. Take the analysis with a grain of salt. There are additional considerations to such an analysis. First, different "loads" would probably have different COI's as well as different dispersions. Second, since 5-shot groups are about optimal for ES, then 20 total shots should be shot as four 5-shot groups. The average of 4 groups would have a much better precision than the ES of one 20-shot group. Third, this analysis ignores fliers</ins>.  </div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins class="diffchange diffchange-inline"></ol></ins></div></td></tr>
</table>Herbhttp://ballistipedia.com/index.php?title=Leslie_1993&diff=1086&oldid=prevHerb: /* Corrections */2015-06-09T19:59:24Z<p><span dir="auto"><span class="autocomment">Corrections</span></span></p>
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<td colspan="2" style="background-color: #fff; color: #222; text-align: center;">Revision as of 19:59, 9 June 2015</td>
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<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Note that, like Grubbs, Leslie estimates MR by sampling the mean of radii.  This is less efficient than using the Rayleigh estimator on the radii, and than [[Closed_Form_Precision#Mean_Radius_.28MR.29|computing MR based on the sample Rayleigh parameter]].  The latter process is equally and maximally efficient for all invariant measures that are products of the Rayleigh parameter σ.</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Note that, like Grubbs, Leslie estimates MR by sampling the mean of radii.  This is less efficient than using the Rayleigh estimator on the radii, and than [[Closed_Form_Precision#Mean_Radius_.28MR.29|computing MR based on the sample Rayleigh parameter]].  The latter process is equally and maximally efficient for all invariant measures that are products of the Rayleigh parameter σ.</div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del style="font-weight: bold; text-decoration: none;"></del></div></td><td colspan="2"> </td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del style="font-weight: bold; text-decoration: none;">= Corrections =</del></div></td><td colspan="2"> </td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del style="font-weight: bold; text-decoration: none;"></del></div></td><td colspan="2"> </td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del style="font-weight: bold; text-decoration: none;">Ref 3 should it be  '''Stephen''' not Steven (?), and '''Mosin-Nagant''' not Moisin-Nagant(?)</del></div></td><td colspan="2"> </td></tr>
</table>Herbhttp://ballistipedia.com/index.php?title=Leslie_1993&diff=977&oldid=prevHerb: /* Corrections */2015-06-07T00:54:06Z<p><span dir="auto"><span class="autocomment">Corrections</span></span></p>
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<td colspan="2" style="background-color: #fff; color: #222; text-align: center;">Revision as of 00:54, 7 June 2015</td>
</tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l15" >Line 15:</td>
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<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>= Corrections =</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>= Corrections =</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>Ref 3 should be  '''Stephen''' not Steven, and '''Mosin-Nagant''' not Moisin-Nagant</div></td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>Ref 3 should <ins class="diffchange diffchange-inline">it </ins>be  '''Stephen''' not Steven <ins class="diffchange diffchange-inline">(?)</ins>, and '''Mosin-Nagant''' not Moisin-Nagant<ins class="diffchange diffchange-inline">(?)</ins></div></td></tr>
</table>Herbhttp://ballistipedia.com/index.php?title=Leslie_1993&diff=976&oldid=prevHerb at 00:42, 7 June 20152015-06-07T00:42:02Z<p></p>
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<td colspan="2" style="background-color: #fff; color: #222; text-align: center;">Revision as of 00:42, 7 June 2015</td>
</tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l12" >Line 12:</td>
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<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Note that, like Grubbs, Leslie estimates MR by sampling the mean of radii.  This is less efficient than using the Rayleigh estimator on the radii, and than [[Closed_Form_Precision#Mean_Radius_.28MR.29|computing MR based on the sample Rayleigh parameter]].  The latter process is equally and maximally efficient for all invariant measures that are products of the Rayleigh parameter σ.</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Note that, like Grubbs, Leslie estimates MR by sampling the mean of radii.  This is less efficient than using the Rayleigh estimator on the radii, and than [[Closed_Form_Precision#Mean_Radius_.28MR.29|computing MR based on the sample Rayleigh parameter]].  The latter process is equally and maximally efficient for all invariant measures that are products of the Rayleigh parameter σ.</div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;"></ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">= Corrections =</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;"></ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">Ref 3 should be  '''Stephen''' not Steven, and '''Mosin-Nagant''' not Moisin-Nagant</ins></div></td></tr>
</table>Herbhttp://ballistipedia.com/index.php?title=Leslie_1993&diff=975&oldid=prevHerb: test for wiki page about specific paper2015-06-07T00:19:47Z<p>test for wiki page about specific paper</p>
<p><b>New page</b></p><div>= Leslie, 1993, ''Is "Group Size" the Best Measure of Accuracy?'' =<br />
[[Media:Is_Group_Size_the_Best_Measure_of_Accuracy_by_J.E._Leslie_III.pdf|''Is "Group Size" the Best Measure of Accuracy?'', John "Jack" E. Leslie III, 1993]]. <br />
<br />
Abstract:<br />
* Extreme Spread: Maximum distance between any two shots in group. Notes that this effectively only uses two data points.<br />
* 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. Like Diagonal, FoM becomes more efficient than Extreme Spread for larger group sizes.<br />
* Mean Radius: Average distance to center of group for all shots.<br />
* Radial Standard Deviation: Sqrt (Horizontal Variance + Vertical Variance).<br />
* Found military using RSD and Mean Radius as early a 1918.<br />
<br />
His Monte Carlo analysis shows sample RSD to be most efficient predictor of precision, followed closely by Mean Radius. I.e., they can distinguish between loads of different inherent precision more accurately and using fewer sample shots than the other measures.<br />
<br />
Note that, like Grubbs, Leslie estimates MR by sampling the mean of radii. This is less efficient than using the Rayleigh estimator on the radii, and than [[Closed_Form_Precision#Mean_Radius_.28MR.29|computing MR based on the sample Rayleigh parameter]]. The latter process is equally and maximally efficient for all invariant measures that are products of the Rayleigh parameter σ.</div>Herb