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<td align="center" width="75" nowrap><a href="join.htm"><font color="#FFFFFF" size="1" face="Arial">JOIN-COUNT</font></a></td>
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<td><a href="validate.htm#Validation of Moran’s I and Geary’s C"><font size="1">Validation
of Moran’s I and Geary’s C</font></a></td>
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<td><a href="validate.htm#Validation of the Join-Count Statistic"><font size="1">Validation
of the Join-Count Statistic</font></a></td>
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<td><a href="validate.htm#Validation of the Local Spatial Autocorrelation (LSA) Statistics – Gi, G*i"><font size="1">Verification of the Local Spatial Autocorrelation (LSA) Statistics</font></a></td>
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<td><a href="validate.htm#References:"><font size="1">References</font></a></td>
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<h1>Rook’s Case Program and Algorithm Validation</h1>
<p><font size="2">The following outlines the published datasets that are used to verify
the operation and correctness of the calculations within Rook’s Case v0.9. Each time
Rook’s Case is modified or altered by myself these datasets are re-analyzed in order
to ensure that the computations are kept correct therein and through the development
process. </font></p>
<h2><a name="Validation of Moran’s I and Geary’s C">Validation of Moran’s I
and Geary’s C</a> <font size="1">||| <a href="validate.htm#top">Top</a> |||</font></h2>
<p><font size="2">Validation of the calculation of Moran’s I and Geary’s C is
most easily done since many other programs calculate Moran’s I and/or Geary’s C.
First, Griffith (1987:37) provides three 3x3 matrices for which he manually calculates
Morans’ I and Geary’s C.</font></p>
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<td align="center" valign="top" width="34%"><font size="2"><b>A</b></font></td>
<td align="center" valign="top" width="33%"><font size="2"><b>B</b></font></td>
<td align="center" valign="top" width="33%"><font size="2"><b>C</b></font></td>
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<td valign="top" width="34%"><img src="rcgifs/image33.gif" WIDTH="94" HEIGHT="80"></td>
<td valign="top" width="33%"><img src="rcgifs/image34.gif" WIDTH="90" HEIGHT="79"></td>
<td valign="top" width="33%"><img src="rcgifs/image35.gif" WIDTH="92" HEIGHT="82"></td>
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<p> </p>
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<td valign="top" width="13%"><font size="2"><b>Scenario</b></font></td>
<td valign="top" width="10%"><font size="2"><b>I</b></font></td>
<td valign="top" width="13%"><font size="2"><b>z-Normal</b></font></td>
<td valign="top" width="21%"><font size="2"><b>z-Randomization</b></font></td>
<td valign="top" width="9%"><font size="2"><b>C</b></font></td>
<td valign="top" width="13%"><font size="2"><b>z-Normal</b></font></td>
<td valign="top" width="21%"><font size="2"><b>z-Randomization</b></font></td>
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<td valign="top" width="13%"><font size="2">a</font></td>
<td valign="top" width="10%"><font size="2">0.5, </font></td>
<td valign="top" width="13%"><font size="2">2.7116</font></td>
<td valign="top" width="21%"><font size="2">2.6726</font></td>
<td valign="top" width="9%"><font size="2">0.333</font></td>
<td valign="top" width="13%"><font size="2">2.8284</font></td>
<td valign="top" width="21%"><font size="2">2.8341</font></td>
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<td valign="top" width="13%"><font size="2">b</font></td>
<td valign="top" width="10%"><font size="2">-0.25</font></td>
<td valign="top" width="13%"><font size="2">-0.5423</font></td>
<td valign="top" width="21%"><font size="2">-0.5345</font></td>
<td valign="top" width="9%"><font size="2">1</font></td>
<td valign="top" width="13%"><font size="2">0</font></td>
<td valign="top" width="21%"><font size="2">0</font></td>
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<td valign="top" width="13%"><font size="2">c</font></td>
<td valign="top" width="10%"><font size="2">-0.875</font></td>
<td valign="top" width="13%"><font size="2">-3.2540</font></td>
<td valign="top" width="21%"><font size="2">-3.207</font></td>
<td valign="top" width="9%"><font size="2">1.8333</font></td>
<td valign="top" width="13%"><font size="2">-3.5355</font></td>
<td valign="top" width="21%"><font size="2">-3.5426</font></td>
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</center></div>
<p><font size="2">The Results From Rook’s Case v0.9 are:</font></p>
<p><font size="2">Scenario A</font></p>
<p align="center"><img src="rcgifs/ver1.gif" alt="ver1.gif (33849 bytes)" WIDTH="400" HEIGHT="327"></p>
<p><font size="2">Scenario B</font></p>
<p align="center"><img src="rcgifs/ver2.gif" alt="ver2.gif (31767 bytes)" WIDTH="400" HEIGHT="337"></p>
<p><font size="2">Scenario C</font></p>
<p align="center"><img src="rcgifs/ver3.gif" alt="ver3.gif (32438 bytes)" WIDTH="400" HEIGHT="341"></p>
<p><font size="2">NOTE: You may notice a small discrepancy with the z-scores between
Rook’s Case v0.9 and the z-scores reported by Griffith, in that, the z-scores for
Geary’s C are positive as reported by Rook’s Case and negative as reported by
Griffith but the absolute values are identical. This is because Griffith uses the negation
of the observed minus the mean divided by the standard deviation. Rook’s Case above
doesn’t use the negation. Griffith presumably uses the negation so that spatial
fields which are negatively autocorrelated (C between 0 and 1) have a negative z-value and
vice-versa. This seems to make sense and so Rook’s Case now reports the negation of
the z-values for Geary’s C, however, either way is correct.</font></p>
<p><font size="2">As a second test of the Rook’s Case v0.9 calculation, a small
section of a DEM
modelii.zip （84个子文件） 
modelii 
MODELII.xla 46KB
datafmt.gif 5KB modelii.htm 5KB modellii2.gif 10KB modellii1.gif 10KB RooksCaseManual usrman install.htm 5KB rcgifs ver1.gif 33KB image33.gif 2KB
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