topic Moran'I Expected value in Spatial Statistics Questions https://community.esri.com/t5/spatial-statistics-questions/moran-i-expected-value/m-p/470475#M1476 <HTML><HEAD></HEAD><BODY><SPAN>Hi evereboy !</SPAN><BR /><BR /><SPAN>I have a mathemathical question.</SPAN><BR /><BR /><SPAN>The tool "Spatial Autocorrelation" use the value of -1/(n-1) with n = number of indexed relation. This formula is also found in wikipedia. </SPAN><BR /><BR /><SPAN>I have not found it in others sources. The formula proposed by Moran is slightly different -(nm-n-m)/(nm(nm-1)) with n an m index of entity</SPAN><BR /><SPAN> </SPAN><BR /><SPAN>In the article from Anselin, he says that E(Ii) = Wij/(n-1)</SPAN><BR /><BR /><SPAN>The simple rule of addition of expected value say that, as I = SUM(Ii), </SPAN><BR /><SPAN>E(I) = -(Sum(Wij))/(n-1)</SPAN><BR /><BR /><SPAN>what do you think ? can you show how we derived -1/(n-1) </SPAN><BR /><SPAN>or is there a old mistake somewhere ?</SPAN><BR /><BR /><SPAN>Thanks !</SPAN></BODY></HTML> Thu, 28 Jun 2012 12:10:14 GMT GillianMilani 2012-06-28T12:10:14Z Moran'I Expected value https://community.esri.com/t5/spatial-statistics-questions/moran-i-expected-value/m-p/470475#M1476 <HTML><HEAD></HEAD><BODY><SPAN>Hi evereboy !</SPAN><BR /><BR /><SPAN>I have a mathemathical question.</SPAN><BR /><BR /><SPAN>The tool "Spatial Autocorrelation" use the value of -1/(n-1) with n = number of indexed relation. This formula is also found in wikipedia. </SPAN><BR /><BR /><SPAN>I have not found it in others sources. The formula proposed by Moran is slightly different -(nm-n-m)/(nm(nm-1)) with n an m index of entity</SPAN><BR /><SPAN> </SPAN><BR /><SPAN>In the article from Anselin, he says that E(Ii) = Wij/(n-1)</SPAN><BR /><BR /><SPAN>The simple rule of addition of expected value say that, as I = SUM(Ii), </SPAN><BR /><SPAN>E(I) = -(Sum(Wij))/(n-1)</SPAN><BR /><BR /><SPAN>what do you think ? can you show how we derived -1/(n-1) </SPAN><BR /><SPAN>or is there a old mistake somewhere ?</SPAN><BR /><BR /><SPAN>Thanks !</SPAN></BODY></HTML> Thu, 28 Jun 2012 12:10:14 GMT https://community.esri.com/t5/spatial-statistics-questions/moran-i-expected-value/m-p/470475#M1476 GillianMilani 2012-06-28T12:10:14Z