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Difference between revisions of "Shannon"

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[[Validate output by making calculations by hand]]
 
[[Validate output by making calculations by hand]]
  
'''Example Calculations'''
 
  
 +
'''Example Calculations'''
  
'''''*shannon*'''''
+
'''''*.shannon'''''
 
   
 
   
 
These files give the classic Shannon-Weaver Index of diversity.
 
These files give the classic Shannon-Weaver Index of diversity.

Revision as of 15:55, 14 January 2009

Validate output by making calculations by hand


Example Calculations

*.shannon

These files give the classic Shannon-Weaver Index of diversity.


<math>H_{Shannon} = - \sum_{i=1}^{S_{obs}} \frac{S_i}{N} ln \frac{S_i}{N} </math>


For the Amazonian dataset the Shannon Index is 4.35.

To obtain the 95% confidence interval we assume that the variance is normally distributed and can be calculated as


<math>var\left ( H_{Shannon} \right ) = \frac {\sum_{i=1}^{S_{obs}} \frac{S_i}{N} \left ( ln \frac{S_i}{N} \right )^2 - H_{Shannon}^{2}}{N} + \frac{S_{obs} - 1}{2N^{2}}</math>


The variance is 0.0020. This gives a lower and upper bound to the 95% confidence interval of 4.26 and 4.44.