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# Shannon

From mothur

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.