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# Simpson

Validate output by making calculations by hand

***.simpson**

These files give the classic Simpson Index of diversity.

<math>H_{Simpson} = \frac {\sum_{i=1}^{S_{obs}} {S_i \left ( S_i - 1 \right )}}{N \left( N-1 \right )}</math>

For the Amazonian dataset at distance 0.03, the Simpson Index is 0.0044, as shown below.

**File Samples on the Amazonian Dataset**

- .sabund

This file contains data for constructing a rank-abundance plot of the OTU data for each distance level. The first column contains the distance and the second is the number of OTUs observed at that distance. The successive values in the row are the number of OTUs that were found once, twice, etc.

unique 2 94 2 0 2 92 3 0.01 2 88 5 0.02 4 84 2 2 10.03 4 75 6 1 20.04 4 69 9 1 2 0.05 4 55 13 3 2 0.06 4 48 14 2 4 0.07 4 44 16 2 4 0.08 7 36 15 4 2 1 0 1 0.09 7 36 12 4 3 0 0 2 0.1 7 35 12 2 3 0 0 3

- .simpson

The first line contains the labels of all the columns. First numsampled which shows the frequency of the observed calculations. The frequency was set to 10, so after each 10 selected the observed is calculated at each of the distances, with a calculation done after all are sampled. The following labels in the first line are the distances at which the calculations were made, the lci (lower bound of confidence interval) and the hci (higher bound of confidence interval). Note: the entire file is not shown below. Each additional line starts with the number of sequences sampled followed by the simpson calculation at the column's distance and the confidence intervals. For instance, at distance 0.01, after 80 samples simpson was 0.0016, the lci was -0.0002 and the hci was 0.0034.

numsampled 0.01 lci hci 0.02 lci hci 0.03 lci hci 1 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 10 0.0000 0.0000 0.0000 0.0667 -0.0464 0.1797 0.0222 -0.0271 0.0716 20 0.0000 0.0000 0.0000 0.0316 -0.0207 0.0839 0.0053 -0.0078 0.0183 30 0.0000 0.0000 0.0000 0.0161 -0.0082 0.0404 0.0046 -0.0035 0.0127 40 0.0000 0.0000 0.0000 0.0090 -0.0050 0.0230 0.0026 -0.0021 0.0072 50 0.0000 -0.0000 0.0000 0.0073 -0.0020 0.0166 0.0024 -0.0011 0.0060 60 0.0006 -0.0009 0.0021 0.0062 -0.0010 0.0134 0.0017 -0.0008 0.0042 70 0.0015 0.0008 -0.0007 0.0024 0.0046 -0.0008 0.0099 0.0021 -0.0003 80 0.0016 -0.0002 0.0034 0.0041 -0.0003 0.0086 0.0035 0.0003 0.0067 90 0.0012 -0.0002 0.0027 0.0032 -0.0003 0.0068 0.0042 0.0006 0.0079 98 0.0011 -0.0002 0.0023 0.0029 -0.0001 0.0060 0.0044 0.0008 0.0080