Comparing the index of two samples
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A common requirement is to answer the question - Is the observed difference in the diversity or equitability of two samples significant? We can test for significant differences using the randomisation test of Solow (1994). Below we take you through all the stages of the analysis.
First open the data set called tropical butterfly demo.csv
This data set is for the canopy and understory fruit-feeding butterfly communities of a South American rain forest (DeVries and Walla 2001).
Now from the Alpha Diversity tab choose the Shannon Wiener Test ( We could have chosen any other index).
Now left button click on the names of the two samples canopy and understory. A "1" and "2" will appear next to the sample name.
The "1" identifies the first sample in the test results. You can change which is sample "1", as it is simply the first of the two samples you click on. The number assigned to a sample is only important if you are interested in a one-tailed test. This asks the question - Is sample 1 more diverse than sample 2?
Having chosen the sample, now click on the tool bar icon labelled Comparison.
The computation will take some time as the program has to do many resamplings of the data. Finally, the results will be shown.
Delta, the difference between the two indices 2.983-2.641 = 0.34198, is used by the test.
Generally you will be interested in a two-tailed test which asks the question - Is one sample index significantly different from the second sample index?
For our data, none of 10000 simulated pairs of data sets had a delta value with a magnitude greater than that observed, therefore there is no chance that the two samples have the same Shannon-Wiener diversity.
In answer to the question "is sample 1 significantly more diverse than sample 2?", the results of the one-tailed test are also highly significant. Sample 1 is shown statistically to be the more diverse.
In conclusion, using the Solow (1994) randomisation test we have demonstrated that the butterfly diversity of the tropical forest understory is significantly greater than that of the canopy.