Testing for significant differences between indices

After a diversity index method has been run, a randomisation test for a significant difference in diversity between two samples can be undertaken. The method used is described by Solow (1993). A tutorial of this method is available.

In the diversity index output window, first select the two samples for comparison by left clicking with the mouse on their titles. Both rows will be selected as shown below. Which is sample 1 and which is sample 2 is determined by sample order.

Then click the Comparison button at the top of the window.

This test re-samples 10,000 times from a distribution of species abundances produced by a summation of the two samples. Thus, for large data sets, the procedure may take some time. When the procedure is run, a timer gauge is shown to indicate the progress made. While the test is calculating, if, at any time, the Stop button is clicked, the results of the test up to the calculated number of samples will be displayed.

Summary of the method

1. The diversity of each of the samples is calculated and the difference between these indices (delta) calculated.

2. The two samples to be tested for a significant difference in their index are added together to form a single joint sample.

3. The individuals in this joint sample are then randomly assigned to two samples each of which has the same number of individuals as the actual two samples.

4. The diversity index for each of these generated samples is then calculated and the difference between these indices (delta) is stored.

5. 10,000 random assignments and calculation of delta are undertaken.

6. The observed value of delta is compared against the observed distribution of delta values generated at random to determine if the observed value for the difference between the indices of the two samples could have been generated by random chance.

7. If the observed value of delta is greater than that observed from 95% of the randomisations then a one-tailed test will find sample 1 to be significantly more diverse than sample 2.

8. If the absolute magnitude of the difference is greater than 95% of the absolute differences of the index generated at random then there is a significant difference between the indices.