## What is Simpson’s Diversity Index?

**Simpson’s diversity index **(SDI) measures community diversity. Although it’s commonly used to measure biodiversity, it can also be used to gauge diversity differences of populations in schools, communities and other locations.

The range is from 0 to 1, where:

- High scores (close to 1) indicate high diversity.
- Low scores (close to 0) indicate low diversity.

One of more the useful aspects of the index is to compare two sets of data to see which is more diverse. For example, if one has an SDI of 0.5 and another has an SDI of 0.35, then the set with the SDI of 0.5 is more diverse.

## Calculations

- n = number of individuals of each species
- N = total number of individuals of all species

The following solution steps explain how to solve the problem by hand. I actually used Open Office Math to solve this problem. You can download the ODS worksheet, with the formulas, here.

**Sample question:** What is Simpson’s Diversity Index for the following table of 5 species?

Step 1: **Insert the total number in the set (89) into the formula N (N – 1) and solve**:

N (N – 1) = 89 (89 -1) = 7832

Put this number aside for a moment.

Step 2: **Calculate n(n – 1). **

- Subtract 1 from each individual count (see the third column in the table below).
- Take each answer from (1) and multiply by each n (see the fourth column).
- Add up all the values from (2) to get 6488.

Step 3: Calculate D:

- Divide your answer from Step 2 by your answer from Step 1,
- Subtract your answer from 1.

**D = 1 – (6488 / 7832) = 0.17.**

The diversity index for this particular set is 0.17.

**Simpson’s diversity index cannot be negative.** If it is, check your calculations for arithmetic errors.

## References

Beyer, W. H. CRC Standard Mathematical Tables, 31st ed. Boca Raton, FL: CRC Press, pp. 536 and 571, 2002.

Dodge, Y. (2008). The Concise Encyclopedia of Statistics. Springer.

Levine, D. (2014). Even You Can Learn Statistics and Analytics: An Easy to Understand Guide to Statistics and Analytics 3rd Edition. Pearson FT Press

Wheelan, C. (2014). Naked Statistics. W. W. Norton & Company