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# Coefficient of Community

Megan.Coefficient of Community

The** Coefficient of Community (Jaccard Coefficient) **calculator computes the coefficient based on the number of species in two communities and the number of common species between the two communities.

**INSTRUCTION**: Enter the following:

- (
**S**) This is the number of species in community 1_{1} - (
**S**) This is the number of species in community 2_{2} - (
**c**) This is the number of species in common between the two communities

**Coefficient of Community ****(CC):** The calculator returns the coefficient as a real number. However this can be automatically converted to a percentage via the pull-down menu.

#### The Math / Science

The '''Jaccard index'''^{1}, also known as '''Intersection over Union''' and the '''Jaccard similarity coefficient''' (originally coined ''coefficient de communauté'' by Paul Jaccard), is a statistic used for comparing the Similarity measure and diversity index of sample sets. The Jaccard coefficient measures similarity between finite sample sets, and is defined as the size of the intersection divided by the size of the union of the sample sets:

` J(A,B) = {{|A \cap B|}/{|A \cup B|}} = {{|A \cap B|}/{|A| + |B| - |A \cap B|}}.`

(If ''A'' and ''B'' are both empty, we define J(A,B) = 1.)

0 ≤ J(A,B) ≤ 1

The Coefficient of Community (Jaccard Coefficient) is a coefficient that indicates the degree of similarity of two communities based on the number of species that they have in common. The formula for the Coefficient of Community is:

`"CC" = c/(S_1+S_2-c)`

where:

- CC is the Jaccard Coefficient of Community
- S
_{1}is the number of species in community 1 - S
_{2}is the number of species in community 2 - c is the number of species in common between community 1 and community 2

# References

- ^ The description of Jaccard index is from Wikipedia: en.wikipedia.org/wiki/Jaccard_index