Sørensen similarity index

http://en.wikipedia.org/wiki/S%C3%B8rensen_similarity_index

Sørensen similarity index

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The Sørensen index, also known as Sørensen’s similarity coefficient, is a statistic used for comparing the similarity of two samples.
It was developed by the botanist Thorvald Sørensen and published in 1948.

It is often misspelled as Sorenson index, Soerenson index and Sörenson index (also with the correct ending -sen).

Sørensen's original formula was intended to be applied to presence/absence data, and is

where A and B are the number of species in samples A and B, respectively,
and C  is the number of species shared by the two samples;

QS is the quotient of similarity and ranges from 0 - 1.

This expression is easily extended to abundance instead of presence/absence of species.

This quantitative version of the Sørensen index is also known as Czekanowski index.
The Sørensen index is identical to Dice's coefficient^[2] which is always in [0, 1] range.

The Sørensen index used as a distance measure, 1 − QS, is identical to Hellinger distance and Bray Curtis dissimilarity^[3] when applied to quantitative data.

The Sørensen coefficient is mainly useful for ecological community data (e.g. Looman & Campbell, 1960^[4]).

Justification for its use is primarily empirical rather than theoretical (although it can be justified theoretically as the intersection of two fuzzy sets^[5]).
As compared to Euclidean distance, Sørensen distance retains sensitivity in more heterogeneous data sets and gives less weight to outliers ^[6].

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