Sample difference metrics used in ANALOG

In the following equations, n is the number of taxa that are present in both samples to be compared. Subscripted values of s and t denote counts or proportions of taxa in the two samples, respectively. The result d is either a distance measure (low values indicate like samples) or a similarity measure (high values indicate like samples).

Manhattan distance

Squared euclidean distance

Euclidean distance

Canberra distance

Squared chord distance

Squared Chi-squared distance

Jaccard's similarity

where a is the number of taxa that are present in both samples and c is the number of taxa that are present in one sample and absent in the other.

Sorensen's index (similarity)

where a is the number of taxa that are present in the modern sample, b is the number present in the fossil sample, and c is the number of taxa that occur in both samples.

Dot product (similarity)

Correlation (similarity)

where the sums are calculated as i goes from 0 to n-1

Maintained by Peter Schweitzer

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