The score allows the sorting of the descriptors using their discriminant power.
There are three possible sorting methods :
These measures are quantitative assessments of the ability of a descriptor to distinguish between taxa. Here are the formulas and references for these measures. The three discriminant power result of the sum, for all pairs of taxa, of a measure of dissimilarity between taxa for which the descriptor is evaluated.
For the Xper discriminant power, the dissimilarity between two taxa for a descriptor is either 0 or 1 depending on wether they have common descriptor states. In the case of the discriminant power based on the Jaccard dissimilarity index or on the Sokal and Michener index, the dissimilarity between two taxa is comprised between 0 and 1 and depends on the number of common states for a given descriptor.
The discriminant power is calculated using the following parameters:
- the dissimilary according to Xper [Lebbe, 1991] is based on
incompatibility between descriptions. Two taxa are incompatibles (or
dissimilar or discriminated) if for one descriptor there is no common
states of descriptors, i.e. if n11 = 0.
dXper = 1 if n11 = 0
otherwise dXper = 0
- the dissimilarity according to [Jaccard, 1901] take into account at
least the states of the descriptors of one of the two taxa that we
compare.
dJaccard = (n01 + n10) / (n01 + n10 + n11)
Similarity
= (1 – Dissimilarity), i.e. two taxa are even more similar than their
number of common states of descriptors increase.
sJaccard = n11 /
(n01 + n10 + n11)
- the dissimilarity according to Sokal & Michener [Sokal &
Michener, 1958] between two taxa for one descriptor is measured by
taking into account all the possible states existing for the
descriptor and not only those existing for at least only one of the
taxa.
dSM = (n01 + n10) / (n00 + n01 + n10 + n11)
Similarity =
(1 – Dissimilarity), two taxa are even more similar if they share
common present and absent states.
sSM = (n00 + n11) / (n00 + n01 +
n10 + n11)