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COEFFICIENTS OF ASSOCIATION AND SIMILARITY, BASED ON BINARY (PRESENCE-ABSENCE) DATA: AN EVALUATION
ZDENEK HUBÁLEK,
ZDENEK HUBÁLEK
Czechoslovak Academy of Sciences, Institute of Parasitology, Flemingovo nám. 2, 166 32 Prague, Czechoslovakia
Search for more papers by this authorZDENEK HUBÁLEK,
ZDENEK HUBÁLEK
Czechoslovak Academy of Sciences, Institute of Parasitology, Flemingovo nám. 2, 166 32 Prague, Czechoslovakia
Search for more papers by this authorSummary
Forty-three association (similarity) coefficients were collected and evaluated in this survey. Some of them are synonyms or direct correlates with earlier described indices (A8, A9, A12, A31, A33), others are mere transforms from one range of values to another (A10, A24, A33). Several coefficients are incompatible with suggested admissibility conditions of the minimum-maximum value (A13, A16, A27, A28, A29, A31), symmetry (A1, A2, A13, A16, A26), discrimination between positive and negative association (A27, A28, A31) or monotonicity with (χ2) (A19, to A24); A17 yields very low and erratic values.
As a result, 23 coefficients were excluded and the remaining 20 measures were subjected to an empirical trial on interspecific association data among fungi of the genus Chaetomium, with the use of a cluster analysis. The classification produced five main clusters of related coefficients, with several subgroups. It was then demonstrated that representative indices from different clusters yield different dendrograms of interspecific association among Chaetomium, and A34, A14, possibly also A36 and A40 seemed to be less sensible. A set of measures that generally work well (at least in the interspecific association) comprises A4 (Jaccard), A4 (Dice-Sφrensen), A7 (Kulczyński), A11 (Driver-Kroeber-Ochiai) and, with some reservation A30 (Pearson tetrachoric) and A32 (Baroni-Urbani-Buser). For some purposes, however, other ‘admissible’ coefficients would be more optimal, and the choice of a measure should be related to the nature of the data. It is tentatively suggested that three or so alternative coefficients be used and the results compared on the same data basis; moreover, significance tests on association should be carried out whenever possible.
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