Monte Carlo simulation of selected binomial similarity coefficients; II, Effect of sparse data

Abstract

Binary similarity coefficients are applied widely to many types of paleontological data. Unfortunately, many of these paleontological data sets are (i. e., contain substantially more than 50% zeros, or absences, in the data matrix). We have run a series of Monte Carlo simulations with sparse data (10% or p = 0.10) on a series of selected coefficients that have been tested previously using 50% 1 s, or p = 0.50 (Archer and Maples, in press). In decreasing order of ability to approximate the mean of the sparse-data binomial (0.10) and general utility, we rank the coefficients tested as Dice, Braun-Blanquet, Simpson, Jaccard, Baroni-Urbani and Buser, Simple Matching, and Hamann. This ranking is generally the opposite of thatfor Monte Carlo simulations using 50% 1s or p = 0.50 (Archer and Maples, in press). Because the mean has such a low value, Dice, Braun-Blanquet, Simpson, Jaccard, and Baroni-Urbani and Buser all truncate the lower zones of significance. Therefore, statistically meaningful comparisons of the differences between any two samples cannot be made using these coefficients. This does not render these particular coefficients as useless, as long as it is realized that significantly similar linkages will occur at what would normally be interpreted as abnormally low values, especially in comparison with data in which a greater percentage of 1 s is present. In contrast, the Simple Matching and Hamann coefficients greatly overestimate the mean because the mutual absence of a character or taxon is considered to be a trait in common between any two samples. Because of the shifted mean, lower zones of significance are present; however, all linkages are high-even those that are significantly dissimilar. The mutual absence of one or more characters between any two samples is usually meaningless for most paleontological problems; coefficients should therefore be selected with this in mind.