Woollcott Smith, Statistics Department, Temple University

Abstract: We propose two very different statistical procedures that have as a common theme the paired comparison or binary outcomes. Thus, both procedures are related to the classical McNemar test for binary paired comparisons.

First an exact unbiased test for the equality of the limiting marginal distributions for bivariate binary Markov chains is found. The distribution of the test statistics under the null hypothesis of equal marginals depends on the classical cell occupancy statistics for the Bose?Einstein model. The method is applied to the comparison of ribosomal DNA sequences.

Second, a new species overlap measure is proposed that uses a paired binary presence-absence comparison. This overlap measure is defined as the probability that, given a randomly selected species is present in at least one of the two communities, it is present in both communities. Standard maximum likelihood methods are used to estimate the parameters of a modified beta?binomial distribution. This leads directly to estimates of the community overlap measure. In an example from decapod communities on coral reefs, it is shown that this new estimate of community species overlap is 50% larger than the commonly used Jaccard measure of species overlap.