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Using the Beta-Binomial Distribution to Describe Aggregated Patterns of Disease Incidence. G. Hughes, Institute of Ecology and Resource Management, University of Edinburgh, West Mains Road, Edinburgh EH9 3JG, Scotland, UK; L. V. Madden, Department of Plant Pathology, Ohio Agricultural Research and Development Center, Ohio State University, 1680 Madison Avenue, Wooster 44691-4096. Phytopathology 83:759-763. Accepted for publication 22 February 1993. Copyright 1993 The American Phytopathological Society. DOI: 10.1094/Phyto-83-759.

We discuss the use of the beta-binomial distribution for the description of plant disease incidence data, collected on the basis of scoring plants as either “diseased” or “healthy”. The beta-binomial is a discrete probability distribution derived by regarding the probability of a plant being diseased (a constant in the binomial distribution) as a beta-distributed variable. An important characteristic of the beta-binomial is that its variance is larger than that of the binomial distribution with the same mean. The beta-binomial distribution, therefore, may serve to describe aggregated disease incidence data. Using maximum likelihood, we estimated beta-binomial parameters p (mean disease incidence) and ϑ (an index of aggregation) for four previously published sets of disease incidence data in which there were some indications of aggregation. Goodness-of-fit tests showed that, in all these cases, the beta-binomial provided a good description of the observed data and resulted in a better fit than did the binomial distribution. The relationship between the parameters of the beta-binomial distribution and those of variance-mean relationships for aggregated disease-incidence data is shown.