PLANT-DISEASE INCIDENCE - INVERSE SAMPLING, SEQUENTIAL SAMPLING, AND CONFIDENCE-INTERVALS WHEN OBSERVED MEAN INCIDENCE IS ZERO

Sequential and inverse sampling equations were developed for estimatin g the mean proportion of diseased plants (or plant units), disease inc idence (p), where the data were obtained by cluster sampling. With clu ster sampling, the disease status of all n plants in each of N samplin g units is determined. Derived sampling equations were applicable for up to three ways of specifying reliability or precision of estimated p , and the following conditions of spatial heterogeneity: i) random pat tern, with data described by the binomial distribution; ii) aggregated pattern, with data described by the beta-binomial distribution, and c onstant degree of aggregation (assessed with the rho index of the beta -binomial); and nl) aggregated pattern, with data described by the bin ary form of the power law, in which the observed (empirical) variance of incidence is a power function of the theoretical variance for a bin omial distribution. For the third situation, aggregation can vary with p, such that rho is a function of the power law parameters. A selecti on of the sequential estimation equations were evaluated by the simula ted sampling from: 1) data sets of the incidence of grape vines infect ed by Eutypa lata, and 2) simulated data with beta-binomial distributi ons. Results on achieved (observed) coefficient of variation of estima ted p(C), difference between observed and true p, and average sample n umber, were similar to that found for the analogous equations develope d for noncluster simple random sampling of count data with no upper bo und (e.g. insect counts). Equations also were developed to calculate c onfidence intervals for p as a function of n, N, and rho, when all sam pled observations are disease free. These equations used the approxima tion of the negative binomial to the beta-binomial distribution that a pplies when p is small. Copyright (C) 1996 Elsevier Science Ltd