An effective sample size for predicting plant disease incidence in a spatial hierarchy

For aggregated or heterogeneous disease incidence, one can predict the prop ortion of sampling units diseased at a higher scale (e.g., plants) based on the proportion of diseased individuals and heterogeneity of diseased indiv iduals at a lower scale (e.g., leaves) using a function derived from the be ta-binomial distribution. Here, a simple approximation for the beta-binomia l-based function is derived. This approximation has a functional form based on the binomial distribution, but with the number of individuals per sampl ing unit (n) replaced by a parameter (v) that has similar interpretation as , but is not the same as, the effective sample size (n(deff)), often used i n survey sampling. The value of v is inversely related to the degree of het erogeneity of disease and generally is intermediate between n(deff) and n i n magnitude. The choice of v was determined iteratively by finding a parame ter value that allowed the zero term (probability that a sampling unit is d isease free) of the binomial distribution to equal the zero term of the bet a-binomial. The approximation function was successfully tested on observati ons of Eutypa dieback of grapes collected over several years and with simul ated data. Unlike the beta-binomial-based function, the approximation can b e rearranged to predict incidence at the lower scale from observed incidenc e data at the higher scale, making group sampling for heterogeneous data a more practical proposition.