Sequential Sampling for Estimation and Classification of the Incidence of Hop Powdery Mildew I: Leaf Sampling

Hop powdery mildew (caused by Podosphaera macularis) is an important disease of hops (Humulus lupulus) in the Pacific Northwest. Sequential sampling models for estimation and classification of the incidence of powdery mildew on leaves of hop were developed based on the beta-binomial distribution, using parameter estimates of the binary power law determined in previous studies. Stop lines, models that indicate that enough information has been collected to estimate disease incidence and cease sampling, for sequential estimation were validated by bootstrap simulations of a select group of 18 data sets (out of a total of 198 data sets) from the model-construction data, and through simulated sampling of 104 data sets collected independently (i.e., validation data sets). The achieved coefficient of variation (C) approached prespecified C values as the achieved disease incidence ( ) increased. Achieving a C of 0.1 was not possible for data sets in which < 0.10. The 95% confidence interval of the median difference between the true p and included zero for 16 of 18 data sets evaluated at C = 0.2 and all data sets when C = 0.1. For sequential classification, Monte-Carlo simulations were used to determine the probability of classifying mean disease incidence as less than a threshold incidence, p_t (operating characteristic [OC]), and average sample number (ASN) curves for 16 combinations of candidate stop lines and error levels (α and β). Four pairs of stop lines were selected for further evaluation based on the results of the Monte-Carlo simulations. Bootstrap simulations of the 18 selected data sets indicated that the OC and ASN curves of the sequential sampling plans for each of the four sets of stop lines were similar to OC and ASN values determined by Monte Carlo simulation. Correct classification of disease incidence as being above or below preselected thresholds was 2.0 to 7.7% higher when stop lines were determined by the beta-binomial approximation than when stop lines were calculated using the binomial distribution. Correct decision rates differed depending on the location where sampling was initiated in the hop yard; however, in all instances were greater than 86% when stop lines were determined using the beta-binomial approximation. The sequential sampling plans evaluated in this study should allow for rapid and accurate estimation and classification of the incidence of hop leaves with powdery mildew, and aid in sampling for pest management decision making.