Parametric sequential sampling based on multistage estimation of the negative binomial parameter k¹

An intensive survey of two farmer-managed corn and soybean fields in eastern Nebraska was conducted to investigate parametric sequential sampling of weed seedling populations using a multistage procedure to estimate k of the negative binomial distribution. k is a nonspatial aggregation parameter related to the variance at a given mean value. Mean weed seedling density ranged from 0.18 to 3.11 plants 0.38 m^-2 (linear meter of crop row) based on 806 sampling locations. The average value of k, derived from 200 multi- stage estimation procedures, ranged from 0.17 to 0.32. A sequential sampling plan was developed with the goal of estimating the mean with a coefficient of variation (CV) of 10, 20, 30, and 40 % of the sample mean. A sampling plan was also constructed to estimate the mean within a specified distance H of the true mean (H(x̄)= 0.10, 0.50 and 1.0 plants 0.38 m^-2) with 80, 85, and 90% confidence. Estimating mean weed seedling density within a specified CV of the true mean CV(x̄) using parametric sequential sampling techniques was superior to estimating the mean within a specified distance (H(x̄)) of the true mean when considering the frequency of sampling and probability of error, especially at intermediate k values. At a k value of 0.32 and 0.25, the difference between the actual CV(x̄) obtained from sampling and the CV(x̄) specified by the sampler was minimal. However, the accuracy of weed seedling density estimates was reduced with decreasing k values below 0.25, especially as the specified CV(x̄) increased.