Optimal sample size and plot size or point sampling factor based on cost-plus-loss using the Fairfield Smith relationship for plot size

Abstract

The principle of minimizing the cost-plus-loss is used to simultaneously find optimal plot size and sample size for forest sampling using the Fairfield Smith relationship between plot size and the variance among cubic metre volumes per hectare. Loss is defined as the United States Dollar (USD) value of the expected value of the absolute value of the difference between the sample mean and true mean volumes per hectare. Under the assumption of a normal distribution, this loss is a function of the standard error of the mean. Sampling costs include USD values of fixed costs, plot measurement and establishment costs and travel costs; however, fixed costs do not affect the determination of minimum cost-plus-loss. By differentiating the cost-plus-loss function with respect to plot and sample size, equations are derived that can be used to determine plot and sample sizes that minimize cost-plus-loss. Example solutions for fixed-sized plot and point sampling are presented using costs and stumpage values typical for the southern USA. These examples indicate that the costplus- loss criterion results in higher rates of sampling intensity than would be typical for the southern USA for the example scenarios. However, since sampling costs under the cost-plus-loss criterion were only around half a percent of timber value, the cost-plus-loss sampling plans might be justified in cases where very precise valuations are required.