Estimating change in annual timber products output using a stratified sampling with certainty design

A key aspect in understanding patterns in wood demand and harvesting activities is monitoring of timber products output by wood processing facilities. Estimation of change from year-to-year is necessary but is complicated due to shifts in the population as well as changing strata over time. Taking independent samples each year eases complexity, yet suffers from relatively large sampling error in comparison to other designs that take advantage of the covariance arising from correlated samples. In this study, a design intended to maximize the precision of the change estimate by retaining the initial sample to the extent possible was analyzed. Several approaches to estimating the covariance, with the primary challenge being that sometimes only a single sample unit occurred in both samples within a given stratum. Variance underestimation and overestimation were encountered depending on the covariance method. The best outcome was attained using a measure-of-size variable at the population level to approximate the covariance. However, this approach overestimated the variance by 11% in a Monte Carlo simulation. The simulation results suggested a 14% reduction in the standard error of the estimate was attainable from correlated samples relative to independent samples. Due to the challenges introduced for estimating the covariance for changing populations and strata over time, the value of relatively small reductions in sampling error need to be considered in the context of introducing complex and potentially unreliable covariance estimation methods.