Evaluation of the precision of systematic sampling: Nugget effect and covariogram modelling

Abstract

Summary Systematic sampling designs are widely used in stereology. When an estimator of the total amount, Q , of the sampled variable is evaluated by such a procedure, the coefficient of error can be predicted by applying Matheron's theory of regionalized variables. To evaluate the accuracy of the estimate of Q , it is necessary to study the behaviour of the regionalized variable and to model its covariogram. Histological data with a low short‐range variability and agronomic data with a pronounced nugget effect provided the biological material for extreme case studies. Results show that the short‐range variability, if present, cannot be detected when only small samples are available. An underestimation of the coefficient of error is then to be expected. We propose several models of the covariogram, which can be used to test for the presence of a nugget effect. If a nugget effect is present, these models will provide better estimates of the coefficient of error. If there is no nugget effect a simplified method can be used and will provide reliable estimates of the coefficient of error.