Sampling error correlated among observations: origin, impacts, and solutions

ABSTRACT Geoscientific datasets can contain individual data for more than 50 different chemical elements. The association between these variables is as important as their individual values. However, it is commonly overlooked that the observed covariance may be overestimated due to correlated errors. Dependent errors arise from many sources, such as the segregation process of minerals associated with these variables during delimitation, extraction, and preparation steps. This study extends a classical model composed of grade-independent (additive) and grade-proportional (multiplicative) errors to a generalised multivariate model that can estimate the real variance, covariance, and correlation from observations affected by shared errors. The use of estimates of the real covariance is recommended when the study objective is to evaluate or estimate the association between processes instead of the association between observations. A numerical example illustrates the bias in statistics and discusses the relevance of considering shared errors in linear regression and kriging.