Comparison of theories for the variance caused by the sampling of random mixtures of non-identical particles

When sampling a random mixture of nonidentical particles, the minimum sample size can be determined once the relationship between the sample size and the variance is known. Many different theories have been proposed to describe this relationship. This article provides a novel and systematic comparison of existing theories based on a set of objective criteria. It is found that none of the existing theories meet all criteria, making further research into the development of a suitable theory necessary.