The model used by Gy is mathematically equivalent to Poisson sampling.
[3] Using this model, the following equation for the variance of the sampling error in the mass concentration in a sample was derived by Gy: in which V is the variance of the sampling error, N is the number of particles in the population (before the sample was taken), q i is the probability of including the ith particle of the population in the sample (i.e. the first-order inclusion probability of the ith particle), m i is the mass of the ith particle of the population and a i is the mass concentration of the property of interest in the ith particle of the population.
This implies that q i no longer depends on i, and can therefore be replaced by the symbol q. Gy's equation for the variance of the sampling error becomes: where abatch is the concentration of the property of interest in the population from which the sample is to be drawn and Mbatch is the mass of the population from which the sample is to be drawn.
It has been noted that a similar equation had already been derived in 1935 by Kassel and Guy.
[4][5] Two books covering the theory and practice of sampling are available; one is the Third Edition of a high-level monograph[6] and the other an introductory text.