Making a distinction between homogeneous and heterogeneous mixtures is a matter of the scale of sampling. On a coarse enough scale, any mixture can be said to be homogeneous, if the entire article is allowed to count as a "sample" of it. On a fine enough scale, any mixture can be said to be heterogeneous, because a sample could be as small as a single molecule. In practical terms, if the property of interest of the mixture is the same regardless of which sample of it is taken for the examination used, the mixture is homogeneous.
Gy's sampling theory quantitatively defines the heterogeneity of a particle as:
where , , , , and  are respectively: the heterogeneity of the th particle of the population, the mass concentration of the property of interest in the th particle of the population, the mass concentration of the property of interest in the population, the mass of the th particle in the population, and the average mass of a particle in the population.
During sampling of heterogeneous mixtures of particles, the variance of the sampling error is generally non-zero.
Pierre Gy derived, from the Poisson sampling model, the following formula for the variance of the sampling error in the mass concentration in a sample:
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 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 is the mass of the ith particle of the population and a is the mass concentration of the property of interest in the ith particle of the population.
The above equation for the variance of the sampling error is an approximation based on a linearization of the mass concentration in a sample.
In the theory of Gy, correct sampling is defined as a sampling scenario in which all particles have the same probability of being included in the sample. This implies that q 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 a is that concentration of the property of interest in the population from which the sample is to be drawn and M is the mass of the population from which the sample is to be drawn.