Gy's sampling theory is a

theory A theory is a rational type of abstract thinking about a phenomenon, or the results of such thinking. The process of contemplative and rational thinking is often associated with such processes as observational study or research. Theories may be ...

about the sampling of materials, developed by

Pierre Gy Pierre Maurice Gy (; 25 July 1924 – 5 November 2015) was a chemist and statistician. Born in Paris, France, to Felix and Clemence, Gy graduated in chemical engineering from ESPCI ParisTech in 1946. On graduation, Gy worked as a chemical engi ...

from the 1950s to beginning 2000sGy, P (2004), Chemometrics and Intelligent Laboratory Systems, 74, 61-70. in articles and books including: *(1960) Sampling nomogram *(1979) Sampling of particulate materials; theory and practice *(1982) Sampling of particulate materials; theory and practice; 2nd edition *(1992) Sampling of Heterogeneous and Dynamic Material Systems: Theories of Heterogeneity, Sampling and Homogenizing *(1998) Sampling for Analytical Purposes The abbreviation "TOS" is also used to denote Gy's sampling theory.K.H. Esbensen. 50 years of Pierre Gy's “Theory of Sampling”—WCSB1: a tribute. Chemometrics and Intelligent Laboratory Systems. Volume 74, Issue 1, 28 November 2004, pages 3–6. Gy's sampling theory uses a

model A model is an informative representation of an object, person or system. The term originally denoted the plans of a building in late 16th-century English, and derived via French and Italian ultimately from Latin ''modulus'', a measure. Models c ...

in which the sample taking is represented by

independent Independent or Independents may refer to: Arts, entertainment, and media Artist groups * Independents (artist group), a group of modernist painters based in the New Hope, Pennsylvania, area of the United States during the early 1930s * Independ ...

Bernoulli trials In the theory of probability and statistics, a Bernoulli trial (or binomial trial) is a random experiment with exactly two possible outcomes, "success" and "failure", in which the probability of success is the same every time the experiment is c ...

for every particle in the parent population from which the sample is drawn. The two possible outcomes of each Bernoulli trial are: (1) the particle is selected and (2) the particle is not selected. The probability of selecting a particle may be different during each Bernoulli trial. The model used by Gy is mathematically equivalent to

Poisson sampling In survey methodology, Poisson sampling (sometimes denoted as ''PO sampling'') is a sampling process where each element of the population is subjected to an independent Bernoulli trial which determines whether the element becomes part of the sampl ...

. Using this model, the following equation for the

variance In probability theory and statistics, variance is the expectation of the squared deviation of a random variable from its population mean or sample mean. Variance is a measure of dispersion, meaning it is a measure of how far a set of numbe ...

of the

sampling error In statistics, sampling errors are incurred when the statistical characteristics of a population are estimated from a subset, or sample, of that population. Since the sample does not include all members of the population, statistics of the sample ( ...

in the mass concentration in a sample was derived by Gy: :

V = \frac \sum_^N q_i(1-q_i) m_^ \left(a_i - \frac\right)^2 .

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 ''i''th particle of the population in the sample (i.e. the

first-order inclusion probability In statistics, in the theory relating to sampling from finite populations, the sampling probability (also known as inclusion probability) of an element or member of the population, is its probability of becoming part of the sample during the draw ...

of the ''i''th particle), ''m''_''i'' is the mass of the ''i''th particle of the population and ''a''_''i'' is the mass concentration of the property of interest in the ''i''th particle of the population. It is noted that the above equation for the variance of the sampling error is an approximation based on a

linearization In mathematics, linearization is finding the linear approximation to a function at a given point. The linear approximation of a function is the first order Taylor expansion around the point of interest. In the study of dynamical systems, lineari ...

of the mass concentration in a sample. In the theory of Gy,

correct sampling During sampling of granular materials (whether airborne, suspended in liquid, aerosol, or aggregated), correct sampling is defined in Gy's sampling theory as a sampling scenario in which all particles in a population have the same probability of ...

is defined as a sampling scenario in which all particles have the same probability of being included in the sample. 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: :

V = \frac \sum_^N m_^ \left(a_i - a_\text \right)^2 .

where ''a''_batch is the concentration of the property of interest in the population from which the sample is to be drawn and ''M''_batch 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. Two books covering the theory and practice of sampling are available; one is the Third Edition of a high-level monograph and the other an introductory text.

References

{{DEFAULTSORT:Gy's Sampling Theory Sampling (statistics)

See also

References