Gy's sampling theory is a

theory A theory is a systematic and rational form of abstract thinking about a phenomenon, or the conclusions derived from such thinking. It involves contemplative and logical reasoning, often supported by processes such as observation, experimentation, ...

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 engin ...

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 Homogeneity and heterogeneity are concepts relating to the uniformity of a substance, process or image. A homogeneous feature is uniform in composition or character (i.e., color, shape, size, weight, height, distribution, texture, language, i ...

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 , . Models can be divided in ...

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 Pennsylvania, United States * Independentes (English: Independents), a Portuguese artist ...

Bernoulli trials 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 sam ...

. Using this model, the following equation for the

variance In probability theory and statistics, variance is the expected value of the squared deviation from the mean of a random variable. The standard deviation (SD) is obtained as the square root of the variance. Variance is a measure of dispersion ...

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 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 (British English: linearisation) 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 ...

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''_''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