History of statistics

Statistics arose, no later than the 18th century, from the need of states to collect data on their people and economies, in order to administer them. Its meaning broadened in the early 19th century to include the collection and analysis of data in general. Today statistics is widely employed in government, business, and the natural and social sciences.

Because of its origins in government and its data-centric world view, statistics is considered to be not a subfield of mathematics but rather a distinct field that uses mathematics. Its mathematical foundations were laid in the 17th and 18th centuries with the development of probability theory. The method of least squares was invented around the turn of the 19th century by several authors. Since then new techniques of probability and statistics have been in continual development. Modern computers have expedited large-scale statistical computation, and have also made possible new methods that would be impractical to perform manually.

Etymology

The term "statistics" is ultimately derived from the New Latin "statisticum collegium" ("council of state") and the Italian word "statista" ("statesman" or "politician"). The German "Statistik", first introduced by Gottfried Achenwall (1749), originally designated the analysis of data about the state, signifying the "science of state" (then called "political arithmetic" in English). It acquired the meaning of the collection and classification of data generally in the early 19th century. It was introduced into English by Sir John Sinclair.

Thus, the original principal purpose of "Statistik" was data to be used by governmental and (often centralized) administrative bodies. The collection of data about states and localities continues, largely through national and international statistical services. In particular, censuses provide regular information about the population.

Origins in probability

The mathematical methods of statistics emerged from probability theory, which can be dated to the correspondence of Pierre de Fermat and Blaise Pascal (1654). Christiaan Huygens (1657) gave the earliest known scientific treatment of the subject. Jakob Bernoulli's "Ars Conjectandi" (posthumous, 1713) and Abraham de Moivre's "Doctrine of Chances" (1718) treated the subject as a branch of mathematics. [ See Ian Hacking's "The Emergence of Probability" for a history of the early development of the very concept of mathematical probability. ] In the modern era, the work of Kolmogorov has been instrumental in formulating the fundamental model of Probability Theory, which is used throughout statistics.

The theory of errors may be traced back to Roger Cotes' "Opera Miscellanea" (posthumous, 1722), but a memoir prepared by Thomas Simpson in 1755 (printed 1756) first applied the theory to the discussion of errors of observation. The reprint (1757) of this memoir lays down the axioms that positive and negative errors are equally probable, and that there are certain assignable limits within which all errors may be supposed to fall; continuous errors are discussed and a probability curve is given.

Pierre-Simon Laplace (1774) made the first attempt to deduce a rule for the combination of observations from the principles of the theory of probabilities. He represented the law of probability of errors by a curve. He deduced a formula for the mean of three observations. He also gave (1781) a formula for the law of facility of error (a term due to Joseph Louis Lagrange, 1774), but one which led to unmanageable equations. Daniel Bernoulli (1778) introduced the principle of the maximum product of the probabilities of a system of concurrent errors.

The method of least squares, which was used to minimize errors in data measurement, was published independently by Adrien-Marie Legendre (1805), Robert Adrain (1808), and Carl Friedrich Gauss (1809). Gauss had used the method in his famous 1801 prediction of the location of the dwarf planet Ceres. Further proofs were given by Laplace (1810, 1812), Gauss (1823), James Ivory (1825, 1826), Hagen (1837), Friedrich Bessel (1838), W. F. Donkin (1844, 1856), John Herschel (1850), and Morgan Crofton (1870).

Other contributors were Ellis (1844), De Morgan (1864), Glaisher (1872), and Giovanni Schiaparelli (1875). Peters's (1856) formula for $r$, the probable error of a single observation, is well known.

In the nineteenth century authors on the general theory included Laplace, Sylvestre Lacroix (1816), Littrow (1833), Richard Dedekind (1860), Helmert (1872), Hermann Laurent (1873), Liagre, Didion, and Karl Pearson. Augustus De Morgan and George Boole improved the exposition of the theory.

Adolphe Quetelet (1796-1874), another important founder of statistics, introduced the notion of the "average man" ("l'homme moyen") as a means of understanding complex social phenomena such as crime rates, marriage rates, or suicide rates.

Statistics today

During the 20th century, the creation of precise instruments for agricultural research, public health concerns (epidemiology, biostatistics, etc.), industrial quality control, and economic and social purposes (unemployment rate, econometry, etc.) necessitated substantial advances in statistical practices.

Today the use of statistics has broadened far beyond its origins. Individuals and organizations use statistics to understand data and make informed decisions throughout the natural and social sciences, medicine, business, and other areas.

Statistics is generally regarded not as a subfield of mathematics but rather as a distinct, albeit allied, field. Many universities maintain separate mathematics and statistics departments. Statistics is also taught in departments as diverse as psychology, education, and public health.

Important contributors to statistics

* Thomas Bayes
* George E. P. Box
* Pafnuty Chebyshev
* Sir David Cox
* Gertrude Cox
* George Dantzig
* Rene Descartes
* W. Edwards Deming
* Bradley Efron
* Bruno de Finetti
* Sir Ronald Fisher
* Sir Francis Galton
* Carl Friedrich Gauss
* William Sealey Gosset ("Student")
* Andrey Kolmogorov
* Aleksandr Lyapunov
* Abraham De Moivre
* Sir Isaac Newton
* Jerzy Neyman
* Florence Nightingale
* Blaise Pascal
* Karl Pearson
* Adolphe Quetelet
* C. R. Rao
* Walter A. Shewhart
* Charles Spearman
* John Tukey

Bibliography

* Kotz, S., Johnson, N.L. (1992,1992,1997). Breakthroughs in Statistics, Vols I,II,III. ISBN 0-387-94037-5, ISBN 0-387-94039-1, ISBN 0-387-94989-5
* Salsburg, David (2001). "The Lady Tasting Tea: How Statistics Revolutionized Science in the Twentieth Century". ISBN 0-7167-4106-7
*cite book
last = Stigler
first = Stephen M.
authorlink = Stephen Stigler
year = 1990
title = The History of Statistics: The Measurement of Uncertainty before 1900
publisher = Belknap Press/Harvard University Press
id = ISBN 0-674-40341-X

References

External links

* [http://www.jehps.net/indexang.html Electronic Journ@l for History of Probability and Statistics/Journ@l Electronique d'Histoire des Probabilités et de la Statistique]
* [http://www.economics.soton.ac.uk/staff/aldrich/Figures.htm Figures from the History of Probability and Statistics (Univ. of Southampton)]
* [http://www.york.ac.uk/depts/maths/histstat Materials for the History of Statistics (Univ. of York)]
* [http://www.economics.soton.ac.uk/staff/aldrich/Probability%20Earliest%20Uses.htm Probability and Statistics on the Earliest Uses Pages (Univ. of Southampton)]
* [http://members.aol.com/jeff570/stat.html Earliest Uses of Symbols in Probability and Statistics] on [http://members.aol.com/jeff570/mathsym.html Earliest Uses of Various Mathematical Symbols]