Editing Karl Pearson (section)

==Contributions to statistics==
Pearson's work was all-embracing in the wide application and development of mathematical statistics, and encompassed the fields of [[biology]], [[epidemiology]], anthropometry, medicine, [[psychology]] and social history.<ref>Mackenzie, Donald (1981). ''Statistics in Britain, 1865–1930: The Social Construction of Scientific Knowledge'', Edinburgh University Press.</ref> In 1901, with Weldon and Galton, he founded the journal ''[[Biometrika]]'' whose object was the development of statistical theory.<ref>Hald, Anders (1998). ''A History of Mathematical Statistics from 1750 to 1930''. Wiley, p.&nbsp;651.</ref> He edited this journal until his death. Among those who assisted Pearson in his research were a number of female mathematicians who included [[Beatrice Mabel Cave-Browne-Cave]], [[Frances Cave-Browne-Cave]], and [[Alice Lee (mathematician)|Alice Lee]]. He also founded the journal ''Annals of Eugenics'' (now ''[[Annals of Human Genetics]]'') in 1925. He published the ''[[Drapers' Company]] Research Memoirs'' largely to provide a record of the output of the Department of Applied Statistics not published elsewhere.

Pearson's thinking underpins many of the 'classical' statistical methods which are in common use today. Examples of his contributions are:

*[[Pearson product-moment correlation coefficient|Correlation coefficient]]. The correlation coefficient (first developed by [[Auguste Bravais]]<ref>Analyse Mathematique. Sur Les Probabilités des Erreurs de Situation d'un Point ''Mem. Acad. Roy. Sei. Inst. France'', Sci. Math, et Phys., t. 9, p.&nbsp;255–332. 1846</ref><ref>Wright, S., 1921. Correlation and causation. Journal of agricultural research, 20(7), pp.&nbsp;557–585</ref> and [[Francis Galton]]) was defined as a product-moment, and its relationship with [[linear regression]] was studied.<ref>{{Cite journal | doi = 10.1214/ss/1177012580 | last1 = Stigler | first1 = S. M. | year = 1989 | title = Francis Galton's Account of the Invention of Correlation | journal = Statistical Science | volume = 4 | issue = 2| pages = 73–79 | doi-access = free }}</ref>
*[[Method of moments (statistics)|Method of moments]]. Pearson introduced [[Moment (mathematics)|moments]], a concept borrowed from [[physics]], as descriptive statistics and for the fitting of distributions to samples.
*[[Pearson distribution|Pearson's system of continuous curves]]. A system of continuous univariate probability distributions that came to form the basis of the now conventional continuous probability distributions. Since the system is complete up to the fourth moment, it is a powerful complement to the Pearsonian method of moments.
*[[Mahalanobis distance|Chi distance]]. A precursor and special case of the [[Mahalanobis distance]].<ref name="Pearson, On the criterion">{{Cite magazine | last1 = Pearson | first1 = K. | year = 1900 | title = On the Criterion that a given System of Deviations from the Probable in the Case of a Correlated System of Variables is such that it can be reasonably supposed to have arisen from Random Sampling |magazine=Philosophical Magazine |series=Series 5 | volume = 50 | issue = 302| pages = 157–175 | doi=10.1080/14786440009463897}}</ref>
*[[p-value]]. Defined as the probability measure of the complement of the [[Ball (mathematics)|ball]] with the hypothesized value as center point and chi distance as radius.<ref name="Pearson, On the criterion"/>
*Foundations of [[Statistical hypothesis testing|statistical hypothesis testing theory]] and [[Decision theory|statistical decision theory]].<ref name="Pearson, On the criterion"/> In the seminal ''"On the criterion..."'' paper,<ref name="Pearson, On the criterion"/> Pearson proposed testing the validity of hypothesized values by evaluating the chi distance between the hypothesized and the empirically observed values via the p-value, which was proposed in the same paper. The use of [[Type I error|preset evidence criteria]], so called alpha type-I error probabilities, was later proposed by [[Jerzy Neyman]] and [[Egon Pearson]].<ref>{{Cite journal | last1 = Neyman | first1 = J. | last2 = Pearson | first2 = E. S. | year = 1928 | title = On the use and interpretation of certain test criteria for purposes of statistical inference | doi = 10.2307/2331945| journal = Biometrika | volume = 20 | issue = 1/2| pages = 175–240 | jstor = 2331945 }}</ref>
*[[Pearson's chi-squared test]]. A hypothesis test using normal approximation for discrete data.
*[[Principal component analysis]]. The method of fitting a [[linear subspace]] to multivariate data by minimising the [[Mahalanobis distance|chi distances]].<ref>{{Cite magazine | last1 = Pearson | first1 = K. | year = 1901 | title = On Lines and Planes of Closest Fit to Systems of Points is Space |magazine=Philosophical Magazine |series=Series 6 | volume = 2 | issue = 11| pages = 559–572 |doi=10.1080/14786440109462720 }}</ref><ref>Jolliffe, I. T. (2002). ''Principal Component Analysis, 2nd ed''. New York: Springer-Verlag.</ref>
*The first introduction of the [[histogram]] is usually credited to Pearson.<ref name="pearson">{{Cite journal| last1 = Pearson | first1 = K. |author-link=Karl Pearson| title = Contributions to the Mathematical Theory of Evolution. II. Skew Variation in Homogeneous Material| journal = Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences| volume = 186| pages = 343–414| year = 1895| doi = 10.1098/rsta.1895.0010|bibcode = 1895RSPTA.186..343P | doi-access = free}}</ref>