Karl Pearson (March 27th 1857 - April 27th 1936), British mathematician , is one of the founders of the modern statistics. The statistical analysis experiences a great development at the end of the 19th century to the the United Kingdom and Karl Pearson dominates its contemporaries by the extent and the variety of its contributions. It develops methods of analysis for the study of the natural selection and the Eugénisme of which he is a burning promoter. Its principal contribution is the creation of the test χ ² intended to estimate if the variations observed in a whole of variables compared to the theoretical values can be allotted or not to a sampling with the Hasard. It receives the Médaille Darwin in 1898.

Eugenism and statistics in the United Kingdom victorien

Wire of a lawyer in full social rise, Karl Pearson, become after brilliant studies mathematics professor, is pure produced “Méritocratie”, the prototype of these rising intellectual professions, which on the one hand emerge from the working classes and on the other hand run up against the traditional authorities. Socialist élitiste and free thinker positivist, Pearson leaves a scientific work which can be included/understood only in the context of the capitalist United Kingdom and victorien.

It is at the 33 years age that Pearson turns to the statistics. Francis Galton has just published its work Natural Inheritance ( the natural heritage ) and Pearson, to its continuation, then will apply the statistical methods to the study of the Natural selection of Darwin within the framework of the theories of the eugenism in vogue among the new elites.

Following the example Galton of which the dregs a indéfectible friendship, Pearson think that it is possible and even eminently desirable to improve the human race (or at least British) in sélectionnat and supporting the most endowed with its representatives like does it the natural selection for the animals. The statistical analysis must enable him to measure the hereditary determination of the physical and psychic characteristics of the man and their improvement.

Karl Pearson will indissociablement get busy all its life with promotion indissociablement dependant for him of the statistics and its convictions eugenists. Magazine publisher in the forefront of which Biometrika founded in 1901, it publishes many statistical tables and it forms within his laboratory of University College of London several generations of brilliances statisticians.

The test of the χ²

Pearson introduces the Test of the χ ² into articles entitled: “On the criterion to decide if, in the case of a system of variable in correlation, a given whole of deviations compared to the probable value is such as it can be reasonably supposed to be obtained by a sampling randomly”. Is the chance alone responsible for the variations observed compared to the awaited average? Pearson to answer it uses a generalization of the concept of variation and the test on which the judgment is based to reject or not the assumption consists in comparing the χ ² obtained with the theoretical χ_o ²: one randomly rejects the assumption of a distribution for χ ² > χ_o ².

The choice of the χ ² is of great interest because its law of probability can be obtained. It had even been given by Helmert in 1876, but Karl Pearson has the merit to connect it to a systematic research on the tests of statistical assumptions.