Karl Pearson - Contributions To Statistics

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 and social history. In 1901, with Weldon and Galton, he founded the journal Biometrika whose object was the development of statistical theory. 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 and Frances Cave-Browne-Cave. 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:

• Correlation coefficient. The correlation coefficient (first conceived by Francis Galton) was defined as a product-moment, and its relationship with linear regression was studied.
• Method of moments. Pearson introduced moments, a concept borrowed from physics, as descriptive statistics and for the fitting of distributions to samples.
• 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.
• Chi distance. A precursor and special case of the Mahalanobis distance.
• P-value. Defined as the probability measure of the complement of the ball with the hypothesized value as center point and chi distance as radius.
• Foundations of the statistical hypothesis testing theory and the statistical decision theory. In the seminal "On the criterion..." paper, 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 preset evidence criteria, so called alpha type-I error probabilities, was later proposed by Jerzy Neyman and Egon Pearson.
• 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 minimizing the chi distances.