Karl Pearson

Beginning around 1880, three famous mathematicians, Karl Pearson, Francis Galton and Edgeworth created a statistical revolution in Europe. Of the three mathematicians, it was Karl Pearson, along with his ambition and determination, that lead people to consider him the founder of the twentieth-century science of statistics.

Born on March 27, 1857 in London, England, Karl Pearson's early years were spent being educated at home. At age nine, Karl was sent away from home to University College School, London. After receiving a B.A. with mathematical honors from King's College, Cambridge in 1879, Pearson was off to Germany. While in Germany, he continued to educate himself while studying physics, metaphysics, and Darwinism. It was Pearson's belief in his own special variety of social Darwinism that led him to change the spelling of his given name, Carl, to Karl.

Upon leaving Germany and returning to London, Pearson married a young lady named Maria Sharpe. The young couple had three children, Sigrid, Helga, and Egon. This quite long and happy marriage ended when Maria in 1928. Pearson would later re-marry a woman who was a co-worker in his department, Margaret Victoria Child. In order to raise and support his family, Pearson returned to University College where he would excel as a teacher and lecturer. He would continue to work as a professor and lecturer in a small room until just a few months before his death.

Karl Pearson's drive and determination may have outweighed his mathematical ability and may have been a primary reason for his success. Of the three leaders of the statistical revolution, Pearson may not have been the most knowledgeable, but he recognized the power and intelligence of Edgeworth and Galton's work. This recognition is what sparked some of the ideas he created that are still used today.

Pearson and Galton formed a special friendship throughout their years of being acquainted. Although Pearson initially criticized Galton's work, he later changed his direction and sided with Galton. Says Pearson, "It was Galton who first freed me from the prejudice that sound mathematics could only be applied to natural phenomena under the category of causation." It was Galton who funded Pearson financially when Pearson was just beginning his statistical journal Biometrika. Perhaps Galton's support and friendship with Pearson was what lead Pearson to accept the request from Galton's family to write Galton's biography after his death. In 1911, after being named the first Galton professor of eugenics, Pearson began to write what would eventually be three volumes of The Life, Letters and Labors of Francis Galton.

In regards to Edgeworth, there is substantial evidence which suggests that Edgeworth was the pivotal figure in Pearson's intellectual development. Although the two mathematicians have not always been the best of friends, they held mutual respect for one another . While working on his skew curves, Pearson had one goal in mind, to do better than Edgeworth had done. At the same time, Edgeworth wanted to develop his own approach further before Pearson got a chance to do so. The two quarreled with one another by withholding information from the other, helping to reject the other's work, and by performing other childish acts. Eventually, a cordial relationship was established between the two. Nonetheless, it was Edgeworth who had inspired Pearson and changed his way of thinking.

Another significant friend Pearson had was W.F.R. Weldon. The two had become very close friends while studying Galton's law of ancestral heredity. Weldon and Pearson kept in close contact and worked side-by-side for a number of years. Together they applied statistics to biological problems of heredity and evolution, and they developed mathematical methods for studying the process of heredity and evolution. Perhaps the long hours spent researching and studying were what formed a special closeness between Pearson and Weldon. This is probably why Weldon's death was such a tremendous blow to Pearson. This tremendous blow in his life took a heavy toll on Pearson, but his work never suffered.

In July 1900, one of Pearson's most significant contributions to statistics was introduced in a paper which was published. This contribution was the chi-square test.

The equation

X2 = summation [(fi-Fi)2/Fi]

was introduced to the world.

fi-observed frequency in the ith of k mutually exclusive categories

Fi-corresponding theoretical frequency

summationFi= summationfi= N= the total # of independent observations involved

Pearson used these formulas to derive the sampling distribution of X2 in large samples, which he was specifically interested in studying, as a function of k, which turns out to be a specialized form of the Pearson Type 3 distribution now known as "X2 distribution for k-1 degrees of freedom." He also gave a small table of the integral of distribution for X2 from 1 to 70 and k from 3 to 20. This X2 test for goodness of fit is certainly one of Pearson's greatest and most useful contributions in its original form of all statistical tests.

Besides his X2 information, Pearson is known for many important contributions in several different fields including anthropology, biometry, eugenics, scientific method, and statistical theory. His initial fame came from his work on skew curves. In the Nineteenth Century, everyone thought that all distributions were normal. After taking a look at other mathematicians work and expanding from there, Pearson came up with a generalized form of the probability curve which fits with great accuracy such curves. He also showed the flexibility and practicality of his curves, and how these curves furnished a flexible and broadly useful tool for statistical workers.

After being recognized for his work with skew curves, Pearson was on his way to a series full of recognition and honors. In 1893, he began his series of 18 papers entitled Mathematical Contributions to the Theory of Evolution which contain some of his most valuable work. The same year he began these papers, Pearson coined the term "standard deviation," and in 1896, he was a Darwin Medalist. The years from 1906-14 found Pearson devoted to developing a post-graduate center to further develop statistics as a branch of applied mathematics. As mentioned earlier, 1911 was the year Pearson was named the first Galton professor of eugenics while at the same time he began Galton's biography. Finally, in the summer of 1933, after a life-long devotion to advancing statistics, Pearson resigned his position at the University. The fact that after Pearson resigned his position, the department of applied statistics was split into two independent units shows just how abundant Pearson's work load was. Interestingly enough, Pearson's only son Egon was named head of one of the new departments. Even after Karl's death in 1936, his family name would still be one of the most prominent in the field of mathematics.

It is obvious that Pearson's contributions during his lifetime firmly established statistics as a discipline in its own right. Karl Pearson was definitely one of the founders of the twentieth-century science of statistics.