Sunday, April 24, 2016

Karl Pearson: Mathematician, Statistician and a healthy dash of Sketch

Karl Pearson’s impressive career as a statistician was driven by his desire to marry statistics with biological observation. He was a devout social Darwinian who truly wanted to use science and statistics in order to contribute to the idea of “survival of the fittest.” Unfortunately, his philosophy as a social Darwinian can be summed up into a very contentious idea: Eugenics.
But before we embark on the controversy of eugenics, let’s take a step back and discuss Pearson’s early life and educational history. He was the second child of Fanny Smith and William Pearson, a barrister of the Inner Temple. Interestingly, he was born Carl, but at the age of 23 changed his name to Karl, which is how he is known today. It goes without saying that Pearson was highly educated. He, as well as his brother and sister, were educated in the home until the age of nine when he was sent to the University College School in London. He studied there until age 16, when he had to leave due to illness. He was then educated by a private tutor. He received a scholarship to King’s College, Cambridge. During his formal education, he dabbled in everything from literature, writing, law, and must importantly, mathematics.  His primary interest in statistics can be traced to his collaboration with Walter Weldon, with whom he founded biometry, which used mathematical modeling to explain biological sciences. Pearson’s interest in statistics continued through his introduction to Francis Galton, who was Darwin’s cousin and also known as the “father of eugenics.”

After graduating from Cambridge, Karl trained at the University of Heidelberg in Germany. There he studied physics under G.H. Quincke and metaphysics under Kuno Fischer. He traveled to Berlin to attend lectures and was strongly influenced by the courses he took there in physics as well as Roman literature, medieval and 16th century German literature, and socialism. He then moved back to London working first at Cambridge, then took rooms at the Inner Temple but never practiced law. He finally moved to a faculty position at University College, London. There he was appointed to the Chair of Applied Mathematics as a Goldsmid Professor.
At this point, most of Pearsons’ statistical contributions have a distinct air of eugenics about it; he used correlations and regressions to make a point that biological fitness can only be brought about by selective breeding (ie. Eugenics) and cannot be done with social reform.  So… Yeah. His motivations are a little dubious.
Pearson's Chi Square Test Statistic

But his statistical contributions were still impressive. Pearson is considered one of the founding fathers of modern statistics. One of his most recognized contributions is his work establishing the Pearson Chi-Square test which measures a “goodness of fit” between two independent, unpaired categorical variables and their respective categorical frequencies. Additionally, he built on the ideas of Galton, and laid the groundwork for future work by RA Fisher and Egon Pearson. He further developed Galton’s idea of correlation generating the correlation coefficient, known as Pearson’s r. Pearson's r is a measure the linear relationship between two variables. Pearson also developed tests to assess the distribution of data, such as evaluating skewness and kurtosis. Many people before him would often force data into a normal distribution. Last but not least, Pearson is responsible for first introducing the p-value into modern statistics. P-value statistics were further developed by RA Fisher. While Pearson’s motivations are dubious, he did lay the foundation for modern statistics, and without Pearson’s contributions we may not have seen the advancements in statistics that we know today.

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