KARL PEARSON'S CHI‐SQUARED GOODNESS‐OF‐FIT TEST

Karl Pearson's first encounter with the issue of goodness of fit seems to have occurred in 1892. In 1895, Pearson proposed the mean percentage error in the ordinates of a frequency polygon as a measure of goodness of fit. Pearson was the first to have explicitly stated the multivariate normal distribution in its general form. This fact played a key role in Pearson's formulation of his goodness-of-fit test in the groundbreaking 1900 paper entitled 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. This chapter outlines the work on the chi-squared distribution prior to Pearson. Until the 1960s, the chi-squared distribution had been attributed to Friedrich Robert Helmert, until the prior works of Irenee-Jules Bienayme and Ernst Abbe were rediscovered.