STUDENT'S t

Very few achievements in statistics have been as momentous as Student's discovery of the t-distribution. Student's real name was William Sealy Gosset. From Student's interpretations, it is noted that he was reasoning in terms of probabilities of hypotheses and thus his derivation was actually based on inverse probability. Fisher showed that the distribution of the sample regression coefficients could be expressed in terms of Student's z-distribution. A unified treatment of the t-distribution was provided by Fisher also in 1925, in the Metron paper Applications of Student's’ distribution. This chapter outlines some of the studies that anticipated Student's work to some extent. The first major figure is the German geodesist Friedrich Robert Helmert. Helmert proved the independence of the sample mean and sample variance and effectively derived the chi-squared distribution. In 1876, Luroth's derived the t-distribution by using inverse probability.