The distribution of Student’s t

Abstract

The distribution of Student’s t was discovered by the British biometrician William Sealy Gossett (1876–1937), who published a paper on this topic in Biometrika in 1908 under the pseudonym Student. When a sample of observations must be used to test hypotheses concerning the mean μ of of a normal statistical population, Student’s t distribution yields exact probabilities even though the standard deviation σ of that population is unknown. Before the discovery of Student’s t, the normal distribution was used as an approximation in that context, but that procedure was satisfactory only if the sample studied was large (N≥ 30). Student’s t distribution is therefore more accurate in the case of the small samples (N < 30) with which scientists often have to work in many fields, such as experimental biology, ecology, paleontology, etc.. Present-day tables of Student’s t distribution reach rather large sample sizes, and the normal distribution seldom has to be substituted for it as an approximation.