The vector representation of a sample

Abstract

The geometrical or vectorial representation of a sample as a vector with n mutually perpendicular components corresponding to the n observations in the sample was introduced into statistics by Fisher (1), and led to the solution of many theoretical problems of statistical distributions. Subsequently Fisher (2) gave an alternative algebraic method applicable to finding distributions in connection with regression and the analysis of variance. The actual use of symbolic vector notation in deducing some of the properties of the sample vector—besides tending to stress the complementary character of these two different methods of proof, and the common principle underlying the analysis of any sample into its components—indicates also some points in connection with the assumption of the normal law in which it seems almost essential to retain the geometrical side of this vector representation. Moreover, it will be seen that the vector theory used here in reviewing briefly the analysis of a sample of one dependent variate can readily be extended to cover the case of correlated variates.