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

Abstract

Let x₁, x₂ … x _n be a system of deviations from the means of n variables with standard deviations σ₁, σ₂ … σ _n and with correlations r₁₂, r₁₃, r₂₃ … r _{n −1,n}.

The object of this paper is to investigate a criterion of the probability on any theory of an observed system of errors, and to apply it to the determination of goodness of fit in the case of frequency curves.