VII.—The correlation between product moments of any order in samples from a normal population

1. A problem of considerable importance in the theory of statistics is the determination of the accuracy with which a given sample of observations determines the characteristics of the population from which it is derived. Any parameter of this distribution can only in practice be estimated from the sample, and the degree of latitude in our choice of the right function enables considerations of suitability and efficiency of the particular moment statistic to be taken into account. As well as this, however, the probable errors of such frequency constants, or, to be more complete, the distribution of the constants in all possible samples, must be determined. These problems were formulated many years ago by Karl Pearson (1), and his important researches have stimulated and suggested much subsequent work.