An experimental determination of the distribution of the partial correlation coefficient in samples of thirty
J. W. Bispham · Proceedings of the Royal Society of London Series A Containing Papers of a Mathematical and Physical Character · 1920
Abstract In 1908. “Student” dealt experimentally with the distribution of the total correlation coefficient of small samples. In particular, he dealt with values of n as low as 4 for the case of zero correlation in the sampled population. In 1913 H. E. Soper theoretically determined the mean correlation and the standard deviation of the distribution of correlations to second approximations. In 1915 R. A. Fisher gave an equation for the frequency distribution of r, and in 1917, as a result of a co-operative study by H. E. Soper, A. W. Young, B. M. Cave, A. Lee and K. Pearson, this was reduced to suitable form for numerical manipulation, and the frequency distributions and frequency constants for samples of size ranging from n = 3 to n = 400 were given for values of the correlation in the sampled population ranging from ρ = 0 to ρ = 0·9. The present experimental investigation was commenced in 1914, but had to be put aside during the war. It was intended to determine whether the distribution of partial correlation coefficients for samples as small as 30 showed greater dispersion than is observed for total correlation coefficients. Yule has shown that for normal distributions and large samples the standard deviations of the distributions should be of the same magnitude. The experiment can now be related to the complete evaluation of the distributions of total correlations referred to above.