Page:Proceedings of the Royal Society of London Vol 60.djvu/523

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488
On Bravis’ Formulae in the case of Skew

and we may again call

and we may again call

the net coefficient of correlation between and . Expanding the determinants, we have, in fact,

............. (16).

There are six such net coefficients, The above values of the regressions are again those usually obtained on the assumption of normal correlation[1] The net correlation becomes, on that assumption, the coefficient of correlation for any group of the variables associated with fixed types of . If we write , we have, after some rather lengthy reduction,

,

where


normal correlation, is the standard deviation of all arrays associated with fixed types of , and . In general correlation, it is most easily interpreted as the standard error made in estimating by equation (14), from its associated values of , and .

As in the case of three variables, the quantity R may be considered as a coefficient of correlation. It can range between ±+1, and can only become unity if the linear relation (14) hold good in each individual instance.

We showed at the end of the last section that the standard error made in estimating from the relation

  1. Professor Pearson, “Regression, Heredity, and Panmixia.” ‘Phil Trans’ A, vol. 187 (1896), p. 294.