164 
On Theories of Association 
has the same association coefficient as 
a 
c I d 
and that accordingly if the coefficient of association were a valid measure of 
relationship every fourfold could be expressed in a form which led to a Gaussian 
r _ s j n 17 H a d — *Jbc\ _ q 
2 Wad + '/be) 
Thus Pearson's Q s was a direct result of writing the fourfold in the " equalised " 
form 
vW | Vic 
which Mr Yule now proposes as a primary virtue of his method as giving all 
classes their " natural " or equal percentages. The new " coefficient of colligation " 
is thus really an old friend, which under the form Q s did not possess " the funda- 
mentally different properties*" with which Mr Yule credits it, being the direct 
and we venture to think legitimate offspring of the equalised frequency table 
as figured above. 
The next historical point where Mr Yule seems to be at fault — at any rate in 
his criticisms of one of the present writers — is in his interpretation of the word 
correlation. He narrows it down to the significance of correlation coefficient found 
by the product-moment formula, and so obsessed is he by this idea that he applies 
it to a correlation of gross ranks, which is not a correlation of variates at all. 
The word correlation in the statistical as distinguished from the biological sense, 
we believe, was first used by Galton in his memoir of 1889 entitled : " Co-relations 
and their Measurements, chiefly from Anthropometric Dataf," and he gave a 
definition of it which does not involve the conception of the product moment or the 
linearity of regression at all. That definition was extended by one of the present 
writers in a memoir of 1895J — and it runs: "Two organs in the same individual, or 
in a connected pair of individuals, are said to be correlated, when a series of the 
first organ of a definite size being selected, the mean of the sizes of the corresponding 
second organs is found to be a function of the size of the selected first organ. If 
the mean is independent of this size, the organs are said to be non-correlated. 
Correlation is defined mathematically by any constant, or series of constants, which 
determine the above function." It will be seen that this definition of correlation 
has nothing whatever in it that limits the use of the word ' correlation ' to the 
coefficient of correlation as found by the product-moment method. Galton himself 
never used the product-moment method to find his " index of correlation." He 
had generally in view§ the position that the average value of one organ or 
* Journ. of R. S. S. Vol. lxxv. p. 592, footrote. 
t Bonal Sine. Proc. Vol. xlv. p. 135. 
~™ 4, p. 257. 
id to be co-related when the variation of the one is accompanied on 
,tion of the other...." R. 8. Proc. Vol. xlv. p. 135. 
