272 On Theories of Association 
Returning to the relative values of tetrachoric r t and association Q we find: 
Weighted Mean 
Weighted 
Standard Deviation 
Tetrachoric r t 
Association Q 
•4894 
•7258 
•1102 
■1161 
The variation is high for both coefficients, but even here tetrachoric r t is better 
than Q, you must raise the variability of r, 5 - -i°/ o to reach the variability of Q. 
But the worth of the two coefficients is wholly unequal. If we are told the 
correlation of hair and eye colours is about "50, a whole series of ideas is associated 
with this number ; a very little additional information gives the relative standard 
deviations of the two variates — accurately enough for practice — and we picture to 
ourselves the regression lines and the associated changes in pigmentation of hair 
and eye classes. But what does an association coefficient of "73 for special dicho- 
tomies tell us ? We venture to assert that it conveys no information whatever 
to the investigator's mind, and is absolutely incomparable with other association 
coefficients of the same table, because each for the same system depends on the 
values of the variates at which the divisions are made, and because it has not the 
least relation with any physical properties of the distribution. If Mr Yule replies 
to these criticisms, that tetrachoric r t is also unstable, if not to the same extent, 
and that a function of Q does provide (if the table be doctored) a certain difference 
of percentages, we answer that tetrachoric r t is far from so unstable for the distri- 
butions of ordinary practice as he has endeavoured to make it out by selecting : 
(i) pigmentation data, which as long ago as 1901 were recognised as irregular, and 
(ii) markedly skew frequencies*. The instability is man}' times compensated by 
the definite physical significance of the coefficient. 
Further the percentages which Mr Yule's deduced coefficient of colligation 
represents are wholly artificial and incapable of any rational interpretation. If we 
were to equalise the number of vaccinated and unvaccinated in any locality, how 
could we equalise the number of deaths and the number of recoveries, and what 
intelligible meaning can be given to the percentages when it has been done ? 
How can we possibly give any interpretation to the result reached by a disciple 
of Mr Yule that the " index de correlation " — i.e. Mr Yule's Q — between the 
stature of recruits and rent in the 20 districts of the city of Paris is " perfect " ? 
Average stature of recruits for different districts forms a continuous variate system, 
so does average rent, and the two properly correlated would show the nature of 
the regression line, but this disciple of Mr Yule's, in order to save a little absolutely 
* Mr Yule (loc. cit. p. 624) speaks of the selection he has made as "exhibiting moderately skew 
distributions." Unless he means that they are not U- or J-shaped curves, we consider this an entire 
misnomer. 
