284 
On Theories of Association 
coefficients of association and colligation are in our opinion wholly fallacious, they 
represent no true properties of the actual distributions, and they have no adequate 
physical interpretation. The coefficient obtained by the method of pseudo-ranks 
is equally fallacious, unless the variables proceed by and have been grouped by 
discrete units. But both Mr Yule's methods are so easy of application, that those 
who will not devote the small amount of time and energy requisite to the dis- 
cussion of data by more adequate processes at once adopt them without further 
consideration. Thus Mr Yule's coefficient of association is passing into French 
statistical literature as Vindice de correlation, a term originally introduced by 
Galton for the coefficient of correlation and now transferred to the different and we 
hold fallacious Yulean measure of association. Professor Niceforo writes * : " Mais 
pour nos etudes sur la correlation entre les differents phenomenes economiques, 
demographiques et autres, dans les quartiers et les arrondissements des grandes 
villes, oil nos trouvions en presence de series formees par un nombre plutot re- 
straint d'elements (SO, 25, 20) nous avons prefere nous servir de la methode Yule, 
plus rapide et donnant, quoique moins precise que la methode precedente, des 
resultats ties satisfaisants." The preceding method is the method of the product- 
moment which Professor Niceforo discards for Mr Yule's association coefficient, 
using it solely — and apparently with Mr Yule's approval (see loo. cit. p. 324) — 
for absolutely continuous variates, where the coefficient of correlation could be at 
once found and a graph easily drawn of the regression line. Professor Niceforo 
speaks everywhere in his paper of the correlation being this or that, and entitles 
his paper " Contribution a l'etude des correlations entre le bien-etre economique 
et quelques faits de la vie demographique." What his or Mr Yule's test of 
"resultats tres satisfaisants" may be we do not know, but we consider that the 
whole of Professor Niceforo's work will have to be repeated before anything 
can be learnt from his data. 
We have worked out two illustrative cases from Professor Niceforo's material 
to indicate what we consider the extreme danger of Mr Yule's methods. In the 
first case, that of the average stature of conscripts and the average rent in the 20 
arrondissements of Paris, the answer Professor Niceforo gives is Q = 1 + - 0. The 
correlation we are told is perfect. In the second case, that of the correlation 
between the mortality and natality of the same arrondissements, we are told that 
the " correlation... est tres forte." Professor Niceforo gives it as : 
Indice de correlation R = 0"977 + '032,450 (sic !). 
We had failed to give any real interpretation to either of these results, and we 
turned to the original data. These we found hard to discover, because Professor 
Niceforo does not refer at each stage to the exact source of his original material. 
Manouvier gives the mean stature of the 20 arrondissements in 18S0 and 1881 f. 
These appear to be what is given as Statura media in Professor Niceforo's book 
* Journal de la Societe de Statistique de Paris, 52 Annee, pp. 322 — 341 ; see p. 324 and elsewhere, 
t Bulletins de la Societe d' Anthropologic de Paris, Annee 1888, p. 161. 
