280 
Oh Theories of Association 
this signifies that " la correlation est parfaite " is totally misleading. Professor 
Niceforo speaks of the correlation between stature of conscripts and the rent 
of their arrondissements of origin ; he does not say that he is merely dealing with 
the practically unimportant fact that no arrondissement with a mean rent over 
211 has given a mean stature under 1646. But even to state this simple fact 
would be more enlightening than to talk of the index of correlation equalling 
unity. 
The second case we took was that of the mortality and natality of the same 
20 arrondissements. Again we had great difficulty in tracing the original source 
of the information. 
However in the Annuaire Statistique de la Ville de Paris, Annee 1904, we find, 
p. 125, the natality per year based upon 1000 women of ages 15 — 49, and, on 
p. 135, the annual mortality based on 1000 inhabitants for these arrondissements. 
The natality is for the period 1886 — 1895, the mortality is given for the periods 
1886- — 1890 and 1891 — 1895 separately but not combined. As Professor Niceforo 
does not give a reference to the years dealt with, nor the source of this Parisian 
data, we have taken the simple mean of the mortality for the two periods and 
correlated this with the natality for 1886 — 1895. The constants found are : 
Mean Mortality =2173. Mean Natality =79065. 
Standard Deviation = 4-9215. Standard Deviation = 23-7298. 
Correlation = r = '9163 + "0242. 
Regression Line of Natality A" on Mortality M : 
N= 44181 M- 16-94. 
Diagram XXV indicates the position of the observations and their relation to 
the regression line. It conveys as adequate a representation of the whole relation- 
ship as it is possible to give on the data. But if we count up on the graph the 
dots in the quadrants obtained by drawing the lines at the means we obtain the 
fourfold division ^- | leading again to Q = 1 + "0*. What information as to 
the real nature of the correlation is given by such a result ? 
If Professor Niceforo had desired to obtain a rapid approximate value to the 
true correlation in these cases, he should have drawn his divisions at the medians, 
not the means, and used Sheppard's formula 
b r alb 
r = cos 7r j tor -~ — 
a + b b | a 
to find tetrachoric r t . In this case his results would have been the tables 
8 12 . 9 | 1 
T]~8~ and TJT 
r, — - 81 + -05, for rent and stature, 
r, = "95 + '04, for natality and mortality. 
* Professor Niceforo gives -977 probably from slightly different data. 
