310 The Philippine Journal of Science 1922 
variables by a simple diagram, such as is shown in fig. 1, with- 
out entailing mathematical calculations. Such a method, how- 
ever, does not enable one to measure the degree of association 
or correlation. From mere inspection of fig. 1, one may deduce 
that the higher rates correspond to, or, to use the statistical 
term, are “correlated” with, the lower figures in the dwellings. 
The underlying principle of the method of correlation is the 
measurement of the association between two values in terms 
of the coefficient of correlation. This coefficient is expressed 
as follows: S (#, . 2) 
N o, 92 
N12 pam a= 
where 
1,. = the correlation coefficient 
X, and X, = the variables correlated 
x, and x,— the deviations from the means of X, and X,, re- 
spectively ; 
> = summation 
o, and c, =the standard deviations of X, and X, 
N = number of observations (variates). 
The coefficient may vary from 0 to 1, in either the positive 
or the negative direction, depending upon the nature of the 
correlation. The numerical value of this coefficient expresses 
the degree of association, approaching complete correlation as 
the value approaches unity. In other words, if the value is 
either —1 or +1, the correlation is perfect; that is, for every 
change in one variable, there is a definite and constant propor- 
tional change in the other. 
o, and o, are derived according to the following formula: 
Hee (2?) 
oN 
N = number of pairs 
>= summation of x. 
oC 
Before conclusions can be drawn from the coefficient of corre- 
lation it is necessary to know something about the probable 
error. The probable error is a conventional measure of the 
reliability of results. > 
It is a constant so chosen that when its value is added to and subtracted 
from the result obtained or the numerical conclusion reached, it is exactly 
an even chance that the true result or conclusion lies either inside or outside 
the limits set by the probable error in the plus and minus direction. 
