X1v 
VALIDATION OF THE MEASURING INSTRUMENTS 
(Concluded) 
Correlation: Product-moment formula; method of rank differences; four- 
fold table method; Pearson biserial 7; correlation ratio. Coefficient of mean 
square contingency. Coefficient of association. Probable errors of mea- 
sures of correlation. Interpretation of the size of the correlation coefficient. 
THE coefficient of correlation (r) is a convenient numer- 
ical index of the degree of interdependence of two variables. 
It ranges from 1.00 to —1.00. The closer it approaches 
unity, the greater the evidence that one variable varies as 
the other (directly, if the sign is positive, and inversely, if 
the sign is negative). 
The familiar product-moment formula of Karl Pearson is 
the basic one for computing the correlation coefficient: 
Zxy 
(12) 7= ST 
Here x and y represent measurements of an individual in the 
x series and y series under comparison, each measurement 
being expressed as a deviation from the mean of its series. 
N is the number of persons measured, and o, and oc, are the 
standard deviations of the two series of measurements. 
A clear and detailed description of the method of comput- 
ing » may be found in Rugg (157) or Thurstone (196). 
Forms for use in calculating the coefficient of correlation 
have been devised by Thurstone (195), Otis (125), Toops 
(201), Holzinger (74), and others. These forms present the 
process in outline and have blank spaces for inserting the fig- 
ures for the particular problem; they serve, therefore, as 
indispensable time and labor savers and as checks on the in- 
clusion of all the necessary steps. The first three listed are 
LR 
174