44 



EMPIRICAL STUDIES OF MEASUREMENT 



culated and stated, and unless the relationship is uniform (within 

 the limits of chance error) throughout the course of the series a most 

 probable curved line to fit the entire series should be calculated in- 

 stead of the slope of a straight line. 



For instance, the Pearson Coefficient for the relation between 

 adult brother and adult brother in longevity is given by Beeton and 

 Pearson as .2853. The relation is sufficiently close to uniformity for 

 all values of x to make a linear relation at least approximately true 

 (if we consider also the similar relation between sister and sister). 

 The relation is, however, by no means identical with other relations 

 giving a similar coefficient, for the modal relationship is approxi- 

 mately 1.00. This can be seen at a glance from the graphic repre- 

 sentation of the correlation table (Fig. 10) or the distribution of 

 the ratios (deviations are reckoned from 59.4 and 59.4 as central 

 tendencies) in Fig. 11. 



The .2853 then does not mean that the most likely value of 

 B C.T. of B is near .2853 X (A C.T. of A), nor that the forces 

 producing correlation tend to make B/A = .2853, divergencies from 



IS-W 40-65 6S-W W-HS 115-00 



FIG. 11. Frequencies of different degrees of relationship in the case of fra- 

 ternal longevity. The numbers stand for the ratios in per cents, the heights for 

 their relative frequency. The mode is at very, very close resemblance, or ratios 

 of 90 to 115 percent. 



this being due to minor causes producing variations in the correla- 

 tion. On the contrary the .2853 represents a most ambiguous sum- 

 mation of the force of a tendency to identical longevity and many 

 other forces. If the authors had not given the full correlation 

 table, the .2853 would evidently have been definitely misleading. 



The determination of the most likely law of relationship for ft 

 series of pairs may then be theoretically and practically a different 

 problem for eacIT particular case, a problem to solve which we need 

 not only certain mathematical technique but also abundant knowl- 

 edge of other similar relationships and of the entire body of facts 

 relevant to the relationship in question. Thus the same set of pairs 

 could properly be interpreted on the basis of a linear relationship 



