20 



EMPIRICAL STUDIES OF MEASUREMENT 



X 



\ 



FIG. 4. 



the Pearson Coefficient will, if the two series are reduced to equiv- 

 alence in variability, coincide and will equal cosine wf/. 1 This is 

 the case of so-called normaTcUTfeTation approximated in many or- 

 ganic and hereditary anatomical relationships. It is of course only 

 one of many possible types of relationship. The extent to which it 

 prevails in mental and social relationships is not known. Its pre- 

 valence in the case of anatomical facts has probably been over- 

 estimated. 



Table IX. gives the facts of the relationship between two series 

 both of the same form of distribution, almost exactly the so-called 

 normal, and of the same variability, the relationship being devised 

 artificially so that the average of each array of y is .5 X the corre- 

 sponding value of x. This regression of y on x is shown graph- 

 ically in Fig. 4, which gives the average of each array of the i/'s. 

 The regression of x on y is shown graphically in Fig. 5, which gives 

 the average of each array of the x's. The Pearson Coefficient for 

 this case is .53. The Median Ratio is much higher (.60 for the y/x 

 1 U equalling the per cent, of unlike-signed pairs. 



