96 PROCEEDINGS OP THE ANATOMICAL AND ANTHROPOLOGICAL 



lengths is the angle GOL, the line GO being drawn through the 

 peaks of sections parallel to B'OB. These two regressions arc 

 derived by multiplying what is called the rni'jjir/'ciit of correlation by 

 the ratios of the two standard deviations. For example, calling the 



O"i T (7". 



coefficient of correlation /, the two regressions are r - and r - 



The important coefficient to be calculated is, therefore, /. 



Horizontal sections of the surface of frequency are ellipses ; 

 the section by the plane of XY being shown as a dotted ellipse on 

 the figure. 



If all the points on the chart lay on the diagonal DE the cor- 

 relation would be a maximum and the coefficient would be unity. 

 Correlation would in this case be equivalent to causation, i.e., any 

 given deviation from the mean head breadth would necessarily be 

 associated with the same deviation from the mean head length. 

 When the coefficient is less than unity, all we can predict is the 

 average head length of all persons having the same head breadth. 



The coefficient of correlation is calculated by the formula 



N is the total number of persons. 



o-] is the standard deviation about the mean parallel to axes X. 



*^2 * ' " " " " 



To calculate the value of r, plot out all the persons on a sheet of 

 paper divided into equal squares. Draw two lines at right angles 

 representing the arbitrary lengths and breadths, say 195 and 1:V> (the 

 numbers chosen in our last example). 



Calling distances from these axes ac' and y' we find -('f'y') 



This is done by multiplying the frequency in each small square 

 on the chart by the product of its .*' and t/', then adding them all 

 together. In doing this we must remember that the products are 



