S6o 



EVOLUTION, GENETICS, AND EUGENICS 



where d represents the actual deviation and S the sum, n the number 

 of individuals; <r the standard deviation. 



"Correlation tables" show graphically whether or not there is 

 correlation. If, as in Figure 94, we want to find out what is the rela- 

 tionship between total yield of oats and number of culms to the plant, 

 we may make a table with subject classes arranged perpendicularly, 

 and the relative classes, horizontally. If the individuals tend to group 

 themselves about a diagonal ranging from upper left- to lower right- 

 hand corners, the amount of correlation is quite marked. Complete 

 correlation would be represented by a single line of points along this 

 diagonal. No correlation would be shown by random distribution 



2 3 4 5 6 7 



3 

 50 



106 



109 



80 



42 

 7 

 2 

 1 



50 



134 



167 



38 10 1 400 



Fig. 94. — Correlation table of 400 plants of Sixty-Day oats. Total yield of 

 plant in grams, subject. Number of culms per plant, relative. 1910. Coefficient 

 of correlation = 0.712 ±0.017. (From Love and Leighty, IQ14.) 



over the whole rectangle. Inverse correlation would tend to give a 

 grouping about a diagonal ranging from the upper right- to lower 

 left-hand corners. 



In the particular correlation table used for illustration, the coeffi- 

 cient of correlation (r xy ) turns out to be 0.712=1=0.017. Since com- 

 plete correlation would be 1, the degree of positive correlation is very 

 high, as we might expect. The correlation table was used quite 

 effectively by Galton, as we have already shown in chapter xxxvi. 



