Harris, Correlation in the Inflorescence of Sanguinaria. 



The coefficient of correlation of the statistician lies between 

 and plus or minus 1, a constant with the value indicating that 

 there is no relationship between the two characters of the series 

 of individuals under consideration, while constants of the magnitude 

 of 1 show that the interdependence is perfect, i. e. such that 

 knowing the magnitude of one character of an associated pair we 

 can state positively the magnitude of the other. The biologist 

 must remember that the statisticians constant is purely descriptive 

 and not interpretative. Generally we cannot know which character 

 influences the other, or indeed whether both are not merely depen- 

 dent upon some group of causes external to themselves. Being 

 merely a description of the materials in hand, the correlation con- 

 stant may be influenced by age differences or other heterogeneity 

 of the material, and cannot be taken at once as the equivalent of 

 the conception of correlation which the physiologist holds. It 

 would seem to me, however, the most trustworthy and usable tool 

 for analyzing out and measuring this physiological correlation. 



Consider first the relationship between the length of the pedicel 

 and -the length of the fruit. For the 1906 series we find a corre- 

 lation of -335 -019, showing that there is a very substantial rela- 

 tionship between the two characters. This cannot be interpreted 

 as meaning that the length of the stalk has a direct influence on 

 the length of the fruit, or vice versa. Their interdependence 

 may be due merely to their mutual dependence upon some other 

 factor (age, physiological vigor, individual environment) but we have 

 at least demonstrated the existence of the interdependence and 

 measured its intensity on a scale directly comparable with other 

 characters, thus allowing of further studies by comparative or 

 experimental methods. 



In like manner the correlation between length of pedicel and 

 the fertility of the fruit may be obtained. We find: 



Length of pedicel and total ovules per fruit, -323 -019, 



Length of pedicel and total seeds per fruit, -363 -019. 



The closeness of interdependence is therefore about the same 

 as for length of peduncle and length of fruit. 



The correlation for length of pedicel and number of seeds 

 developing is slightly higher than that for length of pedicel and 

 number of ovules formed, but the difference is only -040 -027, 

 hence no biological significance can be attached to it. If the degree 

 of development of the peduncle furnishes some indication of the 

 vigor of the individual one would rather expect to find a closer 

 correlation between it and the number of seeds developing than 

 between it and the number of ovules formed. In Sanguinaria as 

 I have studied it over 75 per cent, of the- ovules develop into seeds 



4) Pearson, K. Proc. Roy. Soc. Lond. Vol. LIX, pp. 301305, 1896. 



