The measure of the dependence of weight on height is given 

 by the coefficient of correlation between the two. The follow- 

 ing table gives the coefficients of correlation of weight with 

 height for the two sexes, for each of the two years: 



TABLE 9 



Coefficients of Correlation of Height and Weight * 

 Boys and Girls, Ages 14 to 15 and 15 to 16 



These coefficients show that, within narrow limits, particu- 

 lar weights are associated with definite heights, and vice versa. 

 The heights and weights increase and decrease together in close 

 correspondence. This is particularly true for the boys, as is 

 shown by the high correlation obtaining in their case. In 

 regard to the girls the correlation is not so high, but is none 

 the less significant; the coefficient in their case being at least 

 as high as that found by Pearson for the inheritance from parent 

 to child of physical characteristics. The lesser correlation for 

 girls than for boys signifies that for any given height the girls 

 range over a greater series of weights than do the boys. This 

 will be seen more clearly in Table 16 (page 37) which contains 

 the standard deviations from the average weights for each inch 

 of height. This is an interesting phenomenon in view of the 

 fact that, as we have seen, their total range of variation is 

 smaller. It will also be noted from Table 9 that the corre- 

 lations decrease with age in the case of both the boys and the 

 girls. 



The above coefficients of correlation are uniformly lower 

 than those found by Boas in his study of the Worcester chil- 

 dren. Thus, at the age 14 to 15, his figure is .87 for boys and 

 .74 for girls. In agreement with Boas, on the other hand, is 

 the fact that the coefficient of correlation for boys is greater 

 than that for girls in each year, and also that there is a decrease 

 in the value of the coefficient for each sex with an increase in 



* These values are based on figures presented in detail in Table 20, 

 Parts A-D, Appendix II. 



17 



