CHANGES IN METABOLISM WITH AGE. 121 



We shall now turn to a more detailed consideration of (4) . To test 

 more critically the linearity of the regression of total heat-production 

 on age we may have recourse to the calculation of the correlation 

 ratio 9 and the application of Blakeman's test for linearity of regression. 



To secure correlation ratios which shall be of value we must group 

 with regard to age. Table 42 shows the age grouping adopted, the 

 number of individuals, and the mean heat-productions in the total 

 men and women. 



For age and total heat-production as deduced from this table the 

 correlation coefficient, r ah , and correlation ratio, Yi ah , are : 



Correlation Correlation 



coefficient, r. ratio, >). 



Men -0.3017 0.0526 0.3575 0.0504 



Women -0.1946 0.0639 0.3458 0.0585 



The correlation coefficients for the two sexes differ so greatly that 

 one would be inclined at first to suspect arithmetical error, but the 

 value for the women ungrouped with respect to age as recorded on 

 page 111 is essentially identical with this constant, i.e., 0.2034 =*= 

 0.0637 as compared with -0.1946 0.0639. 



The correlation ratios are in much closer agreement than the corre- 

 lation coefficients. With regard to their probable errors the correlation 

 ratios do not differ. The difference between the correlations for men 

 and women is 0.1071 0.0827, a value which, while large in comparison 

 with the constants upon which it is based, by no means represents a 

 certainly trustworthy difference. 



Applying Blakeman's criterion 



_! I ' l 



= *, ' 2 



where x : is the value of 0.6744S98/\/# f m Miss Gibson's tables, 10 

 we find : 



For men 

 For women 



Applying the same methods to the problem of the interrelationship 

 between age and total heat-production per kilogram of body weight we 

 have for r , and v\ . : 



ah k >ah k 



Correlation Correlation 



coefficient, r. ratio, TI. 



For men ................ -0.3840 0.0493 0.4414 0.0466 



For women .............. -0.4962 0.0501 0.5695 0.0449 



The correlation coefficients and the correlation ratios are numer- 

 ically higher in both sexes. The correlations are but slightly more 



9 Blakeman, Biometrika, 1906, 4, p. 332. 



10 Gibson, Biometrika, 1906, 4, p. 385. Also in Pearson's Tables for Statisticians and bio- 



metricians, Cambridge, 1914. 



