180 A BIOMETRIC STUDY OF BASAL METABOLISM IN MAN. 



bad results in the case of the women. From mere inspection of the 

 frequency distributions of this series of errors it is impossible to dis- 

 criminate between the value of the three other methods of prediction. 

 Having recourse to the three tests of accuracy of prediction used 

 in the foregoing discussion we find the following results from the 

 ungrouped deviations. The average deviations of the predicted from 

 the actually observed values with regard to sign are the following: 



Calculated from body-Weight Men. Women. Difference. 



By means +15.346 +32.243 +16.897 



By equations - 0.007 - 0.019 + 0.012 



Difference +15.339 +32.224 



Calculated from body-surface 



By means - 0.919 + 2.816 + 1.897 



By equations + 0.015 + 0.029 + 0.014 



Difference + 0.904 + 2.787 



This comparison brings out with great clearness three important 

 results. 



1. The average error with regard to sign of prediction from average 

 heat-production per unit is enormously greater than that in prediction 

 by the use of regression equations. This is true whether body-surface 

 or body-weight be used as a basis of prediction. 



2. The errors in predictions from body-surface by use of the mean 

 heat per unit of body-surface in the standard series is far lower than 

 that resulting from prediction from body- weight. 



3. The errors of prediction are in all cases larger in the calculations 

 for women than the comparable values for men. 



As far as it goes, therefore, this test indicates the superiority of 

 body-surface over body-weight as a basis of prediction. 



The superiority of the regression equations for purposes of predic- 

 tion over the old method of considering heat-production directly 

 proportional to body-weight or body-surface is the most striking, and 

 doubtless the most valuable, feature of this table. The old method 

 of estimation gives average errors of from 0.9 of a calorie to over 

 32 calories per day, depending on the sex and method of prediction 

 used. The new method of prediction does not in any case give an average 

 error of as much as 0.03 calorie per day! 



Turning now to the average deviations without regard to sign of 

 the predicted from the observed values we have the following results : 



Calculated from body-weight Men. Women. Difference. 



By means 122.5 165.3 +42.8 



By equations 97.6 98.0 + 0.4 



Difference + 24.9 + 67.3 



Calculated from body-surface 



By means 93.7 99.7 + 6.0 



By equations 92.0 97.2 + 5.2 



Difference + 1.7 + 2.5 



