20 A BIOMETRIC STUDY OF BASAL METABOLISM IN MAN. 



it is possible to estimate from the observed differences in the constants 

 the chances of the materials being differentiated. This is, of course, 

 the practical application of the principle. The physiologist desires to 

 know, for example, whether an observed difference between two con- 

 stants, one based on athletic and the other on non-athletic individuals, 

 indicates a real biological or physiological difference attributable to ath- 

 letic training, or whether it is merely of the order to be expected as the 

 result of random drawing of groups of subjects of the number dealt with. 



For example, the daily heat-production of 16 athletes is found 

 from table 16 to be 1876.56=1=41.33 calories. That of the first supple- 

 mentary series of 28 men is 1605.18 ==28.19 calories. The difference 

 between these two constants is 271.38 ==50.03 calories. The difference 

 is 5.42 times as large as its probable error and the odds against its 

 being due to errors of random sampling are large. 6 Thus we may 

 conclude that athletes are different from ordinary individuals in their 

 gaseous metabolism. 



Again we note that in a series of 72 men selected by Gephart and 

 Du Bois from the Nutrition Laboratory publications the average heat- 

 production is 1623.46 ==14. 11, whereas in another series of 64 indi- 

 viduals it is 1641.05 ==19.48. The difference is 17.59 ==24.05. Thus 

 the difference is less than its probable error and can not be considered 

 statistically significant. In short the two groups of men may be con- 

 sidered to show the same average metabolism. 



The practical use of the probable error is almost invariably in the 

 carrying out of comparisons. The investigator desires to know whether 

 a particular statistical constant differs either from some preconceived 

 or theoretical standard or from some other constant. For example, 

 the physiologist may wish to know whether the mean metabolism of 

 women differs significantly from that of men. In the case of correlation 

 an apparently, but not essentially, different problem presents itself. 

 One often desires to know whether there be any relationship at all 

 between two variables. He then inquires whether an empirically found 

 value of the correlation coefficient has a "significant" value. This 

 is necessary because of the fact that if correlations were based upon 

 small series of individuals drawn at random from an infinitely large 

 series in which the correlations were zero, a numerical value would in 

 many instances be obtained. This is true for the same reason that a 

 small number of determinations of basal metabolism on a group of 

 febrile patients would show an average value differing from that ob- 

 tained on a small group of normal subjects, whether there be any real 

 influence of fever on metabolism or not. 



In such cases we wish to know whether the correlation differs 



Throughout this volume we have taken differences of 2.5 or 3 times as large as their probable 

 errors to be significant, always remembering that the interpretation of probable errors is difficult 

 when the number of observations is small. 



