INTRODUCTORY. 5 



the whole problem is some measure of the intensity of these and many 

 other interrelationships, expressed on such a scale that comparisons 

 between various characters may be easily and directly made. This end is 

 readily attained by the use of the modern correlation formulas. 



The analysis may be pushed further. We have just said that tall 

 individuals produce on the average a larger number of calories than 

 short ones, and that heavy individuals set free on the average more 

 heat than light ones; but tall individuals are on the average heavier 

 than short ones, and the question naturally arises whether their greater 

 heat-production may not be due exclusively to their greater average 

 weight. This problem can be solved only by correcting the correlation 

 between stature and heat-production for the influence of the correlation 

 of both stature and total heat-production with body- weight. A quite 

 similar method of analysis may be applied when it is desired to correct 

 the relationship between two variables, for example between age and 

 heat-production, for the influence of both of two other variables, say 

 stature and body- weight. 



Knowing the correlation between two variables (for example, body- 

 weight and total heat-production) it is possible within certain limits 

 of accuracy to predict the average value of one from the known magni- 

 tude of the other. Thus it is possible to pass at once from measures of 

 interdependence on the universal scale of correlation to coefficients 

 showing just how much on the average an associated character increases 

 in units of the actual scale on which it is measured for each unit's 

 change in the first variable. These relationships are of the greatest 

 practical importance, in that they enable us to determine the most 

 probable metabolism of an unknown subject of given stature, weight, 

 and age, and these predicted values may serve as a control in cases in 

 which it is desired to investigate the influence of particular conditions, 

 e.g. the incidence of a specific disease, on metabolism. 



Finally, one of the great advantages of the use of the statistical 

 method lies in the system of probable errors which are provided by 

 the biometric constants. Metabolism varies from individual to indi- 

 vidual. If the average value of a series of determinations be employed 

 as a basis of argument concerning some physiological relationship, the 

 worker must fully recognize the fact that a repetition of the measure- 

 ments upon another set of individuals apparently comparable with the 

 first would give averages somewhat different. The probable errors 

 of random sampling, to be discussed in somewhat greater detail in 

 a special section on methods of statistical analysis, do much to 

 establish the limits of trustworthiness of not only the arithmetical 

 means or averages but of all the other statistical constants. Thus 

 the biometric formulas make possible a far more definite conception 

 of the limits of trustworthiness of metabolism constants than has 

 heretofore been possible. 



