18 A BIOMETRIC STUDY OF BASAL METABOLISM IN MAN. 



In certain instances we have found it desirable to determine the 

 relationship between two variables for constant values of two other 

 variables. Thus av ,r th is to be read "the correlation between stature, s, 

 and heat-production, h, for constant age, a, and body-weight, w." 



The actual formulas used in computing the partial correlation 

 coefficients are given in each instance. 



The partial-correlation method has been of great service in this 

 study and will, we believe, prove to be a powerful analytical tool in 

 the investigation of physiological relationships in many fields. 



We now turn to the subject of the probable errors of the statistical 

 constants. 



Because of the differences which obtain between the individual 

 determinations of a series of metabolism measurements, the statistical 

 constants of such measurements will generally differ to some extent 

 from series to series. For example, the average heat-production per 

 square meter of body-surface per 24 hours of 72 men selected by 

 Gephart and DuBois from a Nutrition Laboratory publication is 

 926.65 calories, whereas the average heat-production of 64 other men 

 examined by the Nutrition Laboratory is 924.14 calories. Thus the 

 two series differ in heat-production per square meter of body-surface 

 by 2.51 calories. The standard deviations of heat-production per 

 square meter of the two series are 62.59 and 71.92 calories, or show a 

 difference of 9.33 calories. When another series of measurements is 

 available it will probably give averages and variabilities which differ 

 slightly from either of these. That this should be so is simply a 

 matter of common experience. 



The statistician as such can do nothing whatever to eliminate the 

 individuality of the subjects to which these differences are primarily 

 due or to minimize the slight experimental errors of measurements 

 upon which they to some extent depend. He can, however, furnish 

 criteria of the trustworthiness of statistical constants based on series 

 of observations of known variability and number. These criteria are 

 the so-called probable errors, or more precisely probable errors of random 

 sampling. Such probable errors are entirely statistical in nature and 

 have nothing whatever to do with the possible errors of measurement. 

 They assume the technical or biological correctness of the observations 

 and measure merely the degree of trustworthiness of statistical con- 

 stants based on series of observations. 



In the calculation of the probable error two factors must obviously 

 be taken into account. The first is the variability, the second is the 

 number of the measurements dealt with. If a character, either physical 

 or physiological, is extremely variable it is obvious that an average 

 based upon a given number of determinations will be less trustworthy 

 than one based upon a character which is very slightly variable. For 

 example, the addition of one very heavy individual to a series will 



