SHORTER ARTICLES AND CORRESPONDENCE 



A NOTE ON THE DEGREE OF ACCURACY OF BIO- 

 METRIC CONSTANTS 



The statement is frequently made, either in comment or 

 criticism upon biometric work, that such work is often caused 

 to take on an unwarranted appearance of precision and exactness 

 by the keeping of a larger number of decimal places in the tabled 

 constants than the character of the original data justifies. The 

 contention is made that under no circumstances whatsoever can 

 any statistical constant be more accurate than the data on 

 which it is based. It is held that if one makes a series of meas- 

 urements accurate to a tenth of a millimeter, it is a logical 

 absurdity to table the mean or standard deviation deduced from 

 these measurements to hundredths of a millimeter. Not only 

 is this contention made from time to time by biologists, but 

 occasionally even by a mathematician, a fact which of course 

 tends strongly to confirm the biologist in his opinion. Thus 

 Engberg 1 specifically says (p. 11) referring to mortality statis- 

 tics: "The constants can not be more accurate than the data on 

 which they are based." 2 



The reply which the statistician makes to the criticism 

 that constants can not be more accurate than the data on 

 which they are based is generally that the accuracy of a sta- 

 tistical constant depends not alone on the accuracy of the 

 original measurements but also upon the number of such meas- 

 urements. Further it is pointed out that, because of this fact, 

 it is possible to deduce from measurements known to be individ- 

 ually inaccurate constants of a high degree of accuracy, provided 

 that the errors in the measurements are unbiased (that is as 

 often in excess as in defect of the true value) and tha.t there 

 are enough of the data. Finally the statistician contends that 

 the only proper measure of the accuracy of a statistical constant 



1 Engberg, C. C. The Degree of Accuracy of Statistical Data. Univ. 

 of Nebraska Studies, Vol. Ill, No. 2, pp. 1-14, 1903. 



'In passing it may be said that any one who is sufficiently interested in 

 the phenomenon of a professional mathematician taking this curious position 



Nature. Vol. 69, p. 93, where Engberg 's paper is reviewed. 



238 



