34 Records of the Indian Museum. [Vol. XXIII, 1922.] 



We require some further precise quantitative test. This is 

 supplied by the variability (both absolute, as measured by the 

 Standard Deviation and relative, as measured by the Coefficient 

 of Variation) of the distribution. 1 



V. The variability of the sample should not be significantly 

 greater than the average variability of the same organ for known 

 homogeneous material. 



The Coefficient of Variation, V (multiplication by 100 is merely 

 for arithmetical convenience) is a straightforward measure of 

 variability. It is of course possible to set up other standards by 



choosing some other function of the S.D. and Mean, /( — I , but it 



i & 



is quite unnecessary to enter into such subtleties in the present stage 

 of our knowledge. 



It is quite easy to extend the above condition to the case of 

 more than one organ. In that case we shall have to define va- 

 riability by the generalised 2 or multiple probable error of the group 

 of organs considered. 3 



We have thus got five different tests of cc homogeneity.' ' It 

 should be remembered that we have all along discussed statistical 

 homogeneity. Whether statistical homogeneity necessarily implies 

 anthropological homogeneity and vice versa, is a very difficult 

 question, 4 into which I do not propose to enter. I confine 

 myself to a consideration of purely statistical homogeneity. 



1 For a full discussion see Pearson: Chances of Death "Variation in Man 

 and Woman,'' pp. 255 — 377, specially pp. 272 — 286. Also Appendix I. 



2 K. Pearson and Alice Lee: "On the Generalised Probable Error in Mul- 

 tiple Normal Correlation," Biom. Vol. 6 (1908,, pp. 59 -68. 



Incidentally we may note that variability gives us a convenient method of 

 defining- a " normal " group 1 in a medical, psychological or social sense) of indivi- 

 duals. Tlie normal group (with reference to some particular trait) consists of the 

 individuals Included between the Mean, M, and p times the S.l). a, where/? is an 

 arbitrary number. Thus a "normal " individual is one who docs not differ from 

 the average type of his class by more than p . <r. By a proper choice of p we can 

 make our definition as clastic or as stringenl as we please. We can also extend 

 the definition to cover more than one single trait, with the help of the generalh 

 multiple probable erroi . 

 * K. Pearson: " Craniological Notes. Homogeneity and Heterogeneity in 

 < ollections of Crania," Biom. Vol. 2 (1903), pp.345 — 347. Also see ('. Myer's 

 Reply to above and Pearson's Remarks on the Reply, Biom. Vol. 2 (1903), pp. 

 504- -508, and Aurel \ on Torok's Note and Pearson s Reply. Fbid., pp. 508 — 510. 



