1922.] P. C. Mahalanobis : Analysis of Stature. 67 



earth. At the same time the greater variabilit}^ of the more domi- 

 nant and civilised peoples admit of being interpreted as a result of 

 the lesser severity of the struggle for existence among them. Thus 

 greater variability would be an effect not a cause of the higher 

 state of civilisation.' ' 



Another fact which may be gathered from the above table is 

 this. The more civilised races though more variable, do not in 

 any case occupy the extreme ends of the table. Thus one would 

 probably be justified in inferring that a higher state of civilisation 

 is not associated with extreme degrees of variability. 



We may look at the same question from a different point of 

 view. The less civilised races occupy the extreme ends of the table 

 more frequently than the more civilised races. The less civilised 

 races though on the whole less variable, may thus be associated 

 with extreme degees of variabilities. 



II. The greater variability of more highly civilised races seems to 

 be only moderate in degree and is never excessive. 1 



It seems as if slightly greater variability than the stable type 

 of the species is accompanied by greater adaptability and hence 

 with a higher state of progress. 



Interracial Variability. 



There is another point which deserves attention. By looking 

 at our general list of variabilities, we find some association 

 between average stature (M) and standard deviation or. 



The point which we are considering now is interracial correla- 

 tion between M an o- for the different races.* 



If Pn=S(xy)/N, 



then the correlation coefficient as determined by the product moment 

 method, 3 is given by 



r = l'u/(<Tx.cr y ) 



where <* x and <r y are S.D. of the two variables. 



I find, without grouping, with base numbers 1660 mm. and 

 60 mm. respectively for average stature and S.D. the raw mo- 

 ments to be : — 



For Stature ^' = 5-24 v,' = 1389/48 



' In the selected list (see below) this fact is not so apparent. It seems as if 

 the extremely high variability of less civilised races is due to unreliability of 

 data. 



4 I his is quite distinct from the intra-racial (or within the race) correlation 

 between errors in Mean and errors in S.D. 



In Biom. Vol. 2 (1903), Problem IX, p. 279, is shown that 



In our ease, M 3 is negative, hence a taller subsampte of Anglo-Indians will 

 show less variability and vice versa. This is actually the case with the two 

 subsamples we have already considered. The subsample with a higher average 

 J 658*75 mm. has a S.D. of 68*85 mm - as against the other with Mean = 1657*00 

 tnm. and S. D. =73*26 . 1*3 being small, correlation however, is very small. 



3 See Yule : " Theory of Statistics, " p. iyi. 



