1922.J P. C. Mahalanobis : Analysis of Stature. 41 



Adopting the above values of A and B , we get the following 

 table : — 



N 



h m 



h 



10 



11 



222 



20 



16 



157 



50 



25 



100 



100 



35 



70 



200 



50 



5o 



500 



80 



30 



000 



no 



20 



With small samples of 10, h m is n. Grouping for calculation 

 of frequency constants is thus justified even in the case of small 

 samples. On the other hand for JV = io, h t is over 200 mm. which 

 shows the absolute impossibility of judging the adequacy of fit 

 in the case of small samples. In fact with samples of less than 50 

 (for which ^ = 100 mm.) it is practically impossible to test the 

 goodness of fit and hence to judge the reliability of any inference 

 about the general population. Even with iV=iooo, the lower 

 limit is not reduced below 20 mm. Thus, discontinuities of less 

 than 20 mm. may easily escape in samples of 1000. 



It should be observed that so long as h t is greater than h m , 

 we cannot hope to attain great accuracy in judging the significance 

 of a fit so far as the general population is concerned. We see, 

 however, that with samples of 200, h m —hi — ^o mm. It then 

 becomes only just possible to assert, anything about the population 

 sampled with any certainty. It seems as if 200 is the lower limit 

 of safe sampling for anthropological purposes (at least so far as 

 stature is concerned). 



Type IV. skewness, i,epto-kurtosis. 



For Anglo-Indian Stature, our fundamental constants are (in 

 50 mm. working units). 



Mean =16 5679 ±3*21 36 mm. 



S.D.= 67-38 49 8 ±2.55 85 mm, 



V- 4*06 72 + 



/?, = -06 87 56+ 07 97 81 



ft = 3-50 46 + '6o 17 



Sk.= +*io 53 ± -05 68 



d = yog 63 ±478 18 mm. 



i> 2 - i-8i 62 94+ -12 24 91 



f , s = --64 18 53+ -28 60 80 



/^ = 11*56 14 03 + 1-81 91 17 



ft = -86 66 61 (>) 



1 From Biometric Table XLII {a), p. 78. 



