1922.] 



P. C. Mahalanobis : Analysis of Stature. 



29 



Comparing with our " standard" values we see evident signs 

 of "over correction." With such small samples as 200, the P.K. 

 in terminal frequencies are too great to allow the a's and 6'sto 

 be calculated with any degree of accuracy. The transfer of one 

 individual from one group to another would seriously affect the 

 results. 



In order to test this point, I next calculated the a's and b's 

 with a shorter sub-range, i.e. 40 mm. 



Thus P h =P =^L = 5? = i-25 



h 40 



Hence a/-(i'2S) s .a s 



b s '=(r25Y.b s 



I 430- I 470 



-1510 



-1550 



-1590 



-1630 



-1670 



-1710 



-1750 



-1790 



-1830 



-1870 mm. 



vi 



y% 



ys 



n 





y P -4. 



yp-s 



yp-2 



y P ~\ 



yp 



2 



2-5 



6-o 



18-5 



3 8-o 



5i-o 



40-0 



24-0 



15-0 



I'O 



20 



From these we get 



a ] = + -oo 17 50 

 « 2 = --04 83 33 



a % — + to 



« 4 = -TI 



# 5 = + "04 

 leading to 



a{ — + -oo 21 88 



<= ~ °7 55 21 



<= +"i9 53 13 



< = --26-85 55 



fl 5 ' = + -12 20 70 



These give 



giving 

 and 



&1= 



+ •09 36 67 





^2 = 



-•30 5 







63 = 



+ •50 5 







&4 = 



-•42 







&5 = 



+ t6 







&,' 



= + -ii 



70 



83 



V 



= - '47 



65 63 



w- 



- + -98 63 



28 



V 



= -102 



53 



9* 



V 



= + -48 



82 



81 



fx 2 = 1-89 48 76 86 

 S.D. - 68-82 5 

 Mean = 1656-66 58 mm. 



The values are again quite discrepant from those given above. 



With subrange of 25 mm. still more widely divergent values 

 were obtained. 



Hence we are obliged to conclude that with small samples, 

 the probable errors of the terminal frequencies are much too large 

 to allow P airman and Pearson's "full corrections" being calcu- 

 lated with accuracy. 



