1922.] P. C. Mahalanobis : Analysis of Stature. 57 



The solution 



is 



given by 











w i = 



2-19 75 







w 1 = 



•66 



89 







Since r 2 = 



i-8i 



62 



We get 





<r,= 1-48 24 

 = 74*12 mm. 





<r 2 = '8l 78 63 



= 44*89 mm. 



And 





I " I 4 73 

 W| = — :L 4ri . 200 



1 1-52 86 

 = 150-11 





'38 13 

 1-52 86 

 = 49-89 



It is thus possible to break up the curve into two normal 

 curves with the same Means but widely different Standard Devia- 

 tions. It will be observed that nearly three-fourths of the sample 

 has got a greater variability, while about one-fourth seems to be 

 a very stringently selected group. This particular solution may 

 be only a peculiarity of the sample and may have no reference to 

 actual fact so far as the general population is concerned. A 

 calculation of the probable error of ft may throw some light or/ 

 the question. 



Pearson l gives the percentage variation of ft to be 23-3 in a 

 sample of 500. Multiplying this by 



A/500/200 = ^/2'5, 



we get the percentage variation in a sample of 200 to be 36 84. 

 Hence the probable error in the present case is so large as ±9*28. 



We thus have ft =25*236 + 9-28 



If we take our actual value of ft = 3.5, the necessary condi- 

 tion for a real solution is that ft must be greater than 20*42. If 

 the value of ft for the general population is less than 20-42 

 (with a value of ft = 3*5) then the present method of dissection 

 will fail. 



This limiting value is only 4*82 less than the value of ft in 

 the sample, while the probable error is ±9*28. It is therefore 

 not at all unlikely that ft should be less than 20*42 in the general 

 population. We conclude therefore that it is not unlikely that 

 the possibility of this particular type of dissection is only a pecu- 

 liar property of the sample and has no reference to actual fact in 

 the case of the general population. 



Hence we are not justified, on this evidence alone, in conclud- 

 ing that the sampled population is heterogeneous in character. 



Note added on the 2jth November, 1920. 



In view of the great importance of the question of hetero 

 geneity I thought it desirable to consider this question in greater 



1 K. Pearson: "Skew Correlation and Non-Linear Regression 

 (Draper's Company Research Memoirs). 



