1922.] 



P. C. Mahalanobis : Analysis of Stature. 



39 



gate the statistical properties of the general population. 1 In 

 subsequent analysis we have for this reason always adopted 50 

 mm. as our unit. With finer groupings we are likely to obtain 

 mere individual peculiarities of our sample which may not have 

 any connexion whatever with the properties of the general popu- 

 lation. 



We shall try the effect of other values of Mean and S.D. on 

 " Goodness of Fit." 



With 20 mm., M = 16 562938, S.D. = 67*13 25 



n 



19 



% — 



X -25-59 42, 



P= -io 98 81 



Only once in ten trials the fit will be worse. The end con- 

 tributions being rather large, we again combine the terminal 

 frequencies and obtain a much better fit. 



n'=iy, # 2 = 2i'2o 72, P= -iji2 



That is once in six trials we will get a worse tit. 



Tabi,e 4. 

 Summary of l< Goodness of Fit." 



Mean. 



S.D. 



n'. 



X-2. 



P. 





Unit oj 



: grouping =: 



>o mm. 





1656-29 38 mm, 



67-13 15 



19 



25-59 42 



•10 98 81 







17 



21-20 yT) 



.17 12 



1656-29 38 



67-38 49 8 



19 



22-69 9 



•20 30 09 







17 



18-48 2 



•29 72 74 





Unit oJ 



: grouping = < 



;omm. 





16 56-25 mm. 



69*00 



7 



3'47 



•75 67 24 



16 56-51 



67-21 95 



7 



2-93 82 



•81 56 98 



16 56-25 



67 47 5 



7 



3-02 09 



•80 65 85 



16 56-25 



67-38 49 8 



7 



2-77 88 



•83 33 98 



20 mm. gives a fit of about the same order in each case. 

 Even with such fine grouping, we get an indication that Gaussian 

 distribution is not impossible, but we cannot assert that the normal 

 curve is fully adequate. 



With 50 mm., the fit is excellent in every case. Even with 

 the highest observed value of S.D., namely 69*00 mm., we 



1 This is the reason why 50 mm. is selected as our standard unit of grouping, 

 For purposes of comparison. See pag'e 21. 



