1922.] P. C. Mahalanobis : Analysis of Stature, 43 



homogeneous groups is nearly normal, but what divergence 

 there is lies in the direction of Type IV." 1 In the case of 

 males, the skevvness is always positive and the Mode is greater 

 than the Mean. 2 Powys used very long series of measure- 

 ments extending to several thousands in each age group. The 

 distribution is lepto-kurtic in every case. 



W. R. Macdonell 3 finds in the case of 3,000 English convicts 

 the stature curve to be of Type IV. The skewness is small and 

 negative and there is slight lepto-kurtosis. Mode is less than the 

 Mean. 



In the case of Verona statistics* the stature of 16,203 con- 

 scripts show significant lepto-kurtosis 5 and a Type IV distri- 

 bution while 3,810 selected recruits show equally significant 

 " platy-kurtosis." 6 Both have significant positive asymmetry 

 and Mode is greater than the Mean. 



J. F. Tocher 7 finds lepto-kurtosis for the Scottish Insane, 

 the curve belongs to Type IV, and there is small positive skew- 

 ness, Mode being greater than the Mean 8 . For long series then, 

 viz. New South Wales males, Italian conscripts, Italian recruits 

 and Scottish Insane, there is agreement as to skewness — in all four 

 cases it is significantly positive ; in one case, the American recruits, 9 

 there is quite significant negative asymmetn^.' American recruits 

 also differ in showing meso-kurtosis. 10 



Charles Goring 11 in the case of the English convict found 

 the distribution approximately Gaussian in type for all crime- 

 groups excepting one. In the only case in which the distri- 

 bution is significantly different from the normal, the curve is 

 of Type IV with significant lepto-kurtosis and marked positive 

 skewness. 



Orensteen 12 found in the case of Cairo-born Egyptians, that 

 the distribution was nearly symmetrical. The criterion K how- 

 ever is less than 1, hence the curve really belongs to Type IV. 



1 Ibid., p. 39. 



2 Ibid., p. 43. Powys mentions skewness as negative. This is probably a slip. 

 b YV. R. Macdonell : " On Criminal Anthropometry and the Identification 



of Criminals," Biom. Vol. I (1902), pp. 177 — 227. 



* Quoted in Miscellena, Biom. Vol. 4 (1906), p. 506 and referred to by 

 J. F. Tocher (see below). 



5 Lepto-kurtic curve are more sliarp-topped than the normal cu ve, the 

 rise being' sharper than the Gaussian. 



fi Platy-kurtic is/' flat-topped ' : as compared to the Gaussian. 



7 J. F. Tocher : "Anthropometric characteristics of the Inmates of Asylums 

 in Scotland," Biom. Vol. 5 (1917), pp. 301. 



- Ibid... p. 182. Tocher says that for long series asymmetry is negative. 

 He evidently means n%. This however is slightly ambiguous and may give rise 

 to confusion. I have thought it better to refer to Skewness in each case, which 

 has its sign opposite to that of ^3, so that Mode is greater or less than the Mean 

 according as skewness in positive or negative (and ^3 negative or positive). 



9 K. Pearson. Phil. Trans. Roy. Soc, Vol. 186 A (1894), p. 385 

 J0 Meso-kurtosis signifies about the same degree of flatness as the Gaussian. 

 11 Charles Goring: "The English Convict," p. 199. 



i-2 Myer M. Orensteen : " Correlation if Anthropometric^ Measurements in 

 Cairo-born Natives," Biom. Vol. XI (1915), p. 71. 



