94 PROCEEDINGS OF THE ANATOMICAL ANJ) ANTHROPOLOGICAL 



any two samples drawn from the same material. This maximum 

 possible difference of sampling is calculated by the formula : 



where <r l and o- 2 are the standard deviations of the two groups, and 

 Nj and N 2 the respective numbers in the two groups. 



Let us take as an example of the application of this formula 

 the two groups of children measured by Prof. Matthew Hay and 

 Dr. Leslie Mackenzie in Aberdeen and Edinburgh. 



The following table gives the number measured between the 

 ages of twelve and fifteen years, the average stature, the average 

 length of head and the average breadth. 



No. SUture. L. B. 



Edinburgh 100 55'26 1861 145-3 

 Aberdeen 101 57'3 184 145 



The difference of stature = 57 '3 - 55 - 26 = 2 in. Unfortunately 

 sufficient data are not given in the Report of the Hoyal Commission 

 on Physical Training to determine the standard deviations of the 

 two groups. In other cases of children born within the same twelve 

 months the standard deviation is about three. It will be greater 

 when the range of age is twelve to fifteen. If we take cr = 4 



+ &. 1-7 

 100 + 101 = 



In this case 2 in difference of stature would be significant of a 

 real difference. But if o- = 5 



2 2 



i/\rt + T7\T == ^'1*3 



and in that case the difference would not prove with practical certainty 

 that the difference was significant of a real difference. It might be 

 obtained between two samples taken at random from the same 

 material. 



The same formula applied to the length and breadth of head 

 shows that the differences of these dimensions are certainly not 

 significant. 



