238 , Annals of the South African Museum. 



observations made, and <ri and a^ the standard deviations of the 

 two averages. 



If the difference betv^een the two averages is equal to the square 

 root of the sum of the squares of the standard deviations divided by 

 the number of observations in each group, i.e., 



M, - M. = ^'£ + ;j} 



then it is an even chance that such a difference is due to random 

 selection. If — 



then it is roughly 50 to 1 against the difference being due to 

 random sampling, and if — 



VN, + N, 



it is 1,000 to 1 that the difference is not due to chance selection, 

 but to the action of some definite cause. It is usual to take this 



value, 3^ '- + ^, as definitive, and say that when the difference 



l)etween two averages exceeds this the difference is significant, and 

 when it does not that the possibility of random sampling comes in 

 to an extent which prevents a difference due to some definite cause 

 other than chance being proven. To illustrate by example, the 

 average cephalic index of the Strandlooper skulls was found to be 



_2 



77-1, and the value of ^ for this group was -74. The average 

 index of the Bushmen skulls other than Strandloopers was 75-7, 

 and the value of ^ was -04. The difference of these two averages 

 is 77-1 - 75-7 = 1-4, and the value of— 



Three times this = 2*64, which is greater than 1-4, indeed twice 

 this, 1"76 is greater, so that the difference between the two averages 

 falls well within the limits of possible random selections. 



On the other hand, the average index of the Eastern Bantu 



