cviii Tables for Statisticians and Biometricians [XVIII XX 



and we find from Table XX for n= 14 a probability P 2 (X) well over -25. There 

 appears therefore to be no reason to suspect the existence of further anomalous 

 observations. 



(ii) Consider the following capacities in cubic centimetres of 17 Moriori skulls: 

 1230, 1260, 1318, 1348, 1360, 1364, 1378, 1380, 1380, 

 1410, 1410, 1420, 1445, 1470, 1540, 1545, 1630. 



We may ask: Is the capacity of 1630 so anomalous that it should be rejected? The 

 mean is 1405'18 and the standard deviation 97*83. 



(a) In applying this method we have usually to consider two points : (a) whether 

 one value should exist beyond the last but one, and (6) whether it exists too far 

 away from the last. To test briefly the two points at once it is often adequate to 

 take a value approximating to the last one. In this case, say 1600, we have 



(1600 - 140518)/97'83 = 1'99, 



which leads to ^(1 +) = '9767 and the chance of an individual outside the limits 

 + 1600 = '0466; and accordingly in 17 trials we should expect '792 individuals, or 

 we have no reason for rejecting the 1630 value. 



(/9) Chauvenet's criterion gives 



Thus &o- = 2-18 x 97-83 = 213-27, denoting limits 1191-91 to 1618-45. 



Thus, according to Chauvenet, this skull 1630 is anomalous and should be 

 rejected. Again this test shows too easy rejection. 



(7) If we apply Irwin's test we have (1630 - 1545)/97'83 = '869 for X, which 

 gives us, from Table XIX, Pi(X) for n = 17 in the neighbourhood of -134. Thus 

 the odds are only 6 or 7 to 1 against its occurrence. We are not justified in 

 rejecting it. 



As a matter of fact the skull in question is undoubtedly large, but nevertheless 

 has the typical Moriori characteristics, and one has no hesitation in saying that it 

 belonged to a member of that race. 



N.B. Our Tables XIX and XX are worked out only for the differences 

 between the first and second, and the second and third individuals; we do not know 

 the distribution of differences between the third and fourth, or any other pair of 

 neighbours. But we do know that such differences are less on the average than 

 those between the second and third, if we take care that the pair under con- 

 sideration are on the same side of the mean as our first and second pair. Hence 

 P 2 (X) will give us an upper limit for the probability of a difference between such 

 pairs. This fact enables us readily to test whether outlying groups of observations 

 are possibly anomalous. 



