366 Pigmentation, Selection and Anthropometric Characters 
The method then enables us to test whether both are random samples of a general 
population. This is done in each of the forty-eight cases, and the is found. 
Having calculated the it is then possible to read off the P from Elderton's 
tables. P gives a measure of the probability of the occurrence of such a distribu- 
tion. When P is found to be "1 or more, it cannot be said that the distributions 
are significantly different. This indicates a probability of 1 in 10. - 01 would 
mean 1 in 100, and this would show that the distribution was almost certainly 
not a random sample. Any values of P between - 1 and - 01 which occur in 
the table are worth noticing. There are eight values of P which work out at 
less than "1, but none of them indicative of probability of less than 1 in 50, 
which is in itself hardly significant in 48 trials. When, therefore, we examine 
the table, and find that these low values of P occur entirely at random, we 
cannot draw any conclusions from it. It would be reasonable to expect to find 
one particular age or one disease distinguished by a low value of P. In the 
former case it would indicate that children of that age group were subject to 
selection from disease ; or in the latter case there would be reason to think that 
the disease in question at all ages exercised a selective influence. On looking at 
the columns giving the values of P for the six different diseases, it is clear that one 
column does not tend to show a lower average value of P than the others. As 
regards ages, however, there are some indications which might at first seem to 
show that the distribution of cases was not equally random between the older and 
younger children. In examining the measles column, it is clear that the values of 
P for the younger children are always less than those which we find for the older 
children. If the values of P were low enough to be really significant in the case 
of the younger children, we should have some grounds for thinking that the 
younger children were being selected by measles ; or, in other words, that some 
type represented in one or more of the pigmentation classes was in process of 
elimination owing to a greater susceptibility to measles. But, as regards measles, 
the figures do not warrant any conclusion of the kind ; for, although P is always 
larger for the older children, the difference in the value of P between the two age 
groups is sometimes only slight, as between "298 and '171 ; and further the lowest 
value of P is only - 079, which indicates a probability of 1 in 13, by no means an 
especially low value. All that can be said is that these figures for measles are 
possibly suggestive. 
When we turn to the other diseases, we cannot discover any regular alternation 
of probabilities between older and younger children, such as there is an indication 
of in the case of measles. In the case of whooping cough, what we discovered in 
measles shows some signs of appearing again; but the series is spoilt by the fact 
that the value of P for boys 13 years old is considerably less than for boys 
3 — -7 years old. The other columns do not even show an approach to a regular 
series. Therefore, from this method of regarding the problem, we are justified in 
saying that the distributions of the various diseases appear with these frequencies 
to be entirely random ; and that this is equivalent to saying that there is no 
