Student 
2G5 
tific Management,' the author mentioned three methods of determining correlation, 
p which is to be used for samples smaller than 30, R for samples over 30 and r 
which though acknowledged to be rather more accurate is not to be used at all 
since it takes four times as long to calculate as the others. 
Now to save time at the expense of accuracy is justifiable when, and only when, 
the time saved can be devoted to increasing the number of observations so as to 
obtain greater accuracy on the whole series, otherwise it will take longer to get 
equally trustworthy conclusions, and it seems to be of interest to investigate the 
probable errors of p and R for samples of the size that the employment psycho- 
logist is contemplating. And here we may note that the saving of time only occurs 
when the sample is comparatively small ; as it increases, the labour of grading 
becomes more and more severe till at some point in the neighbourhood of 40 it 
becomes quicker to use the ordinary product moment r if that be possible. 
It should perhaps be pointed out that there are many cases where it is possible 
to grade a sample for some character which is not capable of being measured on a 
scale and it might be thought that in this case large samples could profitably be 
dealt with by the p or R method, but in fact it is just these scaleless characters 
which present the greatest difficulty in grading. 
We have then to consider the variability of p and R and of the derivatives rp 
and r^, determined from small samples, and it seemed worth while to use the 
material of a former sampling experiment so as to get an idea of how small samples 
depart from the results obtained by Prof. Pearson for ideally large samples. The 
material in question consists of 750 samples of four drawn from a population of 
3000 criminals whose height and left middle finger length give an approximately 
normal correlation surface with correlation "66. 
These are capable of being combined easily to give 375 samples of eight and in 
addition there are 100 samples of 30, which may be taken to be a size of sample 
which is no longer quite ' smalL' 
Accounts of the former results were given in Biometrika, vi. p. 1 and p. 302, 
since which time the frequency distributions of the correlation coefficients of small 
samples drawn from normally correlated populations have been very thoroughly 
investigated by Soper, Fisher and the authors of the cooperative paper in Vol. xi. 
p. 328 of Biometrika : it is hoped that some mathematician may be interested in 
the general solution of the problems raised in the present paper which may then 
afford material for checking his results. 
When I came to apply the methods to my samples I found that owing to the 
rather coarse grouping, there were a large number of ties, so that it became neces- 
sary to find out the right correction for ties. 
Prof Pearson had discussed the question of ties and had suggested two ways of 
dealing with them. One way was to rank them all as if they were the highest 
number of the tie which he called the bracket-rank method and the other was to 
rank them all half-way down the tie which he called the mid-rank method. Thus 
