282 Oil the Prohahle Error of Dr Spearman's Correlation Coefficients 
(5) In such cases it should be borne in mind that for STnall samples the 
distribution of p is similar to the distribution of r, but that the mean, even of rp, 
is lower than that of r and the s.D. greater, by amounts which doubtless depend 
on the population correlation. 
(6) R and are not worth determining in serious work ; their use should 
therefore be confined to the elementary statistics for which its author intended K. 
(7) It is interesting to observe that Sheppard's median division fourfold table 
has given for small samples a mean value very much below the population value. 
While this is only what one might have expected, it may in this case be due 
to the coarse grouping which prevented me from making an accurate median 
division. 
(8) The following problems might be of interest to mathematicians : 
(a) The determination of the form of the Rank Correlation Surface. 
(b) The determination of the frequency distribution of p for small samples 
drawn from a normally distributed population. 
(c) The determination of the nature of the correlation surface when a 
standard deviation is taken as one variable and the correlation coefficient as the 
other, both being determined from small samples drawn from a normally distri- 
buted population. 
