H. E. 80PEK, A. W. Young, B. M. Cave, A. Lek, K. Pearson 353 
This is a lower approximation than Soper's second approximation, in similar 
cases, and we know that even Soper's values are not sufficiently accurate when 
n is as large as 25. Hence no very great confidence can be put in (Ixii). 
But there is another point about (Ix) which is of great importance. Fisher's 
equation, our (Ixi), is deduced on the assumption that ^ {p) is constant. In other 
words he assumes a horizontal frequency curve for p, or holds that a 'priori all 
values of p are equally likely to occur. This raises a number of philosophical 
points and difficulties. We ask: 
When we are in absolute ignorance as to p, is it according to our experience 
that all values of the correlation are equally Ukely to occur? We think this 
question must probably if not certainly be answered in the negative. Very high 
correlations are relatively rare, and most biometricians would find it difficult to 
cite straight away a couple of cases of the correlation equal to — -95 although they 
could cite a score in which the correlation was sensibly zero, or again about -S. 
Every biometrician is seeking high correlations, for these are for him the all im- 
portant data, but he knows how difficult and rare they are to find*. The equal 
distribution of ignorance which applies so well to many statistical ratios, does not 
seem valid in the case of correlations f. We generally know quite approximately 
* We have recently had occasion to table (a) nearly 400 correlations between characters of the 
human femur, and (//) over 300 for characters of the human skull. The distributions were very far 
indeed from horizontal straight lines, and to suppose a priori such distributions horizontal could only 
lead to grave errors. 
f A similar problem arises in the case of standard deviations. If 2 be the s.d. of the sample and 
cr of the sampled population, then the frequency curve for s.d.'s is (Biometrika, Vol. x. p. 523) 
1 k22 
V)i-2 — ^ 
Now, if we make this a maximum for variation of cr, we obtain 
V.-i" 
as the "best value" of <t. 
This was pointed out to the Editor by "Student," and was a desirable criticism of the statement 
made (Vol. x. pp. 528-9) that the most reasonable value to give to 2 was the mode of the sampled 
population, i.e. to take the observed S = 2 = \/' — or suppose 
Equations (a) and (§) are not identical. But again (a) is based on the assumption that all values 
of the S.D. are A priori equally likely to occur. But surely this is not a result in accordance with our 
experience ! Values of cr from 0 to oo are not equally within our experience, and there is almost an 
absurdity in talking about a standard deviation varying from 0 to oo ; are we to include all possible 
scales in this distribution? The s.D. of stature might certainly be anything from practically zero to 
infinity if we measured it first in "light years" and then in microns. Or, are we to measure our s.d.'s 
all in the same units, when we suppose the distribution of s.d.'s to be of equal probability from zero 
to infinity ? How is this to be done in the case of an absolute length and an index ? Given a definite 
problem, there is certainly no d priori likelihood that the s.D. will have every value from 0 to oo , if we 
confine ourselves to one scale. It must practically be less than the mean value, and in most actual 
