K. Pearson 
129 
intelligence, we are led to very remarkable conclusions ! I do not propose to 
discuss this point on the present occasion, nor am I urging the view that the 
material I now put before the reader for his judgment is to be considered final. 
I think, however, that it has for more weight than some recent criticisms would 
admit it to have*. Perhaps, only one who was in continual communication with 
the collaborators during the measurements and observations can apj^reciate the 
conscientious care given to the task, and ho alone can estimate the value of the 
preliminary trials and later tests which were made of the categories and measure- 
ments. 
In regard to the association of mental and physical characters, the correlation 
coefficient may in certain cases screen relationships which are more emphasised by 
examining the material from other standpoints. I have already pointed out how 
the correlation ratio and the coefficient of contingency help us in this matter. 
The regression may indeed not be linear, or there may be, as in the case of hair 
colour, no scale arrangement beyond criticism. For such cases I have found the old 
idea of percentages not without value. In the case of intelligence, I take a normal 
scale as my base line and plot up the percentage of the character for each grade of 
intelligence along the centroid vertical of the corresponding range, drawing a 
horizontal line to represent the mean percentage in the population at large. We 
thus obtain a diagram, which I will venture to term an analograph "f*. 
If the percentage increases or decreases continually with intelligence (or with 
the base character, whatever it may be), I term the relationship homoclinal ; if the 
percentage does not reach its maximum with the maximum or minimum of intelli- 
gence, I term the diagram heteroclinal. There may of course be more than one 
maximum in heteroclinal analographs ; the difficulty will be to distinguish 
true percentage maxima from the 'peaks' due to random sampling. They can, 
however, be tested in any particular case by the probable errors of the percentages. 
The advantages of this rough percentage method are : (i) that it enables us to see 
relationships of a heteroclinal nature, which are screened by a fourfold table 
method of finding correlation — especially in those cases where neither a correlation 
ratio nor a coefficient of contingency is calculable on the available data, e.g. in the 
case of alternative psychical characters, such as noisiness and quietness ; and 
(ii) that it provides a graphic method — more impressive to some minds than 
any numerical representation — available in cases where it is quite impossible to 
construct a regression curve. 
I propose to deal with the relation of intelligence to other psychical and to 
non-measurable physical characters in this manner. The data upon which tlie 
analographs are based have been collected in Table XII for boys and Table XIII 
fur girls. The small number of children recorded as Ve^^y Dull leads to a large 
probable error in the percentages of this category. I have accordingly classed the 
* A reply to the criticisms of G. U. Yule will shortly be published. 
t avdXoyou + ypacpa, the former from Euclid, Book V., and tlie contraction is tolerable as in 
dju</)opei5s. 
Biometrika v 17 
