42 
Variation and Correlation in Brain- Weight 
the calculated frequencies {in,.), aud the ratio of the squared difference between the 
two to the calculated i^^*^ — '^^^^ll ^ _ 
Here n the number of frequency groups is 15 and %''^= 11"32. From Elderton's 
Tables* the value of P may be obtained. With-?i' = 15 and 11 the value of P 
as given in the table is •686086. Or, expressed in words, if the brain-weight of 
Swedish males obeyed the " normal " distribution of frequencies wo should expect 
to get a greater divergence between theory and observation in roughly 65 out 
of every 100 trials when the trials were based on random samples of 416 indi- 
viduals each. In other words, the fit may be considered very fair, and certainly 
entirely satisfactory for all practical purposes. 
7. Tlie Gorrelution of Brain-iveight tuith other Characters. 
In the introductory portion of this paper it was stated that one of the chief 
objects for which the work was undertaken was to measure exactly the degree and 
nature of the association between brain-weight and other characters in man. All 
workers on the subject have realized the importance of such determinations and 
numerous attempts have been made to arrive at them. The methods used, 
however, have not been such as to lead to definite and sound conclusions. These 
methods have in the main consisted in tabulating the mean brain-weights for 
various groupings of the other characters under consideration. In this way it can 
of course be determined whether there is any shift of the mean as the other 
character changes. Further than this one cannot go. Besides, in this method 
there lurk numerous pitfalls unless one uses it with a clear understanding of 
some of the fundamentals of statistical science. Different results can be obtained 
as the material is differently grouped. Hence, it is not strange that we find 
conservative anatomists making only very general statements as to the correlation 
of brain-weight with other characters, and, in those cases where an attempt at 
greater precision of statement is made, considerable difference of opinion as to 
what conclusions shall be drawn from the data. What are wanted in the case 
are not simply inspections and general " appreciations " of tabular lists of brain- 
weighings, or of ratios and indices, or even of correlation tables or regression lines, 
but instead definitely determined coefficients of correlation with their probable 
errors. With these we can get in given cases precise statements of the degree of 
correlation between different characters. 
It would of course be highly desirable to measure the correlation between the 
weight of the brain and a great variety of other organs and characters of the body. 
Such characters will at once suggest themselves to anyone interested in the 
problems of correlation. For instance, aside from age, stature and body-weight 
for which material is available, there are the whole range of skull characters; the 
* Biometrika, Vol. i. p. 161. 
