Miscellanea 
127 
This is what Mr Galton has called a coefficient of correlation, and it must be distinguished 
from a coefficient of regression. In the case before us, if we take an " array " of flowers, such 
that the number of stamens in every flower differs from the mean number by Aj, then the mean 
number of pistils in the array will be 
i/p+r^A„ 
0"s 
where — is the "coefficient of regression." Now in this case the quantity which Dr Verschaffelt 
proposes as the measure of correlation is, if I understand him rightly, the mean for all arrays of 
As a/ Mj,' 
i/s 
and by using this value as a measure of correlation. Professor MacLeod has been led to state 
his interesting results in a rather erroneous way. In the first place, since Dr Verschaft'elt's 
measure of correlation is really in part a function of a measure of regression, it has one value 
if we determine the mean number of pistils associated with a given deviation from the mean 
number of stamens, another if we start with known deviation from the mean of pistils, and 
proceed to determine the mean associated deviation of stamens: for the mean number of 
stamens in an array of deviation Ap from the mean number of pistils is 
M, + r^Ap, 
o-p 
and Dr Verschaffelt's measure of correlation in this case is r~ . But, apart from this, the 
o-p i/s ' ^ 
introduction of the ratio between the means of the two variables has so much effect as to 
destroy the value of the quantity proposed as a measure either of regression or of correlation. 
We see this in Professor MacLeod's treatment of his results. 
If we treat Table I., based upon 268 " early " flowers, which appeared between February 27 
and March 17, as we treated the table of "late" flowers, we find 
i/, =26-731343 ; o-^ =3-76088 
i/j, = 17-447761 ; o-p = 3-89425 
r= 0-5065, 
so that the correlation between number of stamens and luaiiber of pistils is very distinctly less 
in early than in late flowers. The probable error of the value of ?• for early flowers is 0-0306, 
and for late flowers it is 0-0153 ; so that the difference between the observed values is certainly 
significant. 
In an array of early flowers, all of which have a number of stamens differing from the mean 
number by Aj, the mean number of pistils should, from the values obtained, be 
0-5065x3-89425 
17-447761 + — 3:^- ---A. 
= 17-447761 +0-524 As, 
or a given deviation from the mean number of stamens should be associated with a deviation of 
little more than half that amount from the mean number of pistils. 
An examination of Table I. will show that this conclusion is as nearly in accord with 
observation as the numbers in the table would lead one to expect. It is certainly far more 
intelligible than that to which we are led by Dr Verschaffelt's method, which induces Professor 
MacLeod to assert that the correlation is in this case nearly perfect,— the diff'erence being due 
to Dr Verschaffelt's use of the ratio between the means, so that the " measure of correlation " 
M 
obtained by his method should be 0-524^ =0-803. 
