OF ERRORS OF JUDGMENT AND ON THE PERSONAL EQUATION. 
263 
for they would be personal to ourselves, and in actual observation they could not be 
eliminated from our own future exj)eriments, nor could the like causes be determined 
for other observers. We are forced to admit, I think, that correlation is a personal 
character of every pair of observers, and to look upon it as a personal constant to 
be determined by experiment. 
Here again, however, arises the very same point as we have considered in 
discussing absolute steadiness of judgment—^we do not in practice know the absolute 
judgments, and so cannot find the correlation of absolute judgments, 
All we can do is to refer the judgments of two observers to a third as standard, 
and then measure the correlation of relative judgment. In this case we have a 
result which is not purely personal; we have superposed on the correlation due to a 
common element in personality, an element of “ spurious correlation.” 
Taking the bright-line experimental result from Table VI., we have for 519 
observations : — 
^32 = -3819 ± -0253, Pi, 33 = -5625 ± '0202, 
^3 = ‘1571 ± -0289, p3, i3 = -3055 ± ‘0268, 
= -0139 ± -0296, p3,2i = -6154 ± -0184. 
The latter series, all that we should usually know, enables us to form no opinion at 
all about the former. The absolute judgments of Dr. Macdonell and myself have 
sensibly no correlation ; our relative judgments have the greatest correlation of all—• 
such are the masking effects of spurious correlation when judgments are referred to a 
third observer as standard ! 
If, from the values of the standard deviations of the absolute judgments, we 
calculate what would be the spurious correlations on the assumption that the absolute 
judgments are not correlated, we have by the method of j:). 241 :— 
0 
o —_ fin_ 
u 1’ 32 //^ 2 t 2\ // 2 I 2\ 
VV^OI ^02 /vC^Ol "T ^U3 / 
Q 
— _ _^2_ 
Pi’ 13 y/(o"02 “ + + O’!)!") 
o 
—_yo3_ 
Hence p^, 33 py, 32 = '1707, p 2 ,13 p.^, 13 = ‘0756, and pg, 21 p^, 21 — ’0859, 
or the effect of the correlation of absolute judgments is to increase in one case and 
decrease in the other two the sjiurious correlation. Without direct experiments 
a d hoc I see no way of determining from the usual data of the personal equation how 
much of the observed correlation of judgments may be due to a common element in 
the personality, and how much is really spurious. The two causes sometimes work in 
the same, sometimes in opposite directions. 
= -3918, 
= -3811, 
= -7013. 
