OF EEROES OP JUDGMENT AND ON THE PERSONAE EQUATION. 
243 
We have thus the series : 
Pi) 23 — 
31 — 
P3512 — 
0 
+ 
- 
0 
^ 23"" 
2 
(TljO-j.j 
erf 
+ 
0 
0 
2 
^23^21 
Tsi" 
+ 
0 
^32" 
0 
2 
(x.). 
These suffice to find the p’s as soon as a series of experiments giving relative 
judgments has been carried out. Tliey will not suffice to differentiate the real and 
the spurious parts of the correlation between tlie relative judgments. 
These results are, of course, quite independent of any theory of normal distrilDution. 
The correlation coefficients will give the probable value of an error of judgment which 
A will make when we know the error that B has made in tiie same observation. 
Thus, if Cgo be the average error made by a second observer when a first makes the 
error we shall not have equal to the personal equation of the second observer, 
but given by 
^02 = iAs - Pod'l2 ^ + ^uU’l2 ^ .(xi.)- 
"01 "oi 
Again, if be the average error made by a second observer relative to a first, when 
a third observer makes an error relative to the first of then Avill not be equal 
to the relative jiersoiial equation of the second observer, but must be determined 
from 
^'12 — P12 V\Z Pli 23 “i“^13 Pl> 23 .(xi- hls). 
ms ms 
It will thus be clear that the reduction of isolated observations to a common 
standard dejsends essentially on a discovery of the intensity of correlation for absolute 
or relative errors. Cq, = will only be true when judgments have been shown to be 
perfectly independent, (q^ = will practically be never true, for the p’s can only 
vanish in the exceptional case in which the s})urious and real correlations just 
balance each other’s influence. 
We shall find as Ave advance need to develop) this theory in certain directions, 
but its main features have now been sufficiently indicated, and we can turn to the 
experimental results. 
(5.) General Description of the Experiments, 
The first series of experiments AAmre made in the summer of 1896 by Dr. Alice 
Lee, Mr. G. U. Yule, and myself. They Avere very simple in character. Sheets 
of white paper ruled with faint blue lines were taken, such as are sold for 
“ scribbling,” and on each blue line two segments of a line Avere obtained by 
2 I 2 
