•238 
PROFESSOR K. PEARSON ON THE MATHEMATICAL THEORA' 
AVe have, if be the miniber of judgments in the series ;— 
<^ 01 ^ = .7 - { X , - 1 )}^ 
'll 
o'uL = ~ ~ f)}“- >.(’•)• 
o-u' = “ ^{Vhi - (>L - ^'i)V 
) 
^\•here S denotes a summation for every judgment of the series. 
Oljviously the goodness of an observer is measui'ed l)y two characters : 
(i.) The smallness of his personal equation, 
(ii.) The smallness of the variability of his judgment, ctq^. 
The first determines the average error of his judgment, tlie second the constancy 
or stability of his judgment. 
The latter is often quite as important a featuin of the mental worth of an 
observer as the former. 
Tills steadiness or reliability of judgment, isdiich I shall term stability of judgment, 
will lie defined as follows :—The relative stability of two observers for a given class 
of observations is measured by the inverse ratio of their standard deviations. Or, 
if we are speaking of the same class of observation the absolute stability of judgment 
s, will measure the steadiness in relative 
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appreciation of two observers ; it serves as a measure of their degree of approxima¬ 
tion to like estimates, and may be called their relative stability. It by no means 
follows, however, that two observers with a large degree of relative stability have 
necessarily large individual absolute stabilities in judgment, nor that their absolute 
personal equations are small. This remark is of considerable importance, for we are 
apt to think that if two out of three observers have a small relative personal 
equation and a large relative stability, then their conclusions are worth more than 
those of a third oljserver with whom they liave large relative ]3ersonal equations and 
smaller inlative stabilities. 
No conclusion of this kind can l)e admitted, if we find that the absolute 
judgments of independent observers are correlated; for, as will be shown later, the 
higher this correlation, i.e., the less independence in judgment, the greater becomes 
the relative stability of the two observers. The more marked this association in 
judgment, the less are we able to set the judgment of two observers against a third. 
The correlation in absolute judgments ])etween two observei's^ is given by 
_ blOy, - (.-j - ?)) (2y, - B )}.(ii.). 
' li — 
VfCTojCToo 
* ‘ Roy. Soc. Piuc.,’ vol. 60, p. 480 et seq. 
is —. In the case of relative judgment 
^01 
