Egon S. Pearson 
89 
In the first place we have seen that neither a secular change in personal equa- 
tion — the variation in series means — nor a simple sessional change such as that 
represented by the straight line or by a second order parabola considered in the 
Trisection Experiment, will account for the whole of the correlation of successive 
judgments. We must therefore conclude that quite apart from the large scale vari- 
ations in judgment which are due to the more gradual changes of state in the 
observer resulting, perhaps, from experience or fatigue, there is a definite relationship 
between the small scale variations in judgment; if judgment yt is greater than the 
average of the five or six preceding judgments, then we shall on the whole 
expect that ijt+i, the next judgment, will also be greater. I propose therefore to 
consider what results will follow from the assumption that yt has a correlation r 
with yt-i and but that for y^+i or constant it has no partial correlation with 
yt..2 and yj+a or judgments at greater intervals. In other words we will suppose 
that the observer's estimation at any moment is only influenced by the preceding 
estimation, and only through this, and not directly, by the earlier estimations. 
Let us take the successive judgments yt, yt+i, yt+n ■■■ yt+k ■■• and suppose that 
the total correlation between yt and yt+u is pk, where = 1, 2, 3, . . . , and p-^ = r. If 
there is no partial correlation between yt and yt+-2, yt+i being constant we must 
have 
p.i — pi" = 0 or p., = r". 
In the same way if there is no partial correlation between yt and yt+s when yt+^ 
(or yt+2) is constant, 
p.: - PiPi = 0 or p,, = r\ 
and in general we find that 
Pk= r'' (xliv). 
In reaching this simple result there is a point however that has been overlooked ; 
it has been assumed that there is some physiological or psychological significance 
in the correlation of an estimate of a quantity and in the preceding estimate, but 
it inust be remembered that the value which the observer records may not be 
exactly that which he wished to record, or in other words he may be unable to 
record his true estimate. Thus in bisecting a line it is likely that the pencil point 
will not strike the paper exactly at the spot intended, or in counting 10 seconds 
the tapping of the key may not be exactly synchronised with the beginning or end 
of the count, and there may be many other little external influences of which the 
observer is unaware, which will all combine to form what may be termed an acci- 
dental error superimposed upon the true correlated estimation. Let us examine 
how the relation (xliv) will be modified by introducing the idea of these accidental 
and uncorrelated errors; we must suppose that the observer's recorded judgment 
yt is made up of two parts, at his actual estimate at the moment of record and jSt 
some complex of accidental errors affecting his record. Then 
yt = oit + i3t (xlv). 
Now if we assume that the accidental errors are as like to be positive as 
negative, and that they will not be correlated in any manner among themselves 
