Egon S. Pearson 
97 
Both of the curves, represented by equation (Ix) and (Ixi), have been drawn in 
Figure 20, and show a satisfactory fit, if the roughness of the data is taken into 
account. 
The results of the Trisection and of the Ten-second Counting Experiments, and 
as far as the rough form of the data will allow, of the Ten-second Estimating 
Experiment, suggest therefore that there is some foundation for the theory of 
relationship between successive estimates put forward at the beginning of the 
present Section. To reach tlie expression qr^ for the correlation of successive 
judgments at intervals of k, it has been necessary in all cases to remove the 
secular change, and in one case a sessional change as well, but if these changes 
correspond in themselves to some definite mental or physical processes which can 
be separated in some degree from the causes underlying the residual variations, 
then we are justified in inquii'ing into the significance of the constants q and r. 
It has been suggested that 
9 = 
.(Ixii), 
so that q is dependent on the ratio between the correlated and the uncorrelated 
parts of the observer's judgment, that is between what I have considered as the 
true estimate and the accidental errors superimposed in the process of record. 
Now using (Ixii) and the relation* 
Ja' + 0' = S' (Ixiii), 
(or S" for the Trisections where it has been necessary to allow for a sessional 
change), we find that 
Vd'^'^qS', ^/3-' = \^{l-q)S' (Ixiv), 
and the values calculated in this way for J<^' and ^^8'- i 
TABLE XIX. 
for Jci- and ■^'8'- are given in Table XIX. 
Experiment 
-S" 
r 
Trisection 
•80 
•080 ( = <S"') in inches 
•071 
•036 
•71 
Bisection (apin'oximate on\y) ... 
•47 
•045 in inches 
•031 
•033 
•72 
Ten-second Counting ... 
•67 
•034 in factor 
•028 
•020 
•79 
Ten-second Estimating 
•18 
•141 in factor 
•060 
•128 
•81 
If the Trisection and Bisection results are compared it will be seen that the 
standard deviations of the accidental errors {J 8"^) are nearly the same but that 
there is a large difference between the measures of the variations of the true 
* It will be seen that owinR to a sessional change iu standard deviation, .S'^" for the Trisections 
(Table XVIII) and .S,.' for the Bisections (Table XI) increase with k. To obtain an approximate value 
for the standard deviation of the whole 1200 observations as opposed to tlmt for the 1000 observations 
of any particular Group /,-, I have used in equations (Ixiii) and (Ixiv) .S" (or S") Riven by 
,S"2 = (Si'2 + So'^ + S-P + . . . + Su"). 
Biometrika xiv 7 
