78 
On the Variations in Personal Equation 
In the first row of Table XIII are given the standard deviations of these 
differences taken from the 61 breaks ; now in 14 of these cases there is what may 
be called a "double break," that is, after making one large variation to yt, the 
judgment returns approximately to its previous state, both yt'^yt_^ and ytf^yt+i 
being greater than or equal to "07. While such cases may represent true variations 
in judgment, it is very possible that they result from some accidental error, a 
slowness in pressing the tapping key or in catching up the counting at the com- 
'i/l-2 / y,+ l\!/t+3 
Fig. 16. Experiment C. Effect of a large breali in judgment. 
mencement of the observation, which was realised at the time and was not due to 
a real change in estimate. In the second row of the Table, therefore, are given the 
standard deviations taken from the 33 sets where there was no double break, and, 
in the third row, the standard deviations of 1st differences (taken from the whole 
1000 judgments) 
between yt and yt+i = Ss = S/ \/2{l — R/), 
yt and ijt+, = ,SV ^2 (1 - R/), 
yt and 1/,+, = S,W2{1-W), (-'^g. 
TABLE XIII. 
Standard Deviatiuits of Dlffevences between Judgnteid after "Break", yt, 
and the Judgments yt-^ to yt+a- 
o 
Previous Judgments 
Succeeding Judgments 
« 
Number of 
Judgments 
6 
yt-^ 
Vt-i 
Vt-'i 
2/(4-1 
Vi+i 
1 
From 61 sctis 
•0692 
•0647 
•0624 
•0624 
•0851 
•0476 
•0541 
•0553 
•0549 
•0623 
± -0042 
± ^0040 
+ •ooss 
+ ^0038 
+ ^0052 
+ ^0029 
+ ^0033 
+ ^0034 
+ ^0034 
+ ^0038 
2 
From 33 sets 
•0757 
•0682 
•0636 
•0667 
•0810 
•0346 
•0421 
•0508 
•0483 
•0635 
+ •ooes 
± -0057 
+ ^0053 
+ -0055 
+ ^0067 
+ ^0029 
+ ^0035 
+ ^0042 
+ ^0040 
+ •0053 
3 
From total 1000 
■0442 
•0416 
•0401 
•0373 
•0338 
•0338 
•0373 
•0401 
•0416 
•0442 
The probable errors are calculated from the usual expression, ± -6745 aj-Jln. 
If we consider the values of these standard deviations together with their 
probable errors, we may say definitely that the effect of a large break or discon- 
tinuity in judgment is quite significant, and that the influence appears to last for 
at least four or five judgments. It cannot of course be decided whether the 
