OF ERROKS OF JUDGMENT AND ON THE PERSONAL EQUATION. 
Table I. 
251 
500 trials. Absolute personal equation. 
Relative personal ecjuation. 
XQ 
X2'. 
X3'. 
X2' - X3'. 
Xs'-Xf. 
Xi' - Xo'. 
.r 1 r + -012.35 
Mean, ungrouped . . . | -00074 
, r + -01230 
: „ grouped • • • I +.00075 
- -00444 
+ -00093 
- -00495 
± -00093 
- -00469 
+ -00079 
- -00377 
± -00080 
+ -00026 
- -00123 
± -00098 
- -01704 
- -01589 
± -00103 
+ -01679 
+ -01712 
± -00106 
Q-n 1 f ‘02464 
&.D., ungrouped . . . | ^ -00053 
, r -02455 
” groaped . • • • | +-00053 
•03068 
+ -00065 
•03065 
± -00065 
•02618 
± -00056 
•02625 
± -00056 ' 
•03236 
± -00069 
•03376 
± -00073 
•03519 
± -00075 
it, and our errors were both to the left of the midpoint.* All these absolute 
equations are seen to be considerable multiples of their probable errors, or are 
undoubtedly significant. While Dr. Ler’s personal equation is, roughly, three times 
as large as Mr. Yule’s or mine, she is steadier in her judgment, our relative steadi¬ 
ness being as -^ 5 - : nearly, or about as 40 ; 32 : 38. 
The absolute personal equations show that the probable errors of tlie means and of the 
standai'd deviations are for all practical purposes identical, whether they are calculated 
from the standard deviations of the ungrouped or grouped observations. From these 
probable errors we see that the ditterences between the ungrouped and grouped 
results are in all cases but two less than the probable error of the quantity ; in one of 
these cases, however, the difference is only very slightly greater, and accordingly it is 
not of any practical importance. In tiie other case, Mr. Yule’s personal equation is 
insignificantly larger than mine for ungrouped results, and slightly smaller than mine 
for grouped results. The effect of this is that our relative personal equation swings 
round from negative to positive as we pass from ungrouped to grouped deviations. 
The, total change is only ‘00149, and as the probable error of the result is ‘00098, we 
are perhaps hardly justified in holding that the grouped results are in disagreement 
with the ungroujDed. I think all we could say is that our absolute personal equations 
are very nearly equal, and that we have sensibly no relative personal equation. The 
differences of the other relative personal equations as found Ijy the two methods are 
less than their j)i’obable errors.! 
* The light fell from the left hand on the paper for all three experimenters during the bisections, 
t The reader will notice at once that the relation ^23 Po-i-poz ao longer holds. If we deduce the 
relative from the absolute personal equations we find ; 
P- 2 Z = - ‘00118, ^^31 = - -01607 and j.q 2 = + ‘01725 instead of 
-•00123 --01589 and +-01712 respectively. 
The differences are, however, quite insignificant, when we consider the probable errors. 
2 K 2 
