Bauhaus-Universität Weimar

Experimental Psychology: A Manual of Laboratory Practice, Vol. II: Quantitative Experiments, part 1: Student's Manual
Titchener, Edward B.
The Metric Methods 
a constant. The value — is sometimes termed a quotient limen 
or QL.—We thus have, in all, the test-values Ar.—, —. 
r r 
If we have determined the lower as well as the upper DL, we have six 
test-values, as follows (u = upper, l = lower) : 
the absolute DL . . . 
- • ■ A rm 
A rt; 
the relative DL . . . 
A ru 
A r, 
r — A rt 
and the QL .... 
^ ml 
(3) Precision of the Observations.— Psychological practice has 
usually been content to take the MV as the measure of precision 
for the results of the method of limits. It is, for some reasons, 
better to give the probable error or PE, a variation from the 
mean of such magnitude that any given variation is as likely to 
exceed it as to fall below it. The PE of a single observation 
may be calculated from the formula PE,—0.6745 v/; —2—, where 2 
is the sign of summation, « is the number of observations, and v 
stands for the differences A—a, A—b, etc., of the formula on 
p. 8. The quantity y/ is termed the error of mean 
square; it is the error whose square is the mean of the squares of 
all the errors.1 In words, then, PE, = two-thirds of the error 
of mean square. The PE of the mean (of Ar) may be calcu¬ 
lated from the formula PEm = 0.6745 t/—~—. Simpler but 
y « («—/) 
somewhat less accurate formulas are : 
PE, — - 
J « (»- 
PE — - 
71 'i 
\J («—- 
1 This is the general definition of the ‘ error of mean square.’ If we were to follow 
it strictly, we should have, not 4 / , but 4 It is, however, shown in mathe- 
Y 71- I Y 71 
matical books that, where the number of observations is small, we insure greater 
accuracy of result by writing n—1 for n in the denominator of the fraction. 
Hence we are not really running counter to our definition ; we are simply making 
the error of mean square the error whose square is the corrected mean of the 
squares of all the errors. See, e.g., M. Merriman, Least Squares, 1900, 71.


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