# Bauhaus-Universität Weimar

### Volltext Experimental Psychology: A Manual of Laboratory Practice, Vol. II: Quantitative Experiments, part 1: Student's Manual (2 (1))

Titel:
Experimental Psychology: A Manual of Laboratory Practice, Vol. II: Quantitative Experiments, part 1: Student's Manual
Person:
Titchener, Edward B.
PURL:
https://digitalesammlungen.uni-weimar.de/viewer/image/lit16066/110/
```64
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
r — A rt
and the QL ....
t'mu
r
r
^ 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, — -
0-8453
2w
J « (»-
-*)
PE — -
0.8453
•Zv
71 'i
\J («—-
0
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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