Bauhaus-Universität Weimar

Experimental Psychology: A Manual of Laboratory Practice, Vol. II: Quantitative Experiments, part 2: Instructor's Manual
Titchener, Edward B.
The Metric Methods 
of observation; and if every error of observation may be ex¬ 
pressed in terms of D, may be considered as a plus or minus or 
zero difference between r1 and r2,—in brief, is the equivalent of. 
some D-magnitude ; then the error curves of the r, w and u cases 
may be drawn as if hD and not hx were the i for the relative 
number of cases in question. Let us see what data we require 
for the drawing, and what the form of the curves is. 
y zu u y 
We know that --|---1—=i ; and that when D=DL. Now (it 
n n n n " x > 
for D=o, we have to assume an equal probability of r and w, so that 
The terms r and w are, in this case, wholly arbitrary ; but the 
assumption is the simplest and most reasonable that can be made. 
(2) For a — D, the present w-cases become r-cases, and conversely. 
It follows that the relative frequency of w for a negative D obeys the 
same law of distribution as the relative frequency of r for a positive D. 
The curves for r and w will therefore intersect at D=o, taking symmetri¬ 
cal paths in opposite directions. (3) The number of u-cases may be de- 
u y zv 
termined by the equation _ = I — — 
n it 
With these data 
to guide us, we may 
draw the three 
curves as shown in 
Fig. 35. The ordi¬ 
nates represent the 
numbers of the 
special cases, whose 
Fig. 35.—Curves showing the distribution of w and u *°tal number is n ; 
cases as determined by Gauss’ Law of Error. From tl>e abscissas are 
Külpe, Grundriss d. Psych., 1893, 73. the values of t=hD 
given in Fechner’s 
Fundamental Table. Ordinates are shown for D=o and D=DL. 
0-0 D = DL 
We now have no difficulty in constructing formulæ whereby 
we may calculate the DL from our results with a given D. These 
formulae will contain h, which is our required measure of ac¬ 
curacy or precision. 
(1) Suppose that D is DL: the relation is evidenced at once


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