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 
by D.” It remains, then, to prove these assumptions: to establish 
the mathematical relation from the theoretical side, to verify it 
by experiment, and to make it practically available for purposes 
of the method.1 
Fechner first of all reduces all cases to r and w cases, by count¬ 
ing the e and d half to r and half to w.2 Next, by a mathematical 
argument which we need not here reproduce, he finds the 
formulae :3 
r'_i + 6. w’_ i—6_ Q—2r' - 2W' 
71 2 ’ n 2 ’ 71 71 ’ 
where r' and w' are the revised numbers of r and w cases re¬ 
spectively, and 6 is the probability integral : 
-4- fV'VA 
V'irJ g 
Finally, he makes out the Table which correlates - with t ~ hD 
(Fundamental Table for the Method of r. and w. cases: see p. 99 
of the text) between the limits - — and- = 1.00.4 The cal- 
culation of the test-value h is now simple. Having obtained a certain 
-, one looks up in the Table the corresponding value of hD, and 
determines h by division of this value by D. The demands of theory 
and of availability are satisfied ; the demand for experimental 
verification is met by Fechner’s weight experiments. 
The principal objection which Müller raises against Fechner’s 
treatment of the method is that Fechner has failed to distinguish 
between a measure of precision and a DL. The DL is that aver¬ 
age value of D which gives 50% of r-judgments ; the measure of 
precision characterises the uncertainty, the limits of variation, of 
our apprehension of the stimuli r1 and r2.5 Both values are im¬ 
portant; both may be derived from the method. But they must 
be kept distinct. Müller accordingly works out the formulæ 
for the r, w and e cases which we have given (in somewhat sim- 
1 El., i., 101 ff. ; R., 24. On Fechner’s h, see R., 48, 50 «., 51 f., 97 f. 
2 El., i., 72, 94; R-, 67 ff. 
8 El., i., 104 ff. For A. F. Möbius’ line illustration, see El., i., 105 ff. ; G., 36 ff., 
42 ff. ; R., 101 ff. 4 El., i., 108, X10 f. ; R., 66 f. 
6 Or, as we take it (see below), of our apprehension of this average D.


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