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 
Since, as a general rule, the values of n are determined from 
the same number of observations, the weights w' will in most 
cases all be = i, and the factor w' in the product w' w" may ac¬ 
cordingly be neglected. Let us term this product w. Our equa¬ 
tions now become : 
wxtx = (.Dx—RL)h, 
w2t2 = (Zb—RL)h, 
wxtx = (Di—RL)h. 
Or, in numerical form (on the assumption that w'= i), 
—0.9062 (0.193) = (0.5— RL)h, 
—0.7639 (0.311) = (1.0—7?Z)//, 
-0.1791 (0.938) = ( i.$—RL)h, 
0.2725 (0.862) = (2.0—RL)h, 
0.5951 (0.492) = (3.0—RL)h, 
0.7965 (0.281) = (4.0—RL)h, 
1.2379 (0.047) = (5-0—RL)h. 
Treating these equations by the Method of Least Squares, we 
obtain the normal equations : 
[P2w\h — \Dw\RL.h = \Dtw\, 
— \D w\h -f [ w\RL.h = —[tzv]. 
The squared bracket is here used as the sign of summation : so that 
[Z>2ru] means (D2xwx -f D22w2 -f . . . D2xwx')\ [Zhu] means 
( Dxwx + Z>2w2 -f . . . D1w1 ) ; and so on. A rough solution, 
with rounding of the fractions to two decimal places, gives : 
16.05/2 — 6.3 7RL.I1 = 1.96, 
— 6.37/2 + 3.12 RL.h =0.23; 
whence we find 
h — 0.49, 
RL = 1.88. 
To those who are not mathematically inclined, the last few pages may 
have appeared somewhat bewilderingly difficult. Let it be said, then, that 
the mathematical operations involved are exceedingly simple. They consist 
(1) in determining from Fechner’s Table the /-values for the given «-values ; 
(2) in determining from Midler’s Table the w"-values for the same «-values ; 
and (3), after the-full series of these determinations has been made, in ap¬ 
plying the scheme of the Method of Least Squares, as indicated above, to 
a half-dozen equations that contain two unknown quantities. So far as the 
calculations go, it is all a matter of simple arithmetic. The understa7iding


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