Bauhaus-Universität Weimar

Experimental Psychology: A Manual of Laboratory Practice, Vol. II: Quantitative Experiments, part 1: Student's Manual
Titchener, Edward B.
The Metrie Methods 
By help of this Table we may write the equations 
t2 = (D2—RL)h, 
t7 — (D7—RL)h 
in numerical form, as follows : 
—0.9062 = (0.5 —RL)h, 
—0.7639 = ( i. o—RL)k, 
—0.1791 = (1.5 —RL)h, 
0.2725 = (2.0 ~RL)h, 
0-595 i = (3-°—RL)h, 
0.7965 = (4.0—RL)h, 
i.2Z79 = {S.o—RL)h. 
These equations can be solved, for RL and h, by the Method of 
Least Squares. 
So far, so good ! We are not yet, however, out of the mathe¬ 
matical wood. If we were to solve the equations as they stand, 
we should be making a mistake in theory, and a mistake which 
is by no means always negligible in practice. We should be pro- 
ceding as if 4, 4, etc., were observed values. Now the values 
really observed are not these /-values, but the «-values. We 
must, therefore, seek (so to say) to transform the lvalues into 
observed values ; and we may do this by compensating the error 
which their direct treatment as observed values would involve. 
We may do it, in other words, by weighting the /-values. 
Each of the values nx, n2, etc., has a weight w' proportional to 
the number of observations upon which it is based. This value 
w' must for our purposes be multiplied by a coefficient w", to 
be determined from the following Table. Then the products 
w\ w"u w'a w"t, etc., are the required weights of the values 
ti, 4, etc.


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