Bauhaus-Universität Weimar

Experimental Psychology: A Manual of Laboratory Practice, Vol. II: Quantitative Experiments, part 1: Student's Manual
Titchener, Edward B.
§ i5- The Law of Error 
will have to occur at length, within the range of a sufficiently 
long experience. It should, however, be said that no graphic 
representation can give an adequate idea of the extreme rapidity 
with which the curve tends toward the axis of x. To the eye, 
the two appear, after a very short course, to merge into each 
other. This shows how small is the chance of even a moderate 
error. Finally, the curve is symmetrical about the axis of y : 
this implies that equal deviations from the mean, in excess and 
defect, tend in the long run to appear with equal frequency. 
The equation of this error curve is not quite so simple as the 
equation of the logarithmic curve given above. It is, however, 
an equation of the same kind. Both alike are ‘ exponential ’ 
equations : that is, equations in which one of the two variables 
(x, y) appears only as the exponent of some other quantity. In¬ 
stead of taking the form y—f (x),—where f is the general sign 
Fig. 17. 
Curves of Gauss’ Law of Error, for observations of less and greater accuracy. 
of function, or functional symbol, and the equation reads “y 
varies in some determinate way whenever .*■ varies,”—the expo¬ 
nential equation takes the form y—f (


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