Outlines of psychology : based upon the results of experimental investigation / by Oswald Külpe ; translated from the German (1893) by Edward Bradford Titchener.

Oswald Külpe

Date:: 1895

Credit: Outlines of psychology : based upon the results of experimental investigation / by Oswald Külpe ; translated from the German (1893) by Edward Bradford Titchener. Source: Wellcome Collection.

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$presupposes two or more stimuli, and admits no judgment except that of equality. 2. If we assert that the formulae employed in the mathematical theory of errors of observation are capable of direct application to psychophysical investigations, we obviously do so upon the assump¬ tion that the deviations from the most probable value in psychophysics are of the same kind as the deviations from the probable value with which mathematics is concerned. The latter are subject to the following general rules. (1) The errors must occur in continuous gradation from o to db a\ or, since the ö-limit cannot be defined with certainty, from o to ± 00. (The extension is indifferent in practice.) In other words, the errors must not be of one definite magnitude, or fall within a series of definite magnitudes, but must appear in all the different magnitudes possible within the stated limits. (2) The larger errors must occur less often than the smaller, and the maximum of frequency must be attained by the error o. (3) Positive errors must appear as often as negative; i.e., the sum of the positive must be equal to the sum of the negative. We may take it for granted that these conditions are realised in what we have called the ‘ accidental variations ’ of sensitivity and sensible discrimina¬ tion : if only for the reason that the errors of observation with which the mathematical theory has principally to deal are really nothing else than accidental variations in the judgments of this same sensiti¬ vity or sensible discrimination. If, then, we are able to abstract from constant variations, we may have recourse for our special purpose not only to the general law of the distribution of errors, but also to the special formulae for the probability of an error of definite magnitude or of the errors within certain fixed limits.—We need do no more than glance very briefly at the values and formulae which the mathematical theory of errors of observation employs. The relative frequency of the various errors can be best indicated by a curve of the form shown in Fig. 5. The abscissae give the magnitude of the errors (d), the ordinates their relative frequency or probability. The curve reaches its maxi¬ mum at the value $ = o. From this point it falls on either side,—symmetrically, since the probabilities of positive and negative errors are equal; and approaches the axis of the abscissae asymptotically by a comparatively quick descent. The relative frequency of an error of definite magnitude a is expressed by the equa¬ tion [XJ W = a _, - h'u' n where h denotes the ‘measure of precision’ of the observation (Gauss), a constant [i] W = Wahrscheinlichkeit, probability. 5$