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Physiology". — • "A feiv reniarhs concerning the method of the true 

 and false cases.'' By Prof. J. K. A. Wertheim Salomonson. 

 (Communicated by Prof. 0. Winkler.) 



The method of the true and false cases was indicated by Fechner 

 and used in his psychophysical investigations. He applied this method 

 in different ways: first to determine tlie measure of precision 

 (Pracisionsmasz) wlien observing difference-thresliolds, afterwards to 

 determine tliese difference-thresholds. 



Already in the course of his first experiences arose the difficulty 

 that not only correct and incorrect answers were obtained, corre- 

 sponding with the "true" and "false" cases, but that also dubious 

 cases occurred, in which the observer could not make sure as to 

 the kind of difference existing between two stimuli, or whether there 

 did exist any difference at all. Fechner himself, and many other 

 investigators after him, have tried in different ways to find a solution 

 to this difficulty. What ought to be done with these dubious cases? 



Fechner has indicated several methods, which he subjected to an 

 elaborate criticism. Finally he concluded that the method to be 

 preferred to all others was that one, in which the dubious cases 

 were distributed equally amongst the false and the true cases. If 

 e. g. he found to true cases, v false cases and t dubious cases, he 

 calculated his measure of precision as if there had been iv -{• \t 

 true cases and \t -\- v false cases. 



Furthermore he showed that a method, employed especially by 

 American experimental physiologists, in which the reagent is urged 

 always to state a result, even if he remains in doubt, practically 

 means the same thing as an equal distribution of the t cases amongst 

 the true and the false cases. 



Fechner still worked out another method, by means of which 

 the threshold value was first calculated from the true cases, then 

 from both the true and dubious cases, whilst the final result was 

 obtained with the aid of both threshold values. 



A most elegant method to calculate the results of the method of 

 the false and true cases has been pointed out by G. E. Muller, 

 starting from this view, that as a matter of necessity the three groups 

 of cases must be present, and that they have equal claims to exist; 

 that the number of cases belonging to each of these groups in any 

 case, are equally governed by the well-known law of errors. From 

 the figures for the true false and dubious cases the thresholdvalue 

 may afterwards be calculated. 



I need not mention some other methods, e.g. that of Foucault, 



