The Philosophical Review/Volume 1/Summary: Merkel - Theoretische und experimentelle Begründung der Fehlermethoden
The article is, for the most part, a mathematical discussion of the method of right and wrong cases, and of the author's allied method of equal and unequal cases.
Taking Gauss’s theory of observation errors as a basis, M. finds formulae for the probable positive and negative errors and for the measure of accuracy for the m. of r. and w. cases where equal stimuli are used, as well as for the distribution of the ‘equal’ cases with stimuli of different intensities. Formulae are also found for the elimination of the constant errors of the method.
Distinguishing between the method of mean gradations with minimal changes when the object is to find a ‘middle’ between two given stimuli, and his own method of mean gradations when ‘middle’ judgments are avoided, the author shows that such ‘middle’ judgments as do occur are to be distributed according to the formulae of his method of equal and unequal cases. A similar plan of distribution is to be followed in case of judgments of ‘double’ in the author’s method of “doubled stimuli.” The relations of the threshold values in the several methods of r. and w. c., of equal and unequal c., and of minimal changes, are also mathematically deduced.