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Whatever be the conscious experience which is being quantitatively studied, the psychologist realizes that it can never be measured numerically in its own terms, but only in terms of the antecedent physical stimulus, the concomitant neural and other histological activities, or the consequent changes in outward behaviour. We can never say that one experienced sensation of sound has twice the intensity of another, or that one person has twice the experienced courage of another. It is now generally admitted that the mathematician who concerns himself with the ultimate data of physics is not primarily interested in the physical significance of the variables with which he deals, and that his conclusions are not necessarily verifiable by experiment nor acceptable in practice by the experimental physicist. So too in psychology: if mathematical operations on the data of psychological experiment are to be of value to the psychologist, each step in such operations must be carefully studied so as to be assured that it is psychologically warranted.

A discussion on the application of quantitative methods to certain problems in psychology