MULTIDIMENSIONAL PSYCHOPHYSICAL ANALYSIS 75 



much greater range, since only the positive difference \C 1 i — C 2i [ af- 

 fects the subsequent members of any chain. 



It is natural to identify this scale of S-values with Thurstone's 

 "psychological scale" (Thurstone, 1927; cf. Guilford, 1936). The psy- 

 chological scale is introduced quite abstractly in psychophysics, the 

 assumptions being that each stimulus-object produces a "discriminal 

 response" which can be measured on this scale, and that repeated 

 presentation of the same object leads to varying responses as so 

 measured, the distribution being normal on this scale. By following 

 a well-defined procedure the empirical frequencies of the judgments 

 can be utilized for determining the modal S associated with each stim- 

 ulus-object, the determination being unique up to a linear transfor- 

 mation. 



In our terms, for any stimulus-object C p , the modal response 

 (on the part of the afferent chain, at the synapse s p ) is S p , while 

 S p + C P is the particular response on a given presentation; if Cp is 

 taken to be normally distributed the identification of our S-scale with 

 that of psychophysics is immediate; otherwise some scale-transfor- 

 mation is required. In either case the methods of psychophysics can 

 be utilized to determine the S P , for each Cp , at least up to a linear 

 transformation. Then if, further, the C P i are directly measurable, the 

 quantities L t can be determined up to a common multiplicative factor. 

 These quantities furnish measures of the relative contributions of the 

 separate modes of stimulation to the judgment as a whole. We note, 

 incidentally, the possible application of factor analysis with a large 

 population of subjects (Thurstone, 1937). 



Physical measurement of the C P t is possible but rarely and in the 

 least interesting of the cases, and psychophysicists have endeavored 

 to obtain from the empirical frequencies an insight into the number 

 of distinct modes of stimulation of the organism by the complex 

 stimulus-objects of a given class. It is clear that from judgments of 

 preference alone no such information is to be had, for by the condi- 

 tions of the experiment the subject is required to make a one-dimen- 

 sional ordering of the objects. But by a slightly revised experimental 

 procedure, interpreted in terms of a suitable neural mechanism, it 

 is possible to obtain the data necessary for such a multidimensional 

 analysis (cf. Householder and Young, 1940; Young and Householder, 

 1941). 



In this procedure each stimulus-object is replaced by a pair, and 

 the subject is now asked which of two given pairs is most unlike. The 

 formal psychophysical analysis required for determining the S corre- 

 sponding to each pair is identical with that required for determining 

 the S for each object in the previous experiment; only the interpre- 



