PSYCHOPHYSICAL DISCRIMINATION 61 



judged to be lighter than the standard. Directly below the first entry- 

 is the number .020 which is the proportion of times the weight of 84 

 gms is judged heavier than the standard when the judgment of "equal- 

 ity" is ruled out, and so on for the other entries. 



In Table 1 (p. 72) are given the corresponding probabilities com- 

 puted by equations (1) through (5), using for the standard deviation 

 of the distribution 5.7 gms, for the threshold h = 2.1 gms, and for the 

 bias or constant error x = 2.75 gms. These values were determined from 

 the three values in parentheses on the left, whence the corresponding 

 values on the right are the same. It is to be noted that the parameters 

 are all measured in grams. This is done for convenience only, as ac- 

 tually there is an unknown constant which must multiply each para- 

 meter to give the values in terms of e and j . Furthermore, a linearity 

 between S and e is implied, which is nearly the case in the small range 

 considered. In both the Table and Figure, the proportions P g , and 

 Pi are used. These are respectively the proportions of judgments of 

 "greater," and "lesser." Their relation to P c and P w is evident. 



The agreement between the theory and experiment is illustrated 

 in Figure 2. Complete agreement would be indicated if all points fell 

 on the line of slope one. The relation between the proportions of 

 judgments of "equality" and the proportions of the correct and wrong 

 responses is also shown in Figure 2. If these results are plotted on 

 probability paper, the predicted results will be simply three parallel 

 lines. The experimental data confirm this rather well (Landahl, 

 1939b) . The results from each of the seven subjects showed the same 

 trend. 



When one considers the visual data by F. M. Urban, one finds 

 that the averaged data for several subjects, as well as those for individ- 

 uals, cannot be so simply interpreted. With judgments of "equality" 

 allowed, neither the proportions of correct responses nor those of 

 wrong responses follow the integral of the normal distribution with- 

 in the limits of experimental error; with judgments of "equality" ex- 

 cluded the proportions are not peculiar. This suggests that the thresh- 

 old h is not constant but is affected by the value of <j x . In order to 

 preserve symmetry, the effect on the threshold of S x > S 2 must be 

 supposed the same as that of S 2 > &i if S t and S 2 are simply inter- 

 changed. We may suppose that the lowering of the threshold h , due 

 to the change of experimental situation when judgments of "equality" 

 are ruled out, is the result of the activity of some outside group of 



ful" judgments has been added to the proportion of "greater than" judgments. 

 In the inset the curve represents the values of h predicted by equation (6) plotted 

 against the difference of the intensities of the two stimuli and the points repre- 

 sent the values computed directly from the data. 



