COMPARING AND ESTIMATING EFFORTS
The ratios and the differences of forces required to depress a lever were factorially varied in an effort discrimination task. Area under the ROC increased with increases in both the ratios and the differences. Accordingly, with the psychophysical function (x)=Ax + C; , C >0; either the Ratio model D(x,y) = F[(x)/(y)] or the Power Difference Theory, D(x,y)= G[(x) - (y)] = G[A(x - y)], with < 1 is permitted. Alternatively, the difference model with logarithmic psychophysical function, D(x,y)=G[log(x + B) - log(y + B)] with B>0, is also an admissible model. In a second experiment, magnitude estimates of efforts were obtained. The average exponent was 1.53. Consequently, the Power-Difference model is rejected. If, however, the exponent obtained from magnitude estimation arises as a consequence of matching subjective number with subjective intensity and with a subjective number exponent of, say, 0.5, then the Power-Difference model can be retained.