On the psychometric function for contrast detection

The frequent current use in probability summation calculations of equations of the form. P = 1 − (1−γ)exp[−(I/α) β] to represent the psychometric function for contrast detection is based on two assumptions: (1) γ can be changed without affecting α and β (the high-threshold assumption) and (2) β is the same for all pattern-detecting mechnisms (the homogeneity assumption). Results of yes-no, rating-scale, and forced-choice experiments contradict the high-threshold assumption: estimates of α and β covary with γ. Contrary to the homogeneity assumption, bipartite fields yield lower values of β than do 12 c/deg gratings. Some consequences of these findings for probability summation calculations are discussed.