Table 3.
Summary of experimental results for each observer and their average (top), and behaviors of two cascade models involving two stages of summation and three stages of nonlinear contrast transduction (middle and bottom). The parameter P is the effective overall exponent and is estimated from the psychophysical results using Pelli’s (1987) approximation. This is the (average) estimate of the slope of the psychometric function (β̅) divided by 1.247. In the models, the overall exponent is given by the product mpu. The exponents m and p were estimated from the SRs in the ‘eyes’ and ‘area’ experiments respectively, leaving u to be set by P. The equivalent uncertainty (U) is described in the Discussion section. No degrees of freedom remained for predicting the SRs in the (main) ‘eyes and area’ experiment. Note that the model parameters in the ‘average’ column are not the averages of those in the other three columns, but the parameters fit to the data of the average observer
| Observer | TSM | RJS | SAW | Average |
|---|---|---|---|---|
| Experimental results | ||||
| Eyes SR | 4.95 | 5.87 | 4.26 | 5.03 |
| Area SR | 5.10 | 4.83 | 5.00 | 4.98 |
| Eyes and area SR | 4.40 | 4.88 | 3.64 | 4.31 |
| Eyes β | 4.1 | 2.5 | 3.6 | 3.3 |
| Area β | 3.8 | 2.6 | 3.6 | 3.3 |
| Eyes and area β | 4.0 | 2.4 | 4.0 | 3.6 |
| β̅ | 3.9 | 2.5 | 3.7 | 3.3 |
| P = (β̅/1.247) | 3.2 | 2.0 | 3.0 | 2.7 |
| Model: Summation across eyes then area | ||||
| m | 1.22 | 1.03 | 1.41 | 1.20 |
| p | 1.60 | 2.26 | 1.47 | 1.76 |
| mp | 1.95 | 2.32 | 2.07 | 2.11 |
| u = P/(mp) | 1.62 | 0.86 | 1.45 | 1.26 |
| Equivalent uncertainty (U) | 14 | N/A | 7 | 3 |
| Predicted SR for ‘eyes and area’ |
4.27 | 4.69 | 3.70 | 4.20 |
| Model: Summation across area then eyes | ||||
| m | 1.95 | 2.32 | 2.08 | 2.11 |
| p | 0.62 | 0.44 | 0.68 | 0.57 |
| mp | 1.22 | 1.03 | 1.41 | 1.20 |
| u = P/(mp) | 2.60 | 1.94 | 2.13 | 2.22 |
| Equivalent uncertainty (U) | 757 | 51 | 111 | 164 |
| Predicted SR for ‘eyes and area’ |
4.95 | 5.87 | 4.26 | 5.02 |