Analysis of the ROC data from the different biasing conditions.

The figures connected to this frame show the receiver operating characteristic (ROC) functions for each bird with color, shape, and redundant displays. These ROC plots represent performance in terms of the birds' hit and false alarm rates across the different blocks of the biasing manipulation. The hit rate is the proportion of Different trials in which the birds correctly reported the presence of a target. The false alarm rate is the proportion of Same trials in which the birds incorrectly reported the presence of a target.

The larger black data points in each plot are the mean hit and false alarm rates from the last six sessions of each of the five test blocks. As mentioned earlier, these data best reflect the cumulative effects of biasing. These last six sessions of each block were used for the fits generated by the maximum likelihood estimation procedure described next. The smaller unfilled data points in each plot are the birds' hit and false alarm rates across all sessions of the experiment as blocked by groups of three successive sessions (30 total points). These data points capture the intermediate changes in the pigeons' response bias as they reacted to the new proportions of trials within and between biasing conditions. It is these unfilled data points that were used in the least squares estimations described later. The black square data points higher and to the right in each ROC plot represent performance from sessions collected under the Different bias condition. The black triangles that are generally lower and to the left represent performance from sessions collected under the Same bias condition. The black circles represent performance from sessions collected under the Equal bias condition.

The curves drawn in each plot represent the best fit of the SDT (solid line) and HTT (dashed line) models as based on these five data points in each plot. These fits were generated using the maximum likelihood estimation procedure. This method involves adjusting the free parameters of each model until the theoretical probability of obtaining the observed distribution of hits, misses, correct rejections, and false alarms reaches the highest possible value. The MLE method was used first to fit the data because it takes into account the error in measurement in both hit and false alarms rates, unlike the more traditional least squares method. The SDT fits were actually performed two ways, once using the equation for logistic distributions and once using an approximation of the Gaussian. For the HTT fits, the equation for a straight line was used in place of the logistic (with one guessing parameter for each biasing condition and one overall discriminability parameter, p), but the MLE procedure was otherwise identical.

Overall, we found that the SDT account of these data provided a better fit than did the HTT model.