Thirty human observers are tested in a visual detection task under the rating receiver operating characteristic (ROC) paradigm. Since most of the observers were not able to use the rating categories as instructed, their data are excluded from the analysis. From the 30 observers, the four best and most experienced are selected to do long experiments (with 1000 presentations). However, the assumption of Gaussians with equal variance of classical ROC theory is not satisfied by the new data. Nevertheless, assuming Gaussian underlying distributions with unequal variances, the three well-known indices of performance dm, de, and dx are calculated in terms of the geometry of the linear fits in normal deviated coordinates. The areas under the ROC curves are also calculated. We found that the power-law ROC, which assumes underlying exponential distributions, fit well our data. Under the exponential-exponential assumption, we derive a new performance (detectability) index that is easily calculated from experimental data and that depends on a single parameter. The obtained values of the proposed index are in agreement with the corresponding values of the dm, de, and dx indices, but with the new index it is much easier to discriminate between observers with similar performance with considerably lower uncertainty.