Background/Question/Methods The Relative Operating Characteristic (ROC) is popular among ecologists to compare a Boolean variable that shows either real presence or real absence viz-à -viz a rank variable that shows priority for diagnosis of presence. The ROC summarizes several thresholds where each threshold converts the rank variable to a Boolean variable of either diagnosed presence or diagnosed absence, then computes for each threshold a two-by-two confusion matrix that generates Hits, Misses, False Alarms and Correct Rejections. This article presents the Total Operating Characteristic (TOC) to replace the ROC, because the TOC presents strictly more information than the ROC. The ROC reports two unitless ratios of relative information at each threshold, whereas the TOC presents all four entries that constitute the total information in the confusion matrix at each threshold. Consequently, the TOC is more interpretable than the ROC. I illustrate the TOC with an example to characterize temporal change for a land cover category, marsh in the Plum Island Ecosystems site, which is part of the United States National Science Foundation’s Long Term Ecological Research network. Specifically, I analyze land cover maps from three time points: 1938, 1972 and 2013. Each time point has three categories: water, marsh and upland. Results/Conclusions The TOC curves for loss show that marsh loses least intensively at intermediate elevations, as the slopes of the TOC curves at intermediate elevations are flatter than the diagonal line. The TOC curves for gain show that marsh gains most intensively nearer the edge of marsh at the start of the time interval and at intermediate elevations, as the slope for the elevation curve is steepest at intermediate elevations. The Area Under Curve is an index between 0 and 1 that reflects both the strength and the monotonicity of the association between the Boolean variable and the rank variable. The TOC curves during the second time interval show that the association of marsh gain with distance to edge is just as strong as with elevation, while the association is monotonic with distance to edge but not monotonic with elevation. In conclusion, I recommend researchers use the TOC instead of the ROC, because the TOC shows the total information in each confusion matrix at every threshold. In contrast, the ROC shows only two bits of relative information at each threshold.
