page_title: Total operating characteristic
section_title: TOC vs. ROC curves
hierarchical_section_title: Total operating characteristic / TOC vs. ROC curves
caption_attribution_description: English: Figure 2: TOC Curve
context_page_description: The Total Operating Characteristic is a statistical method to compare a Boolean variable versus a rank variable. TOC can measure the ability of an index variable to diagnose either presence or absence of a characteristic. The diagnosis of presence or absence depends on whether the value of the index is above a threshold. TOC considers multiple possible thresholds. Each threshold generates a two-by-two contingency table, which contains four entries: hits, misses, false alarms, and correct rejections.
  The Receiver Operating Characteristic also characterizes diagnostic ability, although ROC reveals less information than the TOC. For each threshold, ROC reveals two ratios, hits/ and false alarms/, while TOC shows the total information in the contingency table for each threshold. The TOC method reveals all of the information that the ROC method provides, plus additional important information that ROC does not reveal, i.e. the size of every entry in the contingency table for each threshold. TOC also provides the popular area under the curve of the ROC.
context_section_description: These figures are the TOC and ROC curves using the same data and thresholds.
  Consider the point that corresponds to a threshold of 74. The TOC curve shows the number of hits, which is 3, and hence the number of misses, which is 7. Additionally, the TOC curve shows that the number of false alarms is 4 and the number of correct rejections is 16. At any given point in the ROC curve, it is possible to glean values for the ratios of false alarms/(false alarms+correct rejections) and hits/(hits+misses). For example, at threshold 74, it is evident that the x coordinate is 0.3 and the y coordinate is 0.2. However, these two values are insufficient to construct all entries of the underlying two-by-two contingency table.
caption: TOC Curve
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