page_title: Total operating characteristic
section_title: Interpreting TOC curves
hierarchical_section_title: Total operating characteristic / Interpreting TOC curves
caption_attribution_description: English: Figure 4: TOC curve with higher accuracy at high thresholds.
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: It is common to report the area under the curve (AUC) to summarize a TOC or ROC curve. However, condensing diagnostic ability into a single number fails to appreciate the shape of the curve. The following three TOC curves are TOC curves that have an AUC of 0.75 but have different shapes.
  This TOC curve on the left exemplifies an instance in which the index variable has a high diagnostic ability at high thresholds near the origin, but random diagnostic ability at low thresholds near the upper right of the curve. The curve shows  accurate diagnosis of presence until the curve reaches a threshold of 86. The curve then levels off and predicts around the random line.
  This TOC curve exemplifies an instance in which the index variable has a medium diagnostic ability at all thresholds. The curve is consistently above the random line.
  This TOC curve exemplifies an instance in which the index variable has random diagnostic ability at high thresholds and high diagnostic ability at low thresholds. The curve follows the random line at the highest thresholds near the origin, then the index variable diagnoses absence correctly as thresholds decrease near the upper right corner.
caption: TOC curve with higher accuracy at high thresholds.
exif: {}