# ROC plot

ROC (receiver operating characteristic) curves show the ability of a quantitative diagnostic test to classify subjects correctly as the decision threshold is varied.

The ROC plot shows sensitivity (true positive fraction) on the horizontal axis against 1-specificity (false positive fraction) on the vertical axis over all possible decision thresholds.

A diagnostic test able to perfectly identify subjects with and without the condition produces a curve that passes through the upper left corner (0, 1) of the plot. A diagnostic test with no ability to discriminate better than chance produces a diagonal line from the origin (0, 0) to the top right corner (1, 1) of the plot. Most tests lie somewhere between these extremes. If a curve lies below the diagonal line (0, 0 to 1, 1), you can invert it by swapping the decision criteria to produce a curve above the line.

An empirical ROC curve is the simplest to construct. Sensitivity and specificity are calculated using the empirical distributions for the subjects with and without the condition. This method is nonparametric because no parameters are needed to model the behavior of the curve, and it makes no assumptions about the underlying distribution of the two groups of subjects.

**Related information**

- What is Analyse-it?
- Administrator's Guide
- User's Guide
- Statistical Reference Guide
- Distribution
- Compare groups
- Compare pairs
- Contingency tables
- Correlation and association
- Principal component analysis (PCA)
- Factor analysis (FA)
- Item reliability
- Fit model
- Method comparison
- Measurement systems analysis (MSA)
- Reference interval
- Diagnostic performance
- Measures of diagnostic accuracy
- Estimating sensitivity and specificity of a binary test
- Comparing the accuracy of two binary diagnostic tests
- ROC plot
- Plotting a single ROC curve
- Comparing two or more ROC curves
- Area under curve (AUC)
- Testing the area under a curve
- Difference in area under curve (AUC)
- Testing the difference between the area under two curves
- Decision thresholds
- Decision plot
- Finding the optimal decision threshold
- Predicting the decision threshold
- Study design
- Control charts
- Process capability
- Pareto analysis
- Study Designs
- Bibliography

Version 5.30

Published 15-Apr-2019