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Receiver operating characteristic

As explained in Statistics Every Programmer Needs

A receiver operating characteristic curve plots a binary classifier's true positive rate against its false positive rate across decision thresholds.

A receiver operating characteristic (ROC) curve evaluates a binary classifier across decision thresholds by plotting the true positive rate against the false positive rate. It emphasizes discrimination between positive and negative classes rather than only the proportion of correct predictions. section 5.2.4

Interpret the curve with these related measures:

  • True positive rate measures correctly identified positive cases; false positive rate measures negative cases incorrectly classified as positive. section 5.2.4
  • The area under the ROC curve (AUC) summarizes performance across all possible thresholds on a scale from 0 to 1; values close to 1 indicate very good performance. section 5.2.4
  • Unlike accuracy, AUC focuses on discrimination and can reveal weaker performance when one class dominates the data. section 5.2.4

Raisin classification in Python

Use scikit-learn's roc_curve() to obtain false-positive rates, true-positive rates, and thresholds, then plot them with Matplotlib. The demonstrated logistic regression produces a plot titled “ROC Curve” with AUC = 0.87; roc_auc_score() returns 0.8677777777777779.

How Statistics Every Programmer Needs covers it

How deep it goes
Defines ROC geometry, explains AUC and class imbalance, and demonstrates plotting with scikit-learn; it does not develop a mathematical derivation.
Examples
Uses raisin-variety classification, an AUC of 0.87, and a plotted random-guessing baseline.
What it assumes
Assumes binary labels and predictions while grounding interpretation in confusion-matrix counts and related classification rates.
What you can do after
Evaluate binary classifiers via scikit-learn's roc_auc_score() and roc_curve(), then interpret and plot their discrimination.
How it connects
Connects ROC analysis to logistic regression, confusion matrices, accuracy, sensitivity, specificity, and class imbalance.

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