How deeply does Statistics Slam Dunk cover receiver operating characteristic?

Defines sensitivity, specificity, AUC, and thresholded accuracy, then demonstrates computation and plotting while stopping short of threshold optimization.

Receiver operating characteristic

As explained in Statistics Slam Dunk

A ROC 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. It plots sensitivity—the true positive rate—against specificity, shown here on the x-axis, to reveal how well the model distinguishes positive from negative cases. section 14.6.2

Use ROC analysis to separate threshold-dependent prediction results from overall discriminatory power:

Sensitivity measures correctly identified positive cases, while specificity measures correctly identified negative cases. section 14.6.2
The area under the curve (AUC) summarizes discriminatory power: 1 represents perfect separation, 0.5 represents random performance, and higher values are better. section 14.6.2
Unlike error rate and accuracy, which summarize individual thresholded predictions, AUC evaluates how well the model distinguishes positive from negative instances overall. section 14.6.2

Predicting NBA playoff qualification

A logistic regression predicts whether an NBA team reaches the playoffs. After comparing actual outcomes with predicted values, pROC computes an AUC of 0.73, indicating fairly strong predictive power. Base R then plots the curve with sensitivity on the y-axis and specificity on the x-axis: roc_curve <- roc(actuals$actual_values, predictions$predicted_values2) plot(roc_curve, col = "red", main = "ROC Curve: AUC = 0.73", xlab = "Specificity", ylab = "Sensitivity") section 14.6.2

packages <- c("tidyverse", "patchwork", "ggpubr", "pscl", "SciViews", 
             "questionr", "caret", "pROC")

lapply(packages, library, character.only = TRUE)

Load pROC alongside the modeling and visualization packages used to compute and display ROC curves. section 14.1

How Statistics Slam Dunk covers it

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Also explained in

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Grokking Machine LearningA receiver operating characteristic curve is a plot of classifier sensitivity against its false-positive rate across decision thresholds.
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Starting Data Analytics with Generative AI and PythonA plot of true positive rate against false positive rate across classification thresholds.
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Statistics Every Programmer NeedsA receiver operating characteristic curve plots a binary classifier's true positive rate against its false positive rate across decision thresholds.
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Grokking StatisticsA receiver operating characteristic curve plots a classifier's true-positive rate against its false-positive rate across decision thresholds.
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Machine Learning Algorithms in DepthA receiver operating characteristic curve plots the true positive rate against the false positive rate across classification thresholds.
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Financial AI in PracticeA curve that plots a classifier’s true positive rate against its false positive rate across decision thresholds.

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Related concepts

thresholduses · A threshold is a boundary value against which a quantity is compared to determine whether a condition is met or an action or decision is triggered.
area under the curvemeasured by · The area under a curve is the integral of its values over a specified domain and, in classification evaluation, commonly summarizes performance across decision thresholds.
recalluses · Recall is the fraction of relevant, positive, or target outcomes that a system successfully identifies, retrieves, or captures.
specificityuses · Specificity is the proportion of actual negative cases correctly identified as negative, also called the true-negative rate.
precision-recall curvealternative to · A precision-recall curve is a plot of a classifier’s precision against recall as its decision threshold varies.
logistic regressionproduced by · Logistic regression is a statistical classification model that estimates categorical outcome probabilities by applying a logistic or softmax function to a linear combination of input features.

This explainer was generated by Manning's knowledge graph from the text of Statistics Slam Dunk. The section links point to the parts of the book it draws on.