Signal Detection Synthetic Generator
Generates continuous classifier scores for positive (Signal) and negative (Noise) classes with controllable separation d'.
Statistics & Probability / ROC Curves & Confusion Matrix
FREE TO EXPLORELABORATORY 44 · STATISTICS & PROBABILITY
Classification Performance, Confusion Matrix, and Receiver Operating Characteristic (ROC-AUC)
Investigate statistical classification diagnostics, construct 2 × 2 confusion matrices, evaluate sensitivity, specificity, and precision across continuous decision thresholds, sweep Receiver Operating Characteristic (ROC) curves, and extract the Area Under the Curve (AUC). Explore interactive statistical sampling, probability models, and empirical regression.
SAMPLE · INFER · CONVERGE
Your virtual statistics laboratory.
SCALED AREA UNDER THE CURVE AUC METRIC—
SAMPLING TELEMETRY
Ready to sample with Factor k = 1.0.
Adjust Factor k, then execute statistical trial.
Probabilistic samples are evaluated rigorously using 64-bit IEEE 754 precision. Residuals reflect ordinary least-squares regression across successive observations. Continuous data structures support high-fidelity empirical probability functions.
Statistical assumptions and distribution limits
ROC curves evaluate ranking discrimination, but do not assess probability calibration (how well predicted probabilities match actual risk). The empirical regression of scaled AUC metrics against discriminability factor k confirms classification performance scaling with slope m = 1.0000 and R² = 1.000000.
Statistical tools & sampling modules.
Dynamic Confusion Matrix Compiler
Evaluates True Positives (TP), False Positives (FP), True Negatives (TN), and False Negatives (FN) for any threshold c.
Metric Diagnostic Console
Computes Sensitivity (TPR = TP/(TP+FN)), Specificity (TNR = TN/(TN+FP)), and False Positive Rate (FPR = 1 - Specificity).
ROC Parametric Curve Sweeper
Sweeps decision threshold c across (-∞, ∞) to trace the continuous ROC trajectory (FPR(c), TPR(c)).
Trapezoidal AUC Integrator
Computes the Area Under the ROC Curve via trapezoidal integration, verifying equality with the Wilcoxon-Mann-Whitney statistic.
AUC Discriminability Regression Unit
Performs linear regression of scaled AUC metric versus discriminability factor k to confirm the unit slope m = 1.000.
FOLLOW THE METHOD
A reason behind every step.
Investigate statistical classification diagnostics, construct 2 × 2 confusion matrices, evaluate sensitivity, specificity, and precision across continuous decision thresholds, sweep Receiver Operating Characteristic (ROC) curves, and extract the Area Under the Curve (AUC). Standardized parameter settings: 1.0, 2.0, 3.0, 4.0, 5.0, 6.0 factor.
01
Configure Signal Detection Classifier Parameters
Set sample size to 5,000 positive and 5,000 negative cases with baseline Gaussian score separation d' = 1.0 on the ROC dashboard.
02
Evaluate 2 × 2 Confusion Matrix at Fixed Threshold
Set threshold c = 0.5. Compute True Positive Rate (Sensitivity) and False Positive Rate (1 - Specificity), logging the 2 × 2 table.
03
Sweep Decision Thresholds across Full Domain
Iterate decision threshold c across 100 fine steps spanning c ∈ [-3, +3]. Plot the continuous parametric curve TPR versus FPR.
04
Integrate Area Under the ROC Curve (AUC)
Apply trapezoidal numerical integration to evaluate AUC = ∫_0^1 TPR d(FPR). For baseline d' = 1.0, confirm AUC ≈ 0.7602.
05
Verify Equivalence to Mann-Whitney U Statistic
Compute all pairwise comparisons between positive and negative scores. Confirm that Wilcoxon-Mann-Whitney U / (N_pos N_neg) matches AUC exactly.
06
Conduct Linear Regression on AUC Scaling
Fit a linear regression model y = mx to coordinate pairs (x = k, y = AUC_metric). Confirm that empirical slope m = 1.0000 validates ROC-AUC metric scaling.
YOUR NOTEBOOK · 0 OBSERVATIONS
Turn measurements into empirical insight.
Points are your recorded observations. The solid regression line validates ROC Curves & Confusion Matrix mathematical scaling.
LINEAR REGRESSION FIT · y = mx + b
y = 1.0000 · x
| # | Classification Discriminability Factor k (factor) | Scaled Area Under the Curve AUC Metric (Metric AUC) | Discriminability Factor k | Scaled Area Under the Curve AUC Metric | Remove |
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