Calculate the false positive rate from a confusion matrix and classification results.
The false positive rate (FPR) measures how often the model incorrectly flags a true negative as positive: FPR = FP / (FP + TN) = 1 − specificity. It's the x-axis of the ROC curve, representing the 'cost' side of the sensitivity/specificity tradeoff — as a model's decision threshold is lowered to catch more true positives, FPR typically rises as well, since more true negatives get swept up as false alarms.
FPR = FP / (FP + TN)
The ROC curve plots true positive rate (sensitivity) on the y-axis against false positive rate on the x-axis across every possible classification threshold, visualizing the full tradeoff between catching positives and generating false alarms.
It depends entirely on context — for high-stakes false alarms (e.g. locking out a legitimate user), you want FPR very close to 0; for low-stakes screening where follow-up review is cheap, a higher FPR may be acceptable in exchange for higher sensitivity.
Yes — in classical statistical hypothesis testing terms, FPR is exactly the Type I error rate (rejecting a true null hypothesis, or here, flagging a true negative as positive).