FPRs

False positive rate (FPR) is a measure used in statistics and machine learning to describe how often a test or classifier incorrectly labels a negative instance as positive. It is defined as the number of false positives divided by the total number of actual negatives: FPR = FP / (FP + TN). In other words, it is the probability of a positive result given that the true condition is negative.

FPR is closely related to specificity, which is 1 minus the FPR. It is also related to the concept of a Type I error in hypothesis testing, where the null hypothesis is incorrectly rejected. For many classifiers, the FPR is not fixed but depends on the decision threshold used to declare a positive result. Lowering the threshold usually increases the FPR, while raising it reduces the FPR but can also lower true positives.

In practice, FPR is evaluated using data with known labels and reported alongside other metrics such as true positive rate (sensitivity), precision, and the F1 score. Receiver operating characteristic (ROC) curves plot the FPR against the true positive rate (TPR) at various thresholds, with the area under the curve (AUC) summarizing overall performance.

Applications of FPR include medical screening, security and fraud detection, and email spam filtering. A low FPR is desirable to avoid unnecessary alarm or resource use, but reducing it often comes at the cost of a higher miss rate. Users should consider FPR together with other measures and the prevalence of the positive condition to interpret a test’s practical impact.